TSTP Solution File: SEU147+3 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n029.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 14:48:39 EDT 2022
% Result : Theorem 1.85s 2.07s
% Output : Proof 1.85s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.08/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.33 % Computer : n029.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 : Sat Jun 18 22:22:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.85/2.07 % SZS status Theorem
% 1.85/2.07 (* PROOF-FOUND *)
% 1.85/2.07 (* BEGIN-PROOF *)
% 1.85/2.07 % SZS output start Proof
% 1.85/2.07 1. (subset T_0 (empty_set)) (-. (subset T_0 (empty_set))) ### Axiom
% 1.85/2.07 2. ((singleton (empty_set)) != (singleton (empty_set))) ### Refl(=)
% 1.85/2.07 3. (T_0 = (empty_set)) (T_0 != (empty_set)) ### Axiom
% 1.85/2.07 4. (-. (in T_0 (singleton (empty_set)))) (in T_0 (singleton (empty_set))) ### Axiom
% 1.85/2.07 5. ((in T_0 (singleton (empty_set))) <=> (T_0 = (empty_set))) (-. (in T_0 (singleton (empty_set)))) (T_0 = (empty_set)) ### Equiv 3 4
% 1.85/2.07 6. (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set)))) (T_0 = (empty_set)) (-. (in T_0 (singleton (empty_set)))) ### All 5
% 1.85/2.07 7. (((singleton (empty_set)) = (singleton (empty_set))) <=> (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set))))) (-. (in T_0 (singleton (empty_set)))) (T_0 = (empty_set)) ### Equiv 2 6
% 1.85/2.07 8. (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (T_0 = (empty_set)) (-. (in T_0 (singleton (empty_set)))) ### All 7
% 1.85/2.07 9. ((subset T_0 (empty_set)) => (T_0 = (empty_set))) (-. (in T_0 (singleton (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (subset T_0 (empty_set)) ### Imply 1 8
% 1.85/2.07 10. (All A, ((subset A (empty_set)) => (A = (empty_set)))) (subset T_0 (empty_set)) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (-. (in T_0 (singleton (empty_set)))) ### All 9
% 1.85/2.07 11. ((singleton (empty_set)) != (singleton (empty_set))) ### Refl(=)
% 1.85/2.07 12. (in T_0 (singleton (empty_set))) (-. (in T_0 (singleton (empty_set)))) ### Axiom
% 1.85/2.07 13. (T_0 != (empty_set)) (T_0 = (empty_set)) ### Axiom
% 1.85/2.07 14. ((in T_0 (singleton (empty_set))) <=> (T_0 = (empty_set))) (T_0 != (empty_set)) (in T_0 (singleton (empty_set))) ### Equiv 12 13
% 1.85/2.07 15. (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set)))) (in T_0 (singleton (empty_set))) (T_0 != (empty_set)) ### All 14
% 1.85/2.07 16. (((singleton (empty_set)) = (singleton (empty_set))) <=> (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set))))) (T_0 != (empty_set)) (in T_0 (singleton (empty_set))) ### Equiv 11 15
% 1.85/2.07 17. (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (in T_0 (singleton (empty_set))) (T_0 != (empty_set)) ### All 16
% 1.85/2.07 18. (-. (subset T_0 (empty_set))) (in T_0 (singleton (empty_set))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) ### Refl(subset) 17
% 1.85/2.07 19. (-. ((in T_0 (singleton (empty_set))) <=> (subset T_0 (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) ### NotEquiv 10 18
% 1.85/2.07 20. (-. (All C, ((in C (singleton (empty_set))) <=> (subset C (empty_set))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) ### NotAllEx 19
% 1.85/2.07 21. ((powerset (empty_set)) != (singleton (empty_set))) ((singleton (empty_set)) = (powerset (empty_set))) ### Sym(=)
% 1.85/2.07 22. (((singleton (empty_set)) = (powerset (empty_set))) <=> (All C, ((in C (singleton (empty_set))) <=> (subset C (empty_set))))) ((powerset (empty_set)) != (singleton (empty_set))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) ### Equiv 20 21
% 1.85/2.07 23. (All B, ((B = (powerset (empty_set))) <=> (All C, ((in C B) <=> (subset C (empty_set)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) ((powerset (empty_set)) != (singleton (empty_set))) ### All 22
% 1.85/2.07 24. (All A, (All B, ((B = (singleton A)) <=> (All C, ((in C B) <=> (C = A)))))) ((powerset (empty_set)) != (singleton (empty_set))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) (All B, ((B = (powerset (empty_set))) <=> (All C, ((in C B) <=> (subset C (empty_set)))))) ### All 23
% 1.85/2.07 25. (All A, (All B, ((B = (powerset A)) <=> (All C, ((in C B) <=> (subset C A)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) ((powerset (empty_set)) != (singleton (empty_set))) (All A, (All B, ((B = (singleton A)) <=> (All C, ((in C B) <=> (C = A)))))) ### All 24
% 1.85/2.07 % SZS output end Proof
% 1.85/2.07 (* END-PROOF *)
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