TSTP Solution File: SET585+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET585+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 : n023.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 05:42:26 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n023.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 14:19:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 (* PROOF-FOUND *)
% 0.19/0.53 (* BEGIN-PROOF *)
% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 1. (T_0 != T_0) ### Refl(=)
% 0.19/0.53 2. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_2 T_1) != (intersection T_1 T_2)) ### Sym(=)
% 0.19/0.53 3. (-. (member T_0 (intersection T_1 T_2))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) ### P-NotP 1 2
% 0.19/0.53 4. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom
% 0.19/0.53 5. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_2)) ### And 4
% 0.19/0.53 6. ((member T_0 (intersection T_1 T_2)) <=> ((member T_0 T_1) /\ (member T_0 T_2))) (-. (member T_0 T_2)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) ### Equiv 3 5
% 0.19/0.53 7. (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 T_2)) ### All 6
% 0.19/0.53 8. (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_2)) (member T_0 (intersection T_2 T_1)) (All D, ((member D (intersection T_1 T_2)) <=> ((member D T_1) /\ (member D T_2)))) ### All 7
% 0.19/0.53 9. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 T_2)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 8
% 0.19/0.53 10. (-. ((member T_0 T_2) \/ (member T_0 T_3))) (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 (intersection T_2 T_1)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ### NotOr 9
% 0.19/0.53 11. (-. (member T_0 (union T_2 T_3))) (member T_0 (union T_2 T_3)) ### Axiom
% 0.19/0.53 12. ((member T_0 (union T_2 T_3)) <=> ((member T_0 T_2) \/ (member T_0 T_3))) (-. (member T_0 (union T_2 T_3))) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (member T_0 (intersection T_2 T_1)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### Equiv 10 11
% 0.19/0.53 13. (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 (intersection T_2 T_1)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (-. (member T_0 (union T_2 T_3))) ### All 12
% 0.19/0.53 14. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (union T_2 T_3))) (member T_0 (intersection T_2 T_1)) (All C, ((intersection T_1 C) = (intersection C T_1))) (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) ### All 13
% 0.19/0.53 15. (All C, (All D, ((member D (union T_2 C)) <=> ((member D T_2) \/ (member D C))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 (union T_2 T_3))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 14
% 0.19/0.53 16. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (union T_2 T_3))) (member T_0 (intersection T_2 T_1)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 15
% 0.19/0.53 17. (All B, (All C, ((intersection B C) = (intersection C B)))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 (union T_2 T_3))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### All 16
% 0.19/0.53 18. (-. ((member T_0 (intersection T_2 T_1)) => (member T_0 (union T_2 T_3)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((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, (All C, ((intersection B C) = (intersection C B)))) ### NotImply 17
% 0.19/0.53 19. (-. (All D, ((member D (intersection T_2 T_1)) => (member D (union T_2 T_3))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 18
% 0.19/0.53 20. (-. (subset (intersection T_2 T_1) (union T_2 T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((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, (All C, ((intersection B C) = (intersection C B)))) ### Definition-Pseudo(subset) 19
% 0.19/0.53 21. (-. (All D, (subset (intersection T_2 T_1) (union T_2 D)))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 20
% 0.19/0.53 22. (-. (All C, (All D, (subset (intersection T_2 C) (union T_2 D))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((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, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 21
% 0.19/0.53 23. (-. (All B, (All C, (All D, (subset (intersection B C) (union B D)))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 22
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53 (* END-PROOF *)
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