TSTP Solution File: COM003+2 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 01:45:46 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 20:07:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 (* PROOF-FOUND *)
% 0.19/0.43 (* BEGIN-PROOF *)
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 1. (Ex X, (algorithm_program_decides X)) (-. (Ex X, (algorithm_program_decides X))) ### Axiom
% 0.19/0.43 2. (program T_0) (-. (program T_0)) ### Axiom
% 0.19/0.43 3. ((program T_0) /\ (program_decides T_0)) (-. ((program T_0) /\ (program_decides T_0))) ### Axiom
% 0.19/0.43 4. (-. (program_program_decides T_0)) ((program T_0) /\ (program_decides T_0)) ### Definition-Pseudo(program_program_decides) 3
% 0.19/0.43 5. (-. ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good)))) ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good))) ### Axiom
% 0.19/0.43 6. (program_halts2_halts3_outputs T_0 T_1 T_1 (good)) (-. ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good)))) ### Definition-Pseudo(program_halts2_halts3_outputs) 5
% 0.19/0.43 7. ((program_halts2_halts3_outputs T_0 T_1 T_1 (good)) /\ (program_not_halts2_halts3_outputs T_0 T_1 T_1 (bad))) (-. ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good)))) ### And 6
% 0.19/0.43 8. (All Z, ((program_halts2_halts3_outputs T_0 T_1 Z (good)) /\ (program_not_halts2_halts3_outputs T_0 T_1 Z (bad)))) (-. ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good)))) ### All 7
% 0.19/0.43 9. (All Y, (All Z, ((program_halts2_halts3_outputs T_0 Y Z (good)) /\ (program_not_halts2_halts3_outputs T_0 Y Z (bad))))) (-. ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good)))) ### All 8
% 0.19/0.43 10. ((program_program_decides T_0) => (All Y, (All Z, ((program_halts2_halts3_outputs T_0 Y Z (good)) /\ (program_not_halts2_halts3_outputs T_0 Y Z (bad)))))) (-. ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good)))) ((program T_0) /\ (program_decides T_0)) ### Imply 4 9
% 0.19/0.43 11. (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ((program T_0) /\ (program_decides T_0)) (-. ((program_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (good)))) ### All 10
% 0.19/0.43 12. (-. (program_halts2_halts3_outputs T_0 T_1 T_1 (good))) ((program T_0) /\ (program_decides T_0)) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ### Definition-Pseudo(program_halts2_halts3_outputs) 11
% 0.19/0.43 13. (-. ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad)))) ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad))) ### Axiom
% 0.19/0.43 14. (program_not_halts2_halts3_outputs T_0 T_1 T_1 (bad)) (-. ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad)))) ### Definition-Pseudo(program_not_halts2_halts3_outputs) 13
% 0.19/0.43 15. ((program_halts2_halts3_outputs T_0 T_1 T_1 (good)) /\ (program_not_halts2_halts3_outputs T_0 T_1 T_1 (bad))) (-. ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad)))) ### And 14
% 0.19/0.43 16. (All Z, ((program_halts2_halts3_outputs T_0 T_1 Z (good)) /\ (program_not_halts2_halts3_outputs T_0 T_1 Z (bad)))) (-. ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad)))) ### All 15
% 0.19/0.43 17. (All Y, (All Z, ((program_halts2_halts3_outputs T_0 Y Z (good)) /\ (program_not_halts2_halts3_outputs T_0 Y Z (bad))))) (-. ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad)))) ### All 16
% 0.19/0.43 18. ((program_program_decides T_0) => (All Y, (All Z, ((program_halts2_halts3_outputs T_0 Y Z (good)) /\ (program_not_halts2_halts3_outputs T_0 Y Z (bad)))))) (-. ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad)))) ((program T_0) /\ (program_decides T_0)) ### Imply 4 17
% 0.19/0.43 19. (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ((program T_0) /\ (program_decides T_0)) (-. ((program_not_halts2 T_1 T_1) => (halts3_outputs T_0 T_1 T_1 (bad)))) ### All 18
% 0.19/0.43 20. (-. (program_not_halts2_halts3_outputs T_0 T_1 T_1 (bad))) ((program T_0) /\ (program_decides T_0)) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ### Definition-Pseudo(program_not_halts2_halts3_outputs) 19
% 0.19/0.43 21. (-. ((program_halts2_halts3_outputs T_0 T_1 T_1 (good)) /\ (program_not_halts2_halts3_outputs T_0 T_1 T_1 (bad)))) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ((program T_0) /\ (program_decides T_0)) ### NotAnd 12 20
% 0.19/0.43 22. (-. (All Y, ((program_halts2_halts3_outputs T_0 Y Y (good)) /\ (program_not_halts2_halts3_outputs T_0 Y Y (bad))))) ((program T_0) /\ (program_decides T_0)) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ### NotAllEx 21
% 0.19/0.43 23. (-. ((program T_0) /\ (All Y, ((program_halts2_halts3_outputs T_0 Y Y (good)) /\ (program_not_halts2_halts3_outputs T_0 Y Y (bad)))))) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ((program T_0) /\ (program_decides T_0)) (program T_0) ### NotAnd 2 22
% 0.19/0.43 24. (-. (Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad))))))) (program T_0) ((program T_0) /\ (program_decides T_0)) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ### NotExists 23
