TSTP Solution File: SET639+3 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:43:04 EDT 2022
% Result : Theorem 35.14s 35.38s
% Output : Proof 35.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n004.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 : Sat Jul 9 21:02:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 35.14/35.38 % SZS status Theorem
% 35.14/35.38 (* PROOF-FOUND *)
% 35.14/35.38 (* BEGIN-PROOF *)
% 35.14/35.38 % SZS output start Proof
% 35.14/35.38 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 35.14/35.38 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 35.14/35.38 3. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom
% 35.14/35.38 4. ((member T_0 T_1) => (member T_0 T_2)) (-. (member T_0 T_2)) (member T_0 T_1) ### Imply 2 3
% 35.14/35.38 5. (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (-. (member T_0 T_2)) ### All 4
% 35.14/35.38 6. (-. ((member T_0 T_1) /\ (member T_0 T_2))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ### NotAnd 1 5
% 35.14/35.38 7. (T_0 != T_0) ### Refl(=)
% 35.14/35.38 8. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_1 T_2) != (intersection T_2 T_1)) ### Axiom
% 35.14/35.38 9. (-. (member T_0 (intersection T_2 T_1))) (member T_0 (intersection T_1 T_2)) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### P-NotP 7 8
% 35.14/35.38 10. ((member T_0 (intersection T_1 T_2)) <=> ((member T_0 T_1) /\ (member T_0 T_2))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (intersection T_2 T_1))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) ### Equiv 6 9
% 35.14/35.38 11. (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (-. (member T_0 (intersection T_2 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### All 10
% 35.14/35.38 12. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 35.14/35.38 13. (-. ((member T_0 (intersection T_2 T_1)) /\ (member T_0 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ### NotAnd 11 12
% 35.14/35.38 14. (T_0 != T_0) ### Refl(=)
% 35.14/35.38 15. ((intersection T_2 T_1) = (empty_set)) ((intersection T_2 T_1) != (empty_set)) ### Axiom
% 35.14/35.38 16. (T_1 != T_1) ### Refl(=)
% 35.14/35.38 17. ((intersection (intersection T_2 T_1) T_1) != (intersection (empty_set) T_1)) ((intersection T_2 T_1) = (empty_set)) ### NotEqual 15 16
% 35.14/35.38 18. (-. (member T_0 (intersection (empty_set) T_1))) (member T_0 (intersection (intersection T_2 T_1) T_1)) ((intersection T_2 T_1) = (empty_set)) ### P-NotP 14 17
% 35.14/35.38 19. ((member T_0 (intersection (intersection T_2 T_1) T_1)) <=> ((member T_0 (intersection T_2 T_1)) /\ (member T_0 T_1))) ((intersection T_2 T_1) = (empty_set)) (-. (member T_0 (intersection (empty_set) T_1))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### Equiv 13 18
% 35.14/35.38 20. (All D, ((member D (intersection (intersection T_2 T_1) T_1)) <=> ((member D (intersection T_2 T_1)) /\ (member D T_1)))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (-. (member T_0 (intersection (empty_set) T_1))) ((intersection T_2 T_1) = (empty_set)) ### All 19
% 35.14/35.38 21. (All C, (All D, ((member D (intersection (intersection T_2 T_1) C)) <=> ((member D (intersection T_2 T_1)) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (-. (member T_0 (intersection (empty_set) T_1))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### All 20
% 35.14/35.38 22. (-. (member T_0 (empty_set))) (member T_0 (empty_set)) ### Axiom
% 35.14/35.38 23. ((member T_0 (empty_set)) /\ (member T_0 T_1)) (-. (member T_0 (empty_set))) ### And 22
% 35.14/35.38 24. ((member T_0 (intersection (empty_set) T_1)) <=> ((member T_0 (empty_set)) /\ (member T_0 T_1))) (-. (member T_0 (empty_set))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection (intersection T_2 T_1) C)) <=> ((member D (intersection T_2 T_1)) /\ (member D C))))) ### Equiv 21 23
% 35.14/35.38 25. (All D, ((member D (intersection (empty_set) T_1)) <=> ((member D (empty_set)) /\ (member D T_1)))) (All C, (All D, ((member D (intersection (intersection T_2 T_1) C)) <=> ((member D (intersection T_2 T_1)) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (empty_set))) ### All 24
% 35.14/35.38 26. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (empty_set))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D (intersection (empty_set) T_1)) <=> ((member D (empty_set)) /\ (member D T_1)))) ### All 25
% 35.14/35.38 27. (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (empty_set))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 26
% 35.14/35.38 28. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (empty_set))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ((intersection T_2 T_1) = (empty_set)) ### All 27
% 35.14/35.38 29. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (empty_set))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 28
% 35.14/35.38 30. (member T_0 (empty_set)) (-. (member T_0 (empty_set))) ### Axiom
% 35.14/35.38 31. (All B, (-. (member B (empty_set)))) (member T_0 (empty_set)) ### All 30
% 35.14/35.38 32. (-. ((member T_0 (empty_set)) <=> (member T_0 T_1))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ### NotEquiv 29 31
% 35.14/35.38 33. (-. (All D, ((member D (empty_set)) <=> (member D T_1)))) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) ### NotAllEx 32
% 35.14/35.38 34. (T_1 != (empty_set)) ((empty_set) = T_1) ### Sym(=)
% 35.14/35.38 35. (((empty_set) = T_1) <=> (All D, ((member D (empty_set)) <=> (member D T_1)))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ### Equiv 33 34
% 35.14/35.38 36. (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (T_1 != (empty_set)) ### All 35
% 35.21/35.40 37. (All C, ((intersection T_1 C) = (intersection C T_1))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ### All 36
% 35.21/35.40 38. (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (T_1 != (empty_set)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 37
% 35.21/35.40 39. (All B, (All C, ((intersection B C) = (intersection C B)))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_1) = (empty_set)) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ### All 38
% 35.21/35.40 40. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ((intersection T_2 T_1) = (empty_set)) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (T_1 != (empty_set)) (All B, (All C, ((intersection B C) = (intersection C B)))) ### All 39
% 35.21/35.40 41. (subset T_1 T_2) (All B, (All C, ((intersection B C) = (intersection C B)))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_2 T_1) = (empty_set)) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### Definition-Pseudo(subset) 40
% 35.21/35.40 42. (-. (((subset T_1 T_2) /\ ((intersection T_2 T_1) = (empty_set))) => (T_1 = (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### ConjTree 41
% 35.21/35.40 43. (-. (All C, (((subset T_1 C) /\ ((intersection C T_1) = (empty_set))) => (T_1 = (empty_set))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### NotAllEx 42
% 35.21/35.40 44. (-. (All B, (All C, (((subset B C) /\ ((intersection C B) = (empty_set))) => (B = (empty_set)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 43
% 35.21/35.40 % SZS output end Proof
% 35.21/35.40 (* END-PROOF *)
%------------------------------------------------------------------------------