TSTP Solution File: SEU212+3 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n004.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 : Tue Jul 19 14:49:15 EDT 2022
% Result : Theorem 3.14s 3.33s
% Output : Proof 3.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 15:29:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.14/3.33 % SZS status Theorem
% 3.14/3.33 (* PROOF-FOUND *)
% 3.14/3.33 (* BEGIN-PROOF *)
% 3.14/3.33 % SZS output start Proof
% 3.14/3.33 1. (relation T_0) (-. (relation T_0)) ### Axiom
% 3.14/3.33 2. (function T_0) (-. (function T_0)) ### Axiom
% 3.14/3.33 3. (in T_1 (relation_dom T_0)) (-. (in T_1 (relation_dom T_0))) ### Axiom
% 3.14/3.33 4. (T_2 = (apply T_0 T_1)) (T_2 != (apply T_0 T_1)) ### Axiom
% 3.14/3.33 5. (-. (in (ordered_pair T_1 T_2) T_0)) (in (ordered_pair T_1 T_2) T_0) ### Axiom
% 3.14/3.33 6. ((T_2 = (apply T_0 T_1)) <=> (in (ordered_pair T_1 T_2) T_0)) (-. (in (ordered_pair T_1 T_2) T_0)) (T_2 = (apply T_0 T_1)) ### Equiv 4 5
% 3.14/3.33 7. ((in T_1 (relation_dom T_0)) => ((T_2 = (apply T_0 T_1)) <=> (in (ordered_pair T_1 T_2) T_0))) (T_2 = (apply T_0 T_1)) (-. (in (ordered_pair T_1 T_2) T_0)) (in T_1 (relation_dom T_0)) ### Imply 3 6
% 3.14/3.33 8. (((in T_1 (relation_dom T_0)) => ((T_2 = (apply T_0 T_1)) <=> (in (ordered_pair T_1 T_2) T_0))) /\ ((-. (in T_1 (relation_dom T_0))) => ((T_2 = (apply T_0 T_1)) <=> (T_2 = (empty_set))))) (in T_1 (relation_dom T_0)) (-. (in (ordered_pair T_1 T_2) T_0)) (T_2 = (apply T_0 T_1)) ### And 7
% 3.14/3.33 9. (All C, (((in T_1 (relation_dom T_0)) => ((C = (apply T_0 T_1)) <=> (in (ordered_pair T_1 C) T_0))) /\ ((-. (in T_1 (relation_dom T_0))) => ((C = (apply T_0 T_1)) <=> (C = (empty_set)))))) (T_2 = (apply T_0 T_1)) (-. (in (ordered_pair T_1 T_2) T_0)) (in T_1 (relation_dom T_0)) ### All 8
% 3.14/3.33 10. (All B, (All C, (((in B (relation_dom T_0)) => ((C = (apply T_0 B)) <=> (in (ordered_pair B C) T_0))) /\ ((-. (in B (relation_dom T_0))) => ((C = (apply T_0 B)) <=> (C = (empty_set))))))) (in T_1 (relation_dom T_0)) (-. (in (ordered_pair T_1 T_2) T_0)) (T_2 = (apply T_0 T_1)) ### All 9
% 3.14/3.33 11. (((relation T_0) /\ (function T_0)) => (All B, (All C, (((in B (relation_dom T_0)) => ((C = (apply T_0 B)) <=> (in (ordered_pair B C) T_0))) /\ ((-. (in B (relation_dom T_0))) => ((C = (apply T_0 B)) <=> (C = (empty_set)))))))) (T_2 = (apply T_0 T_1)) (-. (in (ordered_pair T_1 T_2) T_0)) (in T_1 (relation_dom T_0)) (function T_0) (relation T_0) ### DisjTree 1 2 10
% 3.14/3.33 12. (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) (relation T_0) (function T_0) (in T_1 (relation_dom T_0)) (-. (in (ordered_pair T_1 T_2) T_0)) (T_2 = (apply T_0 T_1)) ### All 11
% 3.14/3.33 13. ((in T_1 (relation_dom T_0)) /\ (T_2 = (apply T_0 T_1))) (-. (in (ordered_pair T_1 T_2) T_0)) (function T_0) (relation T_0) (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) ### And 12
% 3.14/3.33 14. (relation T_0) (-. (relation T_0)) ### Axiom
% 3.14/3.33 15. ((relation_dom T_0) != (relation_dom T_0)) ### Refl(=)
% 3.14/3.33 16. (in (ordered_pair T_1 T_2) T_0) (-. (in (ordered_pair T_1 T_2) T_0)) ### Axiom
% 3.14/3.33 17. (-. (Ex D, (in (ordered_pair T_1 D) T_0))) (in (ordered_pair T_1 T_2) T_0) ### NotExists 16
