TSTP Solution File: SET584+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET584+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 : n027.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 05:42:25 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n027.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 : Sun Jul 10 03:13:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 (* PROOF-FOUND *)
% 0.18/0.52 (* BEGIN-PROOF *)
% 0.18/0.52 % SZS output start Proof
% 0.18/0.52 1. (T_0 != T_0) ### Refl(=)
% 0.18/0.52 2. ((union T_1 T_2) = (union T_2 T_1)) ((union T_2 T_1) != (union T_1 T_2)) ### Sym(=)
% 0.18/0.52 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
% 0.18/0.52 4. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom
% 0.18/0.52 5. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom
% 0.18/0.52 6. ((member T_0 T_1) \/ (member T_0 T_2)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) ### Or 4 5
% 0.18/0.52 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
% 0.18/0.52 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
% 0.18/0.52 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
% 0.18/0.52 10. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom
% 0.18/0.52 11. ((member T_0 T_2) => (member T_0 T_3)) (-. (member T_0 T_3)) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_0 T_1)) (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) ### Imply 9 10
% 0.18/0.52 12. (All D, ((member D T_2) => (member D T_3))) (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) (-. (member T_0 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) (-. (member T_0 T_3)) ### All 11
% 0.18/0.52 13. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (member T_0 T_3)) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_0 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 12
% 0.18/0.52 14. (-. ((member T_0 T_3) \/ (member T_0 T_1))) (All D, ((member D T_2) => (member D T_3))) ((union T_1 T_2) = (union T_2 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)))))) ### NotOr 13
% 0.18/0.52 15. (-. (member T_0 (union T_3 T_1))) (member T_0 (union T_3 T_1)) ### Axiom
% 0.18/0.52 16. ((member T_0 (union T_3 T_1)) <=> ((member T_0 T_3) \/ (member T_0 T_1))) (-. (member T_0 (union T_3 T_1))) (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)) ((union T_1 T_2) = (union T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### Equiv 14 15
% 0.18/0.52 17. (All D, ((member D (union T_3 T_1)) <=> ((member D T_3) \/ (member D T_1)))) (All D, ((member D T_2) => (member D T_3))) ((union T_1 T_2) = (union T_2 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)))))) (-. (member T_0 (union T_3 T_1))) ### All 16
% 0.18/0.52 18. (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 (union T_3 T_1))) (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 D, ((member D T_2) => (member D T_3))) (All D, ((member D (union T_3 T_1)) <=> ((member D T_3) \/ (member D T_1)))) ### All 17
% 0.18/0.52 19. (All C, (All D, ((member D (union T_3 C)) <=> ((member D T_3) \/ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (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)))))) (-. (member T_0 (union T_3 T_1))) (All C, ((union T_1 C) = (union C T_1))) ### All 18
% 0.18/0.52 20. (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 (union T_3 T_1))) (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 D, ((member D T_2) => (member D T_3))) ### All 19
% 0.18/0.52 21. (All B, (All C, ((union B C) = (union C B)))) (All D, ((member D T_2) => (member D T_3))) (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)))))) (-. (member T_0 (union T_3 T_1))) ### All 20
% 0.18/0.52 22. (-. ((member T_0 (union T_2 T_1)) => (member T_0 (union T_3 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 B, (All C, ((union B C) = (union C B)))) ### NotImply 21
% 0.18/0.52 23. (-. (All D, ((member D (union T_2 T_1)) => (member D (union T_3 T_1))))) (All B, (All C, ((union B C) = (union C B)))) (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)))))) ### NotAllEx 22
% 0.18/0.52 24. (-. (subset (union T_2 T_1) (union T_3 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 B, (All C, ((union B C) = (union C B)))) ### Definition-Pseudo(subset) 23
% 0.18/0.52 25. (subset T_2 T_3) (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 (union T_2 T_1) (union T_3 T_1))) ### Definition-Pseudo(subset) 24
% 0.18/0.52 26. (-. ((subset T_2 T_3) => (subset (union T_2 T_1) (union T_3 T_1)))) (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 25
% 0.18/0.52 27. (-. (All D, ((subset T_2 T_3) => (subset (union T_2 D) (union T_3 D))))) (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 26
% 0.18/0.52 28. (-. (All C, (All D, ((subset T_2 C) => (subset (union T_2 D) (union C D)))))) (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 27
% 0.18/0.52 29. (-. (All B, (All C, (All D, ((subset B C) => (subset (union B D) (union C D))))))) (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 28
% 0.18/0.52 % SZS output end Proof
% 0.18/0.52 (* END-PROOF *)
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