% 0.19/0.43 25. (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ((program T_0) /\ (program_decides T_0)) (-. (Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad))))))) ### And 24
% 0.19/0.43 26. (program_program_decides T_0) (-. (Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad))))))) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ### Definition-Pseudo(program_program_decides) 25
% 0.19/0.43 27. (Ex W, (program_program_decides W)) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) (-. (Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad))))))) ### Exists 26
% 0.19/0.43 28. ((Ex X, (algorithm_program_decides X)) => (Ex W, (program_program_decides W))) (-. (Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad))))))) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) (Ex X, (algorithm_program_decides X)) ### Imply 1 27
% 0.19/0.43 29. (-. (Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad))))))) (Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad)))))) ### Axiom
% 0.19/0.43 30. ((Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad)))))) => (Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad))))))) (-. (Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad))))))) (Ex X, (algorithm_program_decides X)) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ((Ex X, (algorithm_program_decides X)) => (Ex W, (program_program_decides W))) ### Imply 28 29
% 0.19/0.43 31. (program T_2) (-. (program T_2)) ### Axiom
% 0.19/0.43 32. (program T_2) (-. (program T_2)) ### Axiom
% 0.19/0.43 33. (halts2 T_2 T_2) (-. (halts2 T_2 T_2)) ### Axiom
% 0.19/0.43 34. (-. ((program T_2) /\ (halts2 T_2 T_2))) (halts2 T_2 T_2) (program T_2) ### NotAnd 32 33
% 0.19/0.43 35. (-. (program_halts2 T_2 T_2)) (program T_2) (halts2 T_2 T_2) ### Definition-Pseudo(program_halts2) 34
% 0.19/0.43 36. (halts2 T_2 T_2) (-. (halts2 T_2 T_2)) ### Axiom
% 0.19/0.43 37. ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) (halts2 T_2 T_2) (program T_2) ### Imply 35 36
% 0.19/0.43 38. (-. (-. (halts2 T_2 T_2))) (program T_2) ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) ### NotNot 37
% 0.19/0.43 39. (-. ((program T_2) /\ (-. (halts2 T_2 T_2)))) ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) (program T_2) ### NotAnd 31 38
% 0.19/0.43 40. (-. (program_not_halts2 T_2 T_2)) (program T_2) ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) ### Definition-Pseudo(program_not_halts2) 39
% 0.19/0.43 41. ((halts2 T_2 T_2) /\ (outputs T_2 (good))) (program T_2) ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) ### And 37
% 0.19/0.43 42. (halts2_outputs T_2 T_2 (good)) ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) (program T_2) ### Definition-Pseudo(halts2_outputs) 41
% 0.19/0.43 43. ((program_not_halts2 T_2 T_2) => (halts2_outputs T_2 T_2 (good))) ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) (program T_2) ### Imply 40 42
% 0.19/0.43 44. (program_not_halts2_halts2_outputs T_2 T_2 (good)) (program T_2) ((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) ### Definition-Pseudo(program_not_halts2_halts2_outputs) 43
% 0.19/0.43 45. (((program_halts2 T_2 T_2) => (-. (halts2 T_2 T_2))) /\ (program_not_halts2_halts2_outputs T_2 T_2 (good))) (program T_2) ### And 44
% 0.19/0.43 46. (All Y, (((program_halts2 Y Y) => (-. (halts2 T_2 Y))) /\ (program_not_halts2_halts2_outputs T_2 Y (good)))) (program T_2) ### All 45
% 0.19/0.43 47. ((program T_2) /\ (All Y, (((program_halts2 Y Y) => (-. (halts2 T_2 Y))) /\ (program_not_halts2_halts2_outputs T_2 Y (good))))) ### And 46
% 0.19/0.43 48. (Ex U, ((program U) /\ (All Y, (((program_halts2 Y Y) => (-. (halts2 U Y))) /\ (program_not_halts2_halts2_outputs U Y (good)))))) ### Exists 47
% 0.19/0.43 49. ((Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad)))))) => (Ex U, ((program U) /\ (All Y, (((program_halts2 Y Y) => (-. (halts2 U Y))) /\ (program_not_halts2_halts2_outputs U Y (good))))))) ((Ex X, (algorithm_program_decides X)) => (Ex W, (program_program_decides W))) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) (Ex X, (algorithm_program_decides X)) ((Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad)))))) => (Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad))))))) ### Imply 30 48
% 0.19/0.43 50. (-. (-. (Ex X, (algorithm_program_decides X)))) ((Ex W, ((program W) /\ (All Y, ((program_halts2_halts3_outputs W Y Y (good)) /\ (program_not_halts2_halts3_outputs W Y Y (bad)))))) => (Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad))))))) (All W, ((program_program_decides W) => (All Y, (All Z, ((program_halts2_halts3_outputs W Y Z (good)) /\ (program_not_halts2_halts3_outputs W Y Z (bad))))))) ((Ex X, (algorithm_program_decides X)) => (Ex W, (program_program_decides W))) ((Ex V, ((program V) /\ (All Y, ((program_halts2_halts2_outputs V Y (good)) /\ (program_not_halts2_halts2_outputs V Y (bad)))))) => (Ex U, ((program U) /\ (All Y, (((program_halts2 Y Y) => (-. (halts2 U Y))) /\ (program_not_halts2_halts2_outputs U Y (good))))))) ### NotNot 49
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 (* END-PROOF *)
%------------------------------------------------------------------------------