% 3.14/3.33 18. (-. (in T_1 (relation_dom T_0))) (in T_1 (relation_dom T_0)) ### Axiom
% 3.14/3.33 19. ((in T_1 (relation_dom T_0)) <=> (Ex D, (in (ordered_pair T_1 D) T_0))) (-. (in T_1 (relation_dom T_0))) (in (ordered_pair T_1 T_2) T_0) ### Equiv 17 18
% 3.14/3.33 20. (All C, ((in C (relation_dom T_0)) <=> (Ex D, (in (ordered_pair C D) T_0)))) (in (ordered_pair T_1 T_2) T_0) (-. (in T_1 (relation_dom T_0))) ### All 19
% 3.14/3.33 21. (((relation_dom T_0) = (relation_dom T_0)) <=> (All C, ((in C (relation_dom T_0)) <=> (Ex D, (in (ordered_pair C D) T_0))))) (-. (in T_1 (relation_dom T_0))) (in (ordered_pair T_1 T_2) T_0) ### Equiv 15 20
% 3.14/3.33 22. (All B, ((B = (relation_dom T_0)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) T_0)))))) (in (ordered_pair T_1 T_2) T_0) (-. (in T_1 (relation_dom T_0))) ### All 21
% 3.14/3.33 23. ((relation T_0) => (All B, ((B = (relation_dom T_0)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) T_0))))))) (-. (in T_1 (relation_dom T_0))) (in (ordered_pair T_1 T_2) T_0) (relation T_0) ### Imply 14 22
% 3.14/3.33 24. (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) (relation T_0) (in (ordered_pair T_1 T_2) T_0) (-. (in T_1 (relation_dom T_0))) ### All 23
% 3.14/3.33 25. (relation T_0) (-. (relation T_0)) ### Axiom
% 3.14/3.33 26. (function T_0) (-. (function T_0)) ### Axiom
% 3.14/3.33 27. (relation T_0) (-. (relation T_0)) ### Axiom
% 3.14/3.33 28. (in (ordered_pair T_1 T_2) T_0) (-. (in (ordered_pair T_1 T_2) T_0)) ### Axiom
% 3.14/3.33 29. (T_2 != (apply T_0 T_1)) (T_2 = (apply T_0 T_1)) ### Axiom
% 3.14/3.33 30. ((T_2 = (apply T_0 T_1)) <=> (in (ordered_pair T_1 T_2) T_0)) (T_2 != (apply T_0 T_1)) (in (ordered_pair T_1 T_2) T_0) ### Equiv 28 29
% 3.14/3.33 31. ((in T_1 (relation_dom T_0)) => ((T_2 = (apply T_0 T_1)) <=> (in (ordered_pair T_1 T_2) T_0))) (T_2 != (apply T_0 T_1)) (in (ordered_pair T_1 T_2) T_0) (All B, ((B = (relation_dom T_0)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) T_0)))))) ### Imply 22 30
% 3.14/3.33 32. (((in T_1 (relation_dom T_0)) => ((T_2 = (apply T_0 T_1)) <=> (in (ordered_pair T_1 T_2) T_0))) /\ ((-. (in T_1 (relation_dom T_0))) => ((T_2 = (apply T_0 T_1)) <=> (T_2 = (empty_set))))) (All B, ((B = (relation_dom T_0)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) T_0)))))) (in (ordered_pair T_1 T_2) T_0) (T_2 != (apply T_0 T_1)) ### And 31
% 3.14/3.33 33. (All C, (((in T_1 (relation_dom T_0)) => ((C = (apply T_0 T_1)) <=> (in (ordered_pair T_1 C) T_0))) /\ ((-. (in T_1 (relation_dom T_0))) => ((C = (apply T_0 T_1)) <=> (C = (empty_set)))))) (T_2 != (apply T_0 T_1)) (in (ordered_pair T_1 T_2) T_0) (All B, ((B = (relation_dom T_0)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) T_0)))))) ### All 32
% 3.14/3.33 34. (All B, (All C, (((in B (relation_dom T_0)) => ((C = (apply T_0 B)) <=> (in (ordered_pair B C) T_0))) /\ ((-. (in B (relation_dom T_0))) => ((C = (apply T_0 B)) <=> (C = (empty_set))))))) (All B, ((B = (relation_dom T_0)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) T_0)))))) (in (ordered_pair T_1 T_2) T_0) (T_2 != (apply T_0 T_1)) ### All 33
