TSTP Solution File: SET591+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET591+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 05:42:29 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 12:39:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 (* PROOF-FOUND *)
% 0.19/0.45 (* BEGIN-PROOF *)
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.19/0.45 2. (-. (member T_0 (difference T_2 T_1))) (member T_0 (difference T_2 T_1)) ### Axiom
% 0.19/0.45 3. ((member T_0 T_1) => (member T_0 (difference T_2 T_1))) (-. (member T_0 (difference T_2 T_1))) (member T_0 T_1) ### Imply 1 2
% 0.19/0.45 4. (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (member T_0 T_1) (-. (member T_0 (difference T_2 T_1))) ### All 3
% 0.19/0.45 5. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.19/0.45 6. ((member T_0 T_2) /\ (-. (member T_0 T_1))) (member T_0 T_1) ### And 5
% 0.19/0.45 7. ((member T_0 (difference T_2 T_1)) <=> ((member T_0 T_2) /\ (-. (member T_0 T_1)))) (member T_0 T_1) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) ### Equiv 4 6
% 0.19/0.45 8. (All D, ((member D (difference T_2 T_1)) <=> ((member D T_2) /\ (-. (member D T_1))))) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (member T_0 T_1) ### All 7
% 0.19/0.45 9. (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) (member T_0 T_1) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) ### All 8
% 0.19/0.45 10. (-. ((member T_0 T_1) => (member T_0 (empty_set)))) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) ### NotImply 9
% 0.19/0.45 11. (-. (All D, ((member D T_1) => (member D (empty_set))))) (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) ### NotAllEx 10
% 0.19/0.45 12. (-. (subset T_1 (empty_set))) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) ### Definition-Pseudo(subset) 11
% 0.19/0.45 13. (member T_3 (empty_set)) (-. (member T_3 (empty_set))) ### Axiom
% 0.19/0.45 14. (All B, (-. (member B (empty_set)))) (member T_3 (empty_set)) ### All 13
% 0.19/0.45 15. (-. ((member T_3 (empty_set)) => (member T_3 T_1))) (All B, (-. (member B (empty_set)))) ### NotImply 14
% 0.19/0.45 16. (-. (All D, ((member D (empty_set)) => (member D T_1)))) (All B, (-. (member B (empty_set)))) ### NotAllEx 15
% 0.19/0.45 17. (-. (subset (empty_set) T_1)) (All B, (-. (member B (empty_set)))) ### Definition-Pseudo(subset) 16
% 0.19/0.45 18. (-. ((subset T_1 (empty_set)) /\ (subset (empty_set) T_1))) (All B, (-. (member B (empty_set)))) (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) ### NotAnd 12 17
% 0.19/0.45 19. (T_1 != (empty_set)) (T_1 = (empty_set)) ### Axiom
% 0.19/0.45 20. ((T_1 = (empty_set)) <=> ((subset T_1 (empty_set)) /\ (subset (empty_set) T_1))) (T_1 != (empty_set)) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) (All B, (-. (member B (empty_set)))) ### Equiv 18 19
% 0.19/0.45 21. (All C, ((T_1 = C) <=> ((subset T_1 C) /\ (subset C T_1)))) (All B, (-. (member B (empty_set)))) (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (T_1 != (empty_set)) ### All 20
% 0.19/0.45 22. (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (T_1 != (empty_set)) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (All C, (All D, ((member D (difference T_2 C)) <=> ((member D T_2) /\ (-. (member D C)))))) (All B, (-. (member B (empty_set)))) ### All 21
% 0.19/0.45 23. (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (-. (member B (empty_set)))) (All D, ((member D T_1) => (member D (difference T_2 T_1)))) (T_1 != (empty_set)) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### All 22
% 0.19/0.45 24. (subset T_1 (difference T_2 T_1)) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (T_1 != (empty_set)) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### Definition-Pseudo(subset) 23
% 0.19/0.45 25. (-. ((subset T_1 (difference T_2 T_1)) => (T_1 = (empty_set)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### NotImply 24
% 0.19/0.45 26. (-. (All C, ((subset T_1 (difference C T_1)) => (T_1 = (empty_set))))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) (All B, (-. (member B (empty_set)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 25
% 0.19/0.45 27. (-. (All B, (All C, ((subset B (difference C B)) => (B = (empty_set)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((B = C) <=> ((subset B C) /\ (subset C B))))) ### NotAllEx 26
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45 (* END-PROOF *)
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