TSTP Solution File: SET586+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET586+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 05:42:26 EDT 2022
% Result : Theorem 0.63s 0.85s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % 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 : Mon Jul 11 07:20:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.63/0.85 % SZS status Theorem
% 0.63/0.85 (* PROOF-FOUND *)
% 0.63/0.85 (* BEGIN-PROOF *)
% 0.63/0.85 % SZS output start Proof
% 0.63/0.85 1. (T_0 != T_0) ### Refl(=)
% 0.63/0.85 2. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_2 T_1) != (intersection T_1 T_2)) ### Sym(=)
% 0.63/0.85 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
% 0.63/0.85 4. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom
% 0.63/0.85 5. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_2)) ### And 4
% 0.63/0.85 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
% 0.63/0.85 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
% 0.63/0.85 8. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom
% 0.63/0.85 9. ((member T_0 T_2) => (member T_0 T_3)) (-. (member T_0 T_3)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (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)))) ### Imply 7 8
% 0.63/0.85 10. (All D, ((member D T_2) => (member D T_3))) (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_3)) ### All 9
% 0.63/0.85 11. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (-. (member T_0 T_3)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 10
% 0.63/0.85 12. (member T_0 (intersection T_2 T_1)) (-. (member T_0 (intersection T_2 T_1))) ### Axiom
% 0.63/0.85 13. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom
% 0.63/0.85 14. ((member T_0 T_2) /\ (member T_0 T_1)) (-. (member T_0 T_1)) ### And 13
% 0.63/0.85 15. ((member T_0 (intersection T_2 T_1)) <=> ((member T_0 T_2) /\ (member T_0 T_1))) (-. (member T_0 T_1)) (member T_0 (intersection T_2 T_1)) ### Equiv 12 14
% 0.63/0.85 16. (All D, ((member D (intersection T_2 T_1)) <=> ((member D T_2) /\ (member D T_1)))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 T_1)) ### All 15
% 0.63/0.85 17. (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (-. (member T_0 T_1)) (member T_0 (intersection T_2 T_1)) ### All 16
% 0.63/0.85 18. (-. ((member T_0 T_3) /\ (member T_0 T_1))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ### NotAnd 11 17
% 0.63/0.85 19. (-. (member T_0 (intersection T_3 T_1))) (member T_0 (intersection T_3 T_1)) ### Axiom
% 0.63/0.85 20. ((member T_0 (intersection T_3 T_1)) <=> ((member T_0 T_3) /\ (member T_0 T_1))) (-. (member T_0 (intersection T_3 T_1))) (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) ### Equiv 18 19
% 0.63/0.85 21. (All D, ((member D (intersection T_3 T_1)) <=> ((member D T_3) /\ (member D T_1)))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (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 (intersection T_3 T_1))) ### All 20
% 0.63/0.85 22. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (All D, ((member D (intersection T_3 T_1)) <=> ((member D T_3) /\ (member D T_1)))) ### All 21
% 0.63/0.85 23. (All D, ((member D (intersection T_3 T_1)) <=> ((member D T_3) /\ (member D T_1)))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (-. (member T_0 (intersection T_3 T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 22
% 0.63/0.85 24. (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_1))) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 23
% 0.63/0.85 25. (All C, ((intersection T_1 C) = (intersection C T_1))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 (intersection T_3 T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) ### All 24
% 0.63/0.85 26. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_1))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 25
% 0.63/0.85 27. (All B, (All C, ((intersection B C) = (intersection C B)))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 (intersection T_3 T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 26
% 0.63/0.85 28. (-. ((member T_0 (intersection T_2 T_1)) => (member T_0 (intersection T_3 T_1)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotImply 27
% 0.63/0.85 29. (-. (All D, ((member D (intersection T_2 T_1)) => (member D (intersection T_3 T_1))))) (All B, (All C, ((intersection B C) = (intersection C B)))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotAllEx 28
% 0.63/0.85 30. (-. (subset (intersection T_2 T_1) (intersection T_3 T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### Definition-Pseudo(subset) 29
% 0.63/0.85 31. (subset 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)))))) (-. (subset (intersection T_2 T_1) (intersection T_3 T_1))) ### Definition-Pseudo(subset) 30
% 0.63/0.85 32. (-. ((subset T_2 T_3) => (subset (intersection T_2 T_1) (intersection T_3 T_1)))) (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 31
% 0.63/0.85 33. (-. (All D, ((subset T_2 T_3) => (subset (intersection T_2 D) (intersection T_3 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)))))) ### NotAllEx 32
% 0.63/0.85 34. (-. (All C, (All D, ((subset T_2 C) => (subset (intersection T_2 D) (intersection C D)))))) (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 33
% 0.63/0.85 35. (-. (All B, (All C, (All D, ((subset B C) => (subset (intersection B D) (intersection C 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)))))) ### NotAllEx 34
% 0.63/0.86 % SZS output end Proof
% 0.63/0.86 (* END-PROOF *)
%------------------------------------------------------------------------------