TSTP Solution File: SET185+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET185+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 : n005.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 05:40:12 EDT 2022
% Result : Theorem 1.54s 1.76s
% Output : Proof 1.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 10:41:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.54/1.76 % SZS status Theorem
% 1.54/1.76 (* PROOF-FOUND *)
% 1.54/1.76 (* BEGIN-PROOF *)
% 1.54/1.76 % SZS output start Proof
% 1.54/1.76 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 1.54/1.76 2. (-. ((member T_0 T_2) \/ (member T_0 T_1))) (member T_0 T_1) ### NotOr 1
% 1.54/1.76 3. (-. (member T_0 (union T_2 T_1))) (member T_0 (union T_2 T_1)) ### Axiom
% 1.54/1.76 4. ((member T_0 (union T_2 T_1)) <=> ((member T_0 T_2) \/ (member T_0 T_1))) (-. (member T_0 (union T_2 T_1))) (member T_0 T_1) ### Equiv 2 3
% 1.54/1.76 5. (All D, ((member D (union T_2 T_1)) <=> ((member D T_2) \/ (member D T_1)))) (member T_0 T_1) (-. (member T_0 (union T_2 T_1))) ### All 4
% 1.54/1.76 6. (All C, (All D, ((member D (union T_2 C)) <=> ((member D T_2) \/ (member D C))))) (-. (member T_0 (union T_2 T_1))) (member T_0 T_1) ### All 5
% 1.54/1.76 7. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 T_1) (-. (member T_0 (union T_2 T_1))) ### All 6
% 1.54/1.76 8. (-. ((member T_0 T_1) => (member T_0 (union T_2 T_1)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotImply 7
% 1.54/1.76 9. (-. (All D, ((member D T_1) => (member D (union T_2 T_1))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 8
% 1.54/1.76 10. (-. (subset T_1 (union T_2 T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### Definition-Pseudo(subset) 9
% 1.54/1.76 11. (T_3 != T_3) ### Refl(=)
% 1.54/1.76 12. ((union T_1 T_2) = (union T_2 T_1)) ((union T_2 T_1) != (union T_1 T_2)) ### Sym(=)
% 1.54/1.76 13. (-. (member T_3 (union T_1 T_2))) (member T_3 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) ### P-NotP 11 12
% 1.54/1.76 14. (-. (member T_3 T_1)) (member T_3 T_1) ### Axiom
% 1.54/1.76 15. (-. (member T_3 T_2)) (member T_3 T_2) ### Axiom
% 1.54/1.76 16. ((member T_3 T_1) \/ (member T_3 T_2)) (-. (member T_3 T_2)) (-. (member T_3 T_1)) ### Or 14 15
% 1.54/1.76 17. ((member T_3 (union T_1 T_2)) <=> ((member T_3 T_1) \/ (member T_3 T_2))) (-. (member T_3 T_1)) (-. (member T_3 T_2)) ((union T_1 T_2) = (union T_2 T_1)) (member T_3 (union T_2 T_1)) ### Equiv 13 16
% 1.54/1.76 18. (All D, ((member D (union T_1 T_2)) <=> ((member D T_1) \/ (member D T_2)))) (member T_3 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_3 T_2)) (-. (member T_3 T_1)) ### All 17
% 1.54/1.76 19. (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) (-. (member T_3 T_1)) (-. (member T_3 T_2)) ((union T_1 T_2) = (union T_2 T_1)) (member T_3 (union T_2 T_1)) ### All 18
% 1.54/1.76 20. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_3 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_3 T_2)) (-. (member T_3 T_1)) ### All 19
% 1.54/1.76 21. (All C, ((union T_1 C) = (union C T_1))) (-. (member T_3 T_1)) (-. (member T_3 T_2)) (member T_3 (union T_2 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### All 20
% 1.54/1.76 22. (-. (member T_3 T_1)) (member T_3 T_1) ### Axiom
% 1.54/1.76 23. ((member T_3 T_2) => (member T_3 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_3 (union T_2 T_1)) (-. (member T_3 T_1)) (All C, ((union T_1 C) = (union C T_1))) ### Imply 21 22
% 1.54/1.76 24. (All D, ((member D T_2) => (member D T_1))) (All C, ((union T_1 C) = (union C T_1))) (-. (member T_3 T_1)) (member T_3 (union T_2 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### All 23
% 1.54/1.76 25. (-. ((member T_3 (union T_2 T_1)) => (member T_3 T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All C, ((union T_1 C) = (union C T_1))) (All D, ((member D T_2) => (member D T_1))) ### NotImply 24
% 1.54/1.76 26. (-. (All D, ((member D (union T_2 T_1)) => (member D T_1)))) (All D, ((member D T_2) => (member D T_1))) (All C, ((union T_1 C) = (union C T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 25
% 1.54/1.76 27. (-. (subset (union T_2 T_1) T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All C, ((union T_1 C) = (union C T_1))) (All D, ((member D T_2) => (member D T_1))) ### Definition-Pseudo(subset) 26
% 1.54/1.76 28. (-. ((subset T_1 (union T_2 T_1)) /\ (subset (union T_2 T_1) T_1))) (All D, ((member D T_2) => (member D T_1))) (All C, ((union T_1 C) = (union C T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAnd 10 27
% 1.54/1.76 29. ((union T_2 T_1) != T_1) (T_1 = (union T_2 T_1)) ### Sym(=)
% 1.54/1.76 30. ((T_1 = (union T_2 T_1)) <=> ((subset T_1 (union T_2 T_1)) /\ (subset (union T_2 T_1) T_1))) ((union T_2 T_1) != T_1) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All C, ((union T_1 C) = (union C T_1))) (All D, ((member D T_2) => (member D T_1))) ### Equiv 28 29
% 1.54/1.76 31. (All C, ((T_1 = C) <=> ((subset T_1 C) /\ (subset C T_1)))) (All D, ((member D T_2) => (member D T_1))) (All C, ((union T_1 C) = (union C T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ((union T_2 T_1) != T_1) ### All 30
% 1.54/1.76 32. (All B, (All C, ((union B C) = (union C B)))) ((union T_2 T_1) != T_1) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_2) => (member D T_1))) (All C, ((T_1 = C) <=> ((subset T_1 C) /\ (subset C T_1)))) ### All 31
% 1.54/1.76 33. (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (All D, ((member D T_2) => (member D T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ((union T_2 T_1) != T_1) (All B, (All C, ((union B C) = (union C B)))) ### All 32
% 1.54/1.76 34. (subset T_2 T_1) (All B, (All C, ((union B C) = (union C B)))) ((union T_2 T_1) != T_1) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### Definition-Pseudo(subset) 33
% 1.54/1.76 35. (-. ((subset T_2 T_1) => ((union T_2 T_1) = T_1))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) ### NotImply 34
% 1.54/1.76 36. (-. (All C, ((subset T_2 C) => ((union T_2 C) = C)))) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### NotAllEx 35
% 1.54/1.76 37. (-. (All B, (All C, ((subset B C) => ((union B C) = C))))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) ### NotAllEx 36
% 1.54/1.76 % SZS output end Proof
% 1.54/1.76 (* END-PROOF *)
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