Update README

Author: Geoc2022

README.md

@@ -4,6 +4,67 @@ This repository contains an implementation of Alpha Geometry, a system for devel
 
 This implementation uses [Ascent](https://github.com/s-arash/ascent/tree/master), a logic programming language (similar to Datalog) embedded in Rust, for the deductive database component.
 
+## Example Problems
+
+```bash
+==> problems/contri_sas
+Initial Predicates:
+  eqangle C A B F D E
+  cong A B D E
+  cong A B G H
+  cong C A I G
+  eqangle C A B H G I
+  cong C A F D
+
+Goals:
+  contri1 A B C D E F
+  contri2 A B C G H I
+
+=== Iteration 1 ===
+Predicates known: 6 / Goals Known: 0 / Goals: 2
+Missing Goals:  contri1 A B C D E F contri2 A B C G H I
+Found: contri1 D E F A B C via sas_cong
+Found: contri2 A B C G H I via sas_cong
+Added 2020 new predicates
+
+============================================================
+[1] eqangle C A B F D E         | axiom
+[2] cong A B D E                | axiom
+[3] cong A B G H                | axiom
+[4] cong C A I G                | axiom
+[5] eqangle C A B H G I         | axiom
+[6] cong C A F D                | axiom
+[7] contri2 G H I A B C         | sas_cong [4],[3],[5]
+[8] eqangle I G H B A C         | sub_deduction [7]
+[9] contri1 A C B D F E         | sas_cong [1],[6],[2]
+[10] eqangle B A C E D F        | sub_deduction [9]
+[11] contri2 A B C G H I        | sas_cong [8],[4],[3]
+[12] contri1 D E F A B C        | sas_cong [6],[10],[2]
+Solved!
+
+
+==> problems/para_trans
+/Users/geo/Documents/prgm/alphageometry-ascent/temp_ggb_extraction/geogebra.xml
+Initial Predicates:
+  para A B C D
+  para A B E F
+
+Goals:
+  para C D E F
+
+=== Iteration 1 ===
+Predicates known: 2 / Goals Known: 0 / Goals: 1
+Missing Goals:  para C D E F
+Found: para C D F E via AR
+Added 491 new predicates
+
+============================================================
+[1] para A B C D                | axiom
+[2] para A B E F                | axiom
+[3] para C D F E                | AR [1],[2]
+Solved!
+```
+
 To run all the problems in this repository use [`uv`](https://docs.astral.sh/uv/) to run:
 
 ```bash