TSTP Solution File: NUM414+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n020.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 : Mon Jul 18 14:42:14 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 18:44:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 (* PROOF-FOUND *)
% 0.19/0.42 (* BEGIN-PROOF *)
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 1. (ordinal T_0) (-. (ordinal T_0)) ### Axiom
% 0.19/0.42 2. (ordinal T_1) (-. (ordinal T_1)) ### Axiom
% 0.19/0.42 3. (ordinal T_1) (-. (ordinal T_1)) ### Axiom
% 0.19/0.42 4. (ordinal T_0) (-. (ordinal T_0)) ### Axiom
% 0.19/0.42 5. (ordinal T_1) (-. (ordinal T_1)) ### Axiom
% 0.19/0.42 6. (ordinal T_0) (-. (ordinal T_0)) ### Axiom
% 0.19/0.42 7. (-. (ordinal_subset T_1 T_0)) (ordinal_subset T_1 T_0) ### Axiom
% 0.19/0.42 8. (-. (ordinal_subset T_0 T_1)) (ordinal_subset T_0 T_1) ### Axiom
% 0.19/0.42 9. (((ordinal T_1) /\ (ordinal T_0)) => ((ordinal_subset T_1 T_0) \/ (ordinal_subset T_0 T_1))) (-. (ordinal_subset T_0 T_1)) (-. (ordinal_subset T_1 T_0)) (ordinal T_0) (ordinal T_1) ### DisjTree 5 6 7 8
% 0.19/0.42 10. (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (ordinal T_1) (ordinal T_0) (-. (ordinal_subset T_1 T_0)) (-. (ordinal_subset T_0 T_1)) ### All 9
% 0.19/0.42 11. (-. (subset T_1 T_0)) (subset T_1 T_0) ### Axiom
% 0.19/0.42 12. ((ordinal_subset T_1 T_0) <=> (subset T_1 T_0)) (-. (subset T_1 T_0)) (-. (ordinal_subset T_0 T_1)) (ordinal T_0) (ordinal T_1) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) ### Equiv 10 11
% 0.19/0.42 13. (((ordinal T_1) /\ (ordinal T_0)) => ((ordinal_subset T_1 T_0) <=> (subset T_1 T_0))) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (ordinal_subset T_0 T_1)) (-. (subset T_1 T_0)) (ordinal T_0) (ordinal T_1) ### DisjTree 3 4 12
% 0.19/0.42 14. (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) (ordinal T_1) (ordinal T_0) (-. (subset T_1 T_0)) (-. (ordinal_subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) ### All 13
% 0.19/0.42 15. (-. (subset T_0 T_1)) (subset T_0 T_1) ### Axiom
% 0.19/0.42 16. ((ordinal_subset T_0 T_1) <=> (subset T_0 T_1)) (-. (subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_1 T_0)) (ordinal T_0) (ordinal T_1) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) ### Equiv 14 15
% 0.19/0.42 17. (((ordinal T_0) /\ (ordinal T_1)) => ((ordinal_subset T_0 T_1) <=> (subset T_0 T_1))) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) (-. (subset T_1 T_0)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_0 T_1)) (ordinal T_1) (ordinal T_0) ### DisjTree 1 2 16
% 0.19/0.42 18. (All B, (((ordinal T_0) /\ (ordinal B)) => ((ordinal_subset T_0 B) <=> (subset T_0 B)))) (ordinal T_0) (ordinal T_1) (-. (subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_1 T_0)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) ### All 17
% 0.19/0.42 19. (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (-. (subset T_1 T_0)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_0 T_1)) (ordinal T_1) (ordinal T_0) (All B, (((ordinal T_0) /\ (ordinal B)) => ((ordinal_subset T_0 B) <=> (subset T_0 B)))) ### All 18
% 0.19/0.42 20. (ordinal T_0) (ordinal T_1) (-. (subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_1 T_0)) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) ### All 19
% 0.19/0.42 21. (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (-. (subset T_1 T_0)) (-. (subset T_0 T_1)) (ordinal T_1) (ordinal T_0) ### All 20
% 0.19/0.42 22. (T_1 != T_0) (T_0 = T_1) ### Sym(=)
% 0.19/0.42 23. (-. (proper_subset T_0 T_1)) (T_1 != T_0) (ordinal T_0) (ordinal T_1) (-. (subset T_1 T_0)) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) ### Extension/test/not_d8_xboole_0 21 22
% 0.19/0.42 24. (T_1 != T_0) (T_1 = T_0) ### Axiom
% 0.19/0.42 25. (-. (proper_subset T_1 T_0)) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (ordinal T_1) (ordinal T_0) (T_1 != T_0) (-. (proper_subset T_0 T_1)) ### Extension/test/not_d8_xboole_0 23 24
% 0.19/0.42 26. (-. ((ordinal T_0) => (-. ((-. (proper_subset T_1 T_0)) /\ ((T_1 != T_0) /\ (-. (proper_subset T_0 T_1))))))) (ordinal T_1) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) ### ConjTree 25
% 0.19/0.42 27. (-. (All B, ((ordinal B) => (-. ((-. (proper_subset T_1 B)) /\ ((T_1 != B) /\ (-. (proper_subset B T_1)))))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (ordinal T_1) ### NotAllEx 26
% 0.19/0.42 28. (-. ((ordinal T_1) => (All B, ((ordinal B) => (-. ((-. (proper_subset T_1 B)) /\ ((T_1 != B) /\ (-. (proper_subset B T_1))))))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) ### NotImply 27
% 0.19/0.42 29. (-. (All A, ((ordinal A) => (All B, ((ordinal B) => (-. ((-. (proper_subset A B)) /\ ((A != B) /\ (-. (proper_subset B A)))))))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) ### NotAllEx 28
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 (* END-PROOF *)
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