% 3.14/3.33 35. ((relation T_0) => (All B, ((B = (relation_dom T_0)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) T_0))))))) (T_2 != (apply T_0 T_1)) (in (ordered_pair T_1 T_2) T_0) (All B, (All C, (((in B (relation_dom T_0)) => ((C = (apply T_0 B)) <=> (in (ordered_pair B C) T_0))) /\ ((-. (in B (relation_dom T_0))) => ((C = (apply T_0 B)) <=> (C = (empty_set))))))) (relation T_0) ### Imply 27 34
% 3.14/3.33 36. (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) (relation T_0) (All B, (All C, (((in B (relation_dom T_0)) => ((C = (apply T_0 B)) <=> (in (ordered_pair B C) T_0))) /\ ((-. (in B (relation_dom T_0))) => ((C = (apply T_0 B)) <=> (C = (empty_set))))))) (in (ordered_pair T_1 T_2) T_0) (T_2 != (apply T_0 T_1)) ### All 35
% 3.14/3.33 37. (((relation T_0) /\ (function T_0)) => (All B, (All C, (((in B (relation_dom T_0)) => ((C = (apply T_0 B)) <=> (in (ordered_pair B C) T_0))) /\ ((-. (in B (relation_dom T_0))) => ((C = (apply T_0 B)) <=> (C = (empty_set)))))))) (T_2 != (apply T_0 T_1)) (in (ordered_pair T_1 T_2) T_0) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) (function T_0) (relation T_0) ### DisjTree 25 26 36
% 3.14/3.33 38. (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) (relation T_0) (function T_0) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) (in (ordered_pair T_1 T_2) T_0) (T_2 != (apply T_0 T_1)) ### All 37
% 3.14/3.33 39. (-. ((in T_1 (relation_dom T_0)) /\ (T_2 = (apply T_0 T_1)))) (function T_0) (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) (in (ordered_pair T_1 T_2) T_0) (relation T_0) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) ### NotAnd 24 38
% 3.14/3.34 40. (-. ((in (ordered_pair T_1 T_2) T_0) <=> ((in T_1 (relation_dom T_0)) /\ (T_2 = (apply T_0 T_1))))) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) (relation T_0) (function T_0) ### NotEquiv 13 39
% 3.14/3.34 41. (-. (((relation T_0) /\ (function T_0)) => ((in (ordered_pair T_1 T_2) T_0) <=> ((in T_1 (relation_dom T_0)) /\ (T_2 = (apply T_0 T_1)))))) (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) ### ConjTree 40
% 3.14/3.34 42. (-. (All C, (((relation C) /\ (function C)) => ((in (ordered_pair T_1 T_2) C) <=> ((in T_1 (relation_dom C)) /\ (T_2 = (apply C T_1))))))) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) ### NotAllEx 41
% 3.14/3.34 43. (-. (All B, (All C, (((relation C) /\ (function C)) => ((in (ordered_pair T_1 B) C) <=> ((in T_1 (relation_dom C)) /\ (B = (apply C T_1)))))))) (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) ### NotAllEx 42
% 3.14/3.34 44. (-. (All A, (All B, (All C, (((relation C) /\ (function C)) => ((in (ordered_pair A B) C) <=> ((in A (relation_dom C)) /\ (B = (apply C A))))))))) (All A, ((relation A) => (All B, ((B = (relation_dom A)) <=> (All C, ((in C B) <=> (Ex D, (in (ordered_pair C D) A)))))))) (All A, (((relation A) /\ (function A)) => (All B, (All C, (((in B (relation_dom A)) => ((C = (apply A B)) <=> (in (ordered_pair B C) A))) /\ ((-. (in B (relation_dom A))) => ((C = (apply A B)) <=> (C = (empty_set))))))))) ### NotAllEx 43
% 3.14/3.34 % SZS output end Proof
% 3.14/3.34 (* END-PROOF *)
%------------------------------------------------------------------------------