TSTP Solution File: SET592+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET592+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 : n006.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 05:42:30 EDT 2022
% Result : Theorem 66.69s 66.86s
% Output : Proof 66.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 10 09:51:06 EDT 2022
% 0.14/0.36 % CPUTime :
% 66.69/66.86 % SZS status Theorem
% 66.69/66.86 (* PROOF-FOUND *)
% 66.69/66.86 (* BEGIN-PROOF *)
% 66.69/66.86 % SZS output start Proof
% 66.69/66.86 1. (member T_0 (empty_set)) (-. (member T_0 (empty_set))) ### Axiom
% 66.69/66.86 2. (All B, (-. (member B (empty_set)))) (member T_0 (empty_set)) ### All 1
% 66.69/66.86 3. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 66.69/66.86 4. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom
% 66.69/66.86 5. ((member T_0 T_1) => (member T_0 T_2)) (-. (member T_0 T_2)) (member T_0 T_1) ### Imply 3 4
% 66.69/66.86 6. (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (-. (member T_0 T_2)) ### All 5
% 66.69/66.86 7. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 66.69/66.86 8. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom
% 66.69/66.86 9. ((member T_0 T_1) => (member T_0 T_3)) (-. (member T_0 T_3)) (member T_0 T_1) ### Imply 7 8
% 66.69/66.86 10. (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (-. (member T_0 T_3)) ### All 9
% 66.69/66.86 11. (-. ((member T_0 T_2) /\ (member T_0 T_3))) (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) ### NotAnd 6 10
% 66.69/66.86 12. (-. (member T_0 (intersection T_2 T_3))) (member T_0 (intersection T_2 T_3)) ### Axiom
% 66.69/66.86 13. ((member T_0 (intersection T_2 T_3)) <=> ((member T_0 T_2) /\ (member T_0 T_3))) (-. (member T_0 (intersection T_2 T_3))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_3))) ### Equiv 11 12
% 66.69/66.86 14. (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (-. (member T_0 (intersection T_2 T_3))) ### All 13
% 66.69/66.86 15. (-. ((member T_0 (intersection T_2 T_3)) /\ (member T_0 T_3))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) ### NotAnd 14 10
% 66.69/66.86 16. (T_0 != T_0) ### Refl(=)
% 66.69/66.86 17. ((intersection T_2 T_3) = (empty_set)) ((intersection T_2 T_3) != (empty_set)) ### Axiom
% 66.69/66.86 18. (T_3 != T_3) ### Refl(=)
% 66.69/66.86 19. ((intersection (intersection T_2 T_3) T_3) != (intersection (empty_set) T_3)) ((intersection T_2 T_3) = (empty_set)) ### NotEqual 17 18
% 66.69/66.86 20. (-. (member T_0 (intersection (empty_set) T_3))) (member T_0 (intersection (intersection T_2 T_3) T_3)) ((intersection T_2 T_3) = (empty_set)) ### P-NotP 16 19
% 66.69/66.86 21. ((member T_0 (intersection (intersection T_2 T_3) T_3)) <=> ((member T_0 (intersection T_2 T_3)) /\ (member T_0 T_3))) ((intersection T_2 T_3) = (empty_set)) (-. (member T_0 (intersection (empty_set) T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) ### Equiv 15 20
% 66.69/66.86 22. (All D, ((member D (intersection (intersection T_2 T_3) T_3)) <=> ((member D (intersection T_2 T_3)) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (-. (member T_0 (intersection (empty_set) T_3))) ((intersection T_2 T_3) = (empty_set)) ### All 21
% 66.69/66.86 23. (All C, (All D, ((member D (intersection (intersection T_2 T_3) C)) <=> ((member D (intersection T_2 T_3)) /\ (member D C))))) ((intersection T_2 T_3) = (empty_set)) (-. (member T_0 (intersection (empty_set) T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) ### All 22
% 66.69/66.86 24. (-. (member T_0 (empty_set))) (member T_0 (empty_set)) ### Axiom
% 66.69/66.86 25. ((member T_0 (empty_set)) /\ (member T_0 T_3)) (-. (member T_0 (empty_set))) ### And 24
% 66.69/66.86 26. ((member T_0 (intersection (empty_set) T_3)) <=> ((member T_0 (empty_set)) /\ (member T_0 T_3))) (-. (member T_0 (empty_set))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) ((intersection T_2 T_3) = (empty_set)) (All C, (All D, ((member D (intersection (intersection T_2 T_3) C)) <=> ((member D (intersection T_2 T_3)) /\ (member D C))))) ### Equiv 23 25
% 66.69/66.86 27. (All D, ((member D (intersection (empty_set) T_3)) <=> ((member D (empty_set)) /\ (member D T_3)))) (All C, (All D, ((member D (intersection (intersection T_2 T_3) C)) <=> ((member D (intersection T_2 T_3)) /\ (member D C))))) ((intersection T_2 T_3) = (empty_set)) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (-. (member T_0 (empty_set))) ### All 26
