TSTP Solution File: SET201+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET201+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 : n013.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 05:40:20 EDT 2022
% Result : Theorem 1.46s 1.67s
% Output : Proof 1.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.11 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 9 18:38:59 EDT 2022
% 0.11/0.32 % CPUTime :
% 1.46/1.67 % SZS status Theorem
% 1.46/1.67 (* PROOF-FOUND *)
% 1.46/1.67 (* BEGIN-PROOF *)
% 1.46/1.67 % SZS output start Proof
% 1.46/1.67 1. (T_0 != T_0) ### Refl(=)
% 1.46/1.67 2. ((intersection T_1 T_2) = (intersection T_2 T_1)) ((intersection T_2 T_1) != (intersection T_1 T_2)) ### Sym(=)
% 1.46/1.67 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
% 1.46/1.67 4. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom
% 1.46/1.67 5. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_2)) ### And 4
% 1.46/1.67 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
% 1.46/1.67 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
% 1.46/1.67 8. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom
% 1.46/1.67 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
% 1.46/1.67 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
% 1.46/1.67 11. (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_3)) (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 D, ((member D T_2) => (member D T_3))) ### All 10
% 1.46/1.67 12. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 T_3)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 11
% 1.46/1.67 13. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_3)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) ### All 12
% 1.46/1.67 14. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom
% 1.46/1.67 15. ((member T_0 T_1) /\ (member T_0 T_2)) (-. (member T_0 T_1)) ### And 14
% 1.46/1.67 16. ((member T_0 (intersection T_1 T_2)) <=> ((member T_0 T_1) /\ (member T_0 T_2))) (-. (member T_0 T_1)) ((intersection T_1 T_2) = (intersection T_2 T_1)) (member T_0 (intersection T_2 T_1)) ### Equiv 3 15
% 1.46/1.67 17. (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_1)) ### All 16
% 1.46/1.67 18. (-. (member T_0 T_4)) (member T_0 T_4) ### Axiom
% 1.46/1.67 19. ((member T_0 T_1) => (member T_0 T_4)) (-. (member T_0 T_4)) ((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 17 18
% 1.46/1.67 20. (All D, ((member D T_1) => (member D T_4))) (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_4)) ### All 19
% 1.46/1.67 21. (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_4)) (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 D, ((member D T_1) => (member D T_4))) ### All 20
% 1.46/1.67 22. (All C, (All D, ((member D (intersection T_1 C)) <=> ((member D T_1) /\ (member D C))))) (All D, ((member D T_1) => (member D T_4))) (member T_0 (intersection T_2 T_1)) (-. (member T_0 T_4)) (All C, ((intersection T_1 C) = (intersection C T_1))) ### All 21
% 1.46/1.67 23. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (-. (member T_0 T_4)) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_1) => (member D T_4))) ### All 22
% 1.46/1.67 24. (-. ((member T_0 T_3) /\ (member T_0 T_4))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (All C, ((intersection T_1 C) = (intersection C T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotAnd 13 23
% 1.46/1.67 25. (-. (member T_0 (intersection T_3 T_4))) (member T_0 (intersection T_3 T_4)) ### Axiom
% 1.46/1.67 26. ((member T_0 (intersection T_3 T_4)) <=> ((member T_0 T_3) /\ (member T_0 T_4))) (-. (member T_0 (intersection T_3 T_4))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) ### Equiv 24 25
% 1.46/1.67 27. (All D, ((member D (intersection T_3 T_4)) <=> ((member D T_3) /\ (member D T_4)))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (All C, ((intersection T_1 C) = (intersection C T_1))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_4))) ### All 26
% 1.46/1.67 28. (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) (-. (member T_0 (intersection T_3 T_4))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All C, ((intersection T_1 C) = (intersection C T_1))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) ### All 27
% 1.46/1.67 29. (All B, (All C, ((intersection B C) = (intersection C B)))) (All D, ((member D T_1) => (member D T_4))) (All D, ((member D T_2) => (member D T_3))) (member T_0 (intersection T_2 T_1)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (intersection T_3 T_4))) (All C, (All D, ((member D (intersection T_3 C)) <=> ((member D T_3) /\ (member D C))))) ### All 28
% 1.46/1.67 30. (-. (member T_0 (intersection T_3 T_4))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (member T_0 (intersection T_2 T_1)) (All D, ((member D T_2) => (member D T_3))) (All D, ((member D T_1) => (member D T_4))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### All 29
% 1.46/1.67 31. (-. ((member T_0 (intersection T_2 T_1)) => (member T_0 (intersection T_3 T_4)))) (All B, (All C, ((intersection B C) = (intersection C B)))) (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 (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### NotImply 30
% 1.46/1.67 32. (-. (All D, ((member D (intersection T_2 T_1)) => (member D (intersection T_3 T_4))))) (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 D, ((member D T_1) => (member D T_4))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 31
% 1.46/1.67 33. (-. (subset (intersection T_2 T_1) (intersection T_3 T_4))) (All B, (All C, ((intersection B C) = (intersection C B)))) (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 (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### Definition-Pseudo(subset) 32
% 1.46/1.67 34. (subset T_1 T_4) (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)))) (-. (subset (intersection T_2 T_1) (intersection T_3 T_4))) ### Definition-Pseudo(subset) 33
% 1.46/1.67 35. (subset T_2 T_3) (-. (subset (intersection T_2 T_1) (intersection T_3 T_4))) (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 T_1 T_4) ### Definition-Pseudo(subset) 34
% 1.46/1.67 36. (-. (((subset T_2 T_3) /\ (subset T_1 T_4)) => (subset (intersection T_2 T_1) (intersection T_3 T_4)))) (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)))) ### ConjTree 35
% 1.46/1.67 37. (-. (All E, (((subset T_2 T_3) /\ (subset T_1 E)) => (subset (intersection T_2 T_1) (intersection T_3 E))))) (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 36
% 1.46/1.67 38. (-. (All D, (All E, (((subset T_2 T_3) /\ (subset D E)) => (subset (intersection T_2 D) (intersection T_3 E)))))) (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 37
% 1.46/1.67 39. (-. (All C, (All D, (All E, (((subset T_2 C) /\ (subset D E)) => (subset (intersection T_2 D) (intersection C E))))))) (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 38
% 1.46/1.67 40. (-. (All B, (All C, (All D, (All E, (((subset B C) /\ (subset D E)) => (subset (intersection B D) (intersection C E)))))))) (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 39
% 1.46/1.67 % SZS output end Proof
% 1.46/1.67 (* END-PROOF *)
%------------------------------------------------------------------------------