TSTP Solution File: SET200+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET200+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 : n003.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 05:40:19 EDT 2022
% Result : Theorem 0.38s 0.56s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET200+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n003.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 Jul 10 23:00:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.38/0.56 % SZS status Theorem
% 0.38/0.56 (* PROOF-FOUND *)
% 0.38/0.56 (* BEGIN-PROOF *)
% 0.38/0.56 % SZS output start Proof
% 0.38/0.56 1. (T_0 != T_0) ### Refl(=)
% 0.38/0.56 2. ((union T_1 T_2) = (union T_2 T_1)) ((union T_2 T_1) != (union T_1 T_2)) ### Sym(=)
% 0.38/0.56 3. (-. (member T_0 (union T_1 T_2))) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) ### P-NotP 1 2
% 0.38/0.56 4. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom
% 0.38/0.56 5. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom
% 0.38/0.56 6. ((member T_0 T_1) \/ (member T_0 T_2)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) ### Or 4 5
% 0.38/0.56 7. ((member T_0 (union T_1 T_2)) <=> ((member T_0 T_1) \/ (member T_0 T_2))) (-. (member T_0 T_1)) (-. (member T_0 T_2)) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) ### Equiv 3 6
% 0.38/0.56 8. (All D, ((member D (union T_1 T_2)) <=> ((member D T_1) \/ (member D T_2)))) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) ### All 7
% 0.38/0.56 9. (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) (-. (member T_0 T_1)) (-. (member T_0 T_2)) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) ### All 8
% 0.38/0.56 10. (All C, ((union T_1 C) = (union C T_1))) (member T_0 (union T_2 T_1)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) ### All 9
% 0.38/0.56 11. (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 T_2)) (member T_0 (union T_2 T_1)) (All C, ((union T_1 C) = (union C T_1))) ### All 10
% 0.38/0.56 12. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom
% 0.38/0.56 13. ((member T_0 T_2) => (member T_0 T_3)) (-. (member T_0 T_3)) (All C, ((union T_1 C) = (union C T_1))) (member T_0 (union T_2 T_1)) (-. (member T_0 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### Imply 11 12
% 0.38/0.56 14. (All D, ((member D T_2) => (member D T_3))) (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 C, ((union T_1 C) = (union C T_1))) (-. (member T_0 T_3)) ### All 13
% 0.38/0.56 15. (-. (member T_0 T_4)) (member T_0 T_4) ### Axiom
% 0.38/0.56 16. ((member T_0 T_1) => (member T_0 T_4)) (-. (member T_0 T_4)) (-. (member T_0 T_3)) (All C, ((union T_1 C) = (union C 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)))))) (All D, ((member D T_2) => (member D T_3))) ### Imply 14 15
% 0.38/0.56 17. (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 T_3)) (-. (member T_0 T_4)) ### All 16
% 0.38/0.56 18. (-. ((member T_0 T_3) \/ (member T_0 T_4))) (All C, ((union T_1 C) = (union C 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)))))) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) ### NotOr 17
% 0.38/0.56 19. (-. (member T_0 (union T_3 T_4))) (member T_0 (union T_3 T_4)) ### Axiom
% 0.38/0.56 20. ((member T_0 (union T_3 T_4)) <=> ((member T_0 T_3) \/ (member T_0 T_4))) (-. (member T_0 (union T_3 T_4))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) (All C, ((union T_1 C) = (union C T_1))) ### Equiv 18 19
% 0.38/0.56 21. (All D, ((member D (union T_3 T_4)) <=> ((member D T_3) \/ (member D T_4)))) (All C, ((union T_1 C) = (union C 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)))))) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) (-. (member T_0 (union T_3 T_4))) ### All 20
% 0.38/0.56 22. (All C, (All D, ((member D (union T_3 C)) <=> ((member D T_3) \/ (member D C))))) (-. (member T_0 (union T_3 T_4))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) (All C, ((union T_1 C) = (union C T_1))) ### All 21
% 0.38/0.56 23. (All B, (All C, ((union B C) = (union C B)))) (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)))))) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) (-. (member T_0 (union T_3 T_4))) (All C, (All D, ((member D (union T_3 C)) <=> ((member D T_3) \/ (member D C))))) ### All 22
% 0.38/0.56 24. (-. (member T_0 (union T_3 T_4))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) (All B, (All C, ((union B C) = (union C B)))) ### All 23
% 0.38/0.56 25. (-. ((member T_0 (union T_2 T_1)) => (member T_0 (union T_3 T_4)))) (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 D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) ### NotImply 24
% 0.38/0.56 26. (-. (All D, ((member D (union T_2 T_1)) => (member D (union T_3 T_4))))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (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 25
% 0.38/0.56 27. (-. (subset (union T_2 T_1) (union T_3 T_4))) (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 D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) ### Definition-Pseudo(subset) 26
% 0.38/0.56 28. (subset T_1 T_4) (All D, ((member D T_2) => (member D T_3))) (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)))) (-. (subset (union T_2 T_1) (union T_3 T_4))) ### Definition-Pseudo(subset) 27
% 0.38/0.56 29. (subset T_2 T_3) (-. (subset (union T_2 T_1) (union T_3 T_4))) (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)))))) (subset T_1 T_4) ### Definition-Pseudo(subset) 28
% 0.38/0.56 30. (-. (((subset T_2 T_3) /\ (subset T_1 T_4)) => (subset (union T_2 T_1) (union T_3 T_4)))) (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)))) ### ConjTree 29
% 0.38/0.56 31. (-. (All E, (((subset T_2 T_3) /\ (subset T_1 E)) => (subset (union T_2 T_1) (union T_3 E))))) (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)))))) ### NotAllEx 30
% 0.38/0.56 32. (-. (All D, (All E, (((subset T_2 T_3) /\ (subset D E)) => (subset (union T_2 D) (union T_3 E)))))) (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 31
% 0.38/0.56 33. (-. (All C, (All D, (All E, (((subset T_2 C) /\ (subset D E)) => (subset (union T_2 D) (union C E))))))) (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)))))) ### NotAllEx 32
% 0.38/0.56 34. (-. (All B, (All C, (All D, (All E, (((subset B C) /\ (subset D E)) => (subset (union B D) (union C E)))))))) (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 33
% 0.38/0.56 % SZS output end Proof
% 0.38/0.56 (* END-PROOF *)
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