% 66.69/66.86 28. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (empty_set))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) ((intersection T_2 T_3) = (empty_set)) (All D, ((member D (intersection (empty_set) T_3)) <=> ((member D (empty_set)) /\ (member D T_3)))) ### All 27
% 66.69/66.86 29. (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ((intersection T_2 T_3) = (empty_set)) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_2))) (-. (member T_0 (empty_set))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 28
% 66.69/66.86 30. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (-. (member T_0 (empty_set))) (All D, ((member D T_1) => (member D T_2))) (member T_0 T_1) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) ((intersection T_2 T_3) = (empty_set)) ### All 29
% 66.69/66.86 31. (-. ((member T_0 T_1) <=> (member T_0 (empty_set)))) ((intersection T_2 T_3) = (empty_set)) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) ### NotEquiv 2 30
% 66.69/66.86 32. (-. (All D, ((member D T_1) <=> (member D (empty_set))))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) ((intersection T_2 T_3) = (empty_set)) ### NotAllEx 31
% 66.69/66.86 33. (T_1 != (empty_set)) (T_1 = (empty_set)) ### Axiom
% 66.69/66.86 34. ((T_1 = (empty_set)) <=> (All D, ((member D T_1) <=> (member D (empty_set))))) (T_1 != (empty_set)) ((intersection T_2 T_3) = (empty_set)) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) ### Equiv 32 33
% 66.69/66.86 35. (All C, ((T_1 = C) <=> (All D, ((member D T_1) <=> (member D C))))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) ((intersection T_2 T_3) = (empty_set)) (T_1 != (empty_set)) ### All 34
% 66.69/66.86 36. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (T_1 != (empty_set)) ((intersection T_2 T_3) = (empty_set)) (All D, ((member D (intersection T_2 T_3)) <=> ((member D T_2) /\ (member D T_3)))) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) ### All 35
% 66.71/66.89 37. (All C, (All D, ((member D (intersection T_2 C)) <=> ((member D T_2) /\ (member D C))))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) (All D, ((member D T_1) => (member D T_3))) ((intersection T_2 T_3) = (empty_set)) (T_1 != (empty_set)) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### All 36
% 66.71/66.89 38. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (T_1 != (empty_set)) ((intersection T_2 T_3) = (empty_set)) (All D, ((member D T_1) => (member D T_3))) (All D, ((member D T_1) => (member D T_2))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) ### All 37
% 66.71/66.89 39. (subset T_1 T_3) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All D, ((member D T_1) => (member D T_2))) ((intersection T_2 T_3) = (empty_set)) (T_1 != (empty_set)) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### Definition-Pseudo(subset) 38
% 66.71/66.89 40. (subset T_1 T_2) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (T_1 != (empty_set)) ((intersection T_2 T_3) = (empty_set)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (subset T_1 T_3) ### Definition-Pseudo(subset) 39
% 66.71/66.89 41. (-. (((subset T_1 T_2) /\ ((subset T_1 T_3) /\ ((intersection T_2 T_3) = (empty_set)))) => (T_1 = (empty_set)))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### ConjTree 40
% 66.71/66.89 42. (-. (All D, (((subset T_1 T_2) /\ ((subset T_1 D) /\ ((intersection T_2 D) = (empty_set)))) => (T_1 = (empty_set))))) (All B, (All C, ((B = C) <=> (All D, ((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, (-. (member B (empty_set)))) ### NotAllEx 41
% 66.71/66.89 43. (-. (All C, (All D, (((subset T_1 C) /\ ((subset T_1 D) /\ ((intersection C D) = (empty_set)))) => (T_1 = (empty_set)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### NotAllEx 42
% 66.71/66.89 44. (-. (All B, (All C, (All D, (((subset B C) /\ ((subset B D) /\ ((intersection C D) = (empty_set)))) => (B = (empty_set))))))) (All B, (All C, ((B = C) <=> (All D, ((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, (-. (member B (empty_set)))) ### NotAllEx 43
% 66.71/66.89 % SZS output end Proof
% 66.71/66.89 (* END-PROOF *)
%------------------------------------------------------------------------------