TSTP Solution File: SEU090+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU090+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 : n010.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 14:48:17 EDT 2022
% Result : Theorem 75.21s 75.40s
% Output : Proof 75.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU090+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n010.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 : Sun Jun 19 08:41:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 75.21/75.40 % SZS status Theorem
% 75.21/75.40 (* PROOF-FOUND *)
% 75.21/75.40 (* BEGIN-PROOF *)
% 75.21/75.40 % SZS output start Proof
% 75.21/75.40 1. (finite T_0) (-. (finite T_0)) ### Axiom
% 75.21/75.40 2. (finite T_1) (-. (finite T_1)) ### Axiom
% 75.21/75.40 3. (finite T_2) (-. (finite T_2)) ### Axiom
% 75.21/75.40 4. (-. (finite (cartesian_product3 T_0 T_1 T_2))) (finite (cartesian_product3 T_0 T_1 T_2)) ### Axiom
% 75.21/75.40 5. (((finite T_0) /\ ((finite T_1) /\ (finite T_2))) => (finite (cartesian_product3 T_0 T_1 T_2))) (-. (finite (cartesian_product3 T_0 T_1 T_2))) (finite T_2) (finite T_1) (finite T_0) ### DisjTree 1 2 3 4
% 75.21/75.40 6. (All C, (((finite T_0) /\ ((finite T_1) /\ (finite C))) => (finite (cartesian_product3 T_0 T_1 C)))) (finite T_0) (finite T_1) (finite T_2) (-. (finite (cartesian_product3 T_0 T_1 T_2))) ### All 5
% 75.21/75.40 7. (All B, (All C, (((finite T_0) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 T_0 B C))))) (-. (finite (cartesian_product3 T_0 T_1 T_2))) (finite T_2) (finite T_1) (finite T_0) ### All 6
% 75.21/75.40 8. (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (finite T_0) (finite T_1) (finite T_2) (-. (finite (cartesian_product3 T_0 T_1 T_2))) ### All 7
% 75.21/75.40 9. (finite T_3) (-. (finite T_3)) ### Axiom
% 75.21/75.40 10. (-. (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3)) ### Axiom
% 75.21/75.40 11. (((finite (cartesian_product3 T_0 T_1 T_2)) /\ (finite T_3)) => (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) (-. (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) (finite T_3) (finite T_2) (finite T_1) (finite T_0) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) ### DisjTree 8 9 10
% 75.21/75.40 12. (All B, (((finite (cartesian_product3 T_0 T_1 T_2)) /\ (finite B)) => (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) B)))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (finite T_0) (finite T_1) (finite T_2) (finite T_3) (-. (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) ### All 11
% 75.21/75.40 13. (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (-. (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) (finite T_3) (finite T_2) (finite T_1) (finite T_0) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) ### All 12
% 75.21/75.40 14. (-. (subset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) ### Refl(subset)
% 75.21/75.40 15. (-. (element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3)))) (element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) ### Axiom
% 75.21/75.40 16. ((element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) <=> (subset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) (-. (element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3)))) ### Equiv 14 15
% 75.21/75.40 17. (All B, ((element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) B))) (-. (element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3)))) ### All 16
% 75.21/75.40 18. ((cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) != (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3)) ### Refl(=)
% 75.21/75.40 19. ((cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) != (cartesian_product4 T_0 T_1 T_2 T_3)) ### Definition-Pseudo(cartesian_product4) 18
% 75.21/75.40 20. (-. (finite (cartesian_product4 T_0 T_1 T_2 T_3))) (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3)) ### P-NotP 19
% 75.21/75.40 21. ((element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) => (finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) (-. (finite (cartesian_product4 T_0 T_1 T_2 T_3))) (All B, ((element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) B))) ### Imply 17 20
% 75.21/75.40 22. (All B, ((element B (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) => (finite B))) (All B, ((element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) B))) (-. (finite (cartesian_product4 T_0 T_1 T_2 T_3))) ### All 21
% 75.21/75.40 23. ((finite (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3)) => (All B, ((element B (powerset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3))) => (finite B)))) (-. (finite (cartesian_product4 T_0 T_1 T_2 T_3))) (All B, ((element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) B))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (finite T_0) (finite T_1) (finite T_2) (finite T_3) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) ### Imply 13 22
% 75.21/75.40 24. (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (finite T_3) (finite T_2) (finite T_1) (finite T_0) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (All B, ((element (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product3 T_0 T_1 T_2) T_3) B))) (-. (finite (cartesian_product4 T_0 T_1 T_2 T_3))) ### All 23
% 75.21/75.40 25. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (finite (cartesian_product4 T_0 T_1 T_2 T_3))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (finite T_0) (finite T_1) (finite T_2) (finite T_3) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) ### All 24
% 75.21/75.40 26. (-. (((finite T_0) /\ ((finite T_1) /\ ((finite T_2) /\ (finite T_3)))) => (finite (cartesian_product4 T_0 T_1 T_2 T_3)))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### ConjTree 25
% 75.21/75.40 27. (-. (All D, (((finite T_0) /\ ((finite T_1) /\ ((finite T_2) /\ (finite D)))) => (finite (cartesian_product4 T_0 T_1 T_2 D))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) ### NotAllEx 26
% 75.21/75.40 28. (-. (All C, (All D, (((finite T_0) /\ ((finite T_1) /\ ((finite C) /\ (finite D)))) => (finite (cartesian_product4 T_0 T_1 C D)))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### NotAllEx 27
% 75.21/75.40 29. (-. (All B, (All C, (All D, (((finite T_0) /\ ((finite B) /\ ((finite C) /\ (finite D)))) => (finite (cartesian_product4 T_0 B C D))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) ### NotAllEx 28
% 75.21/75.41 30. (-. (All A, (All B, (All C, (All D, (((finite A) /\ ((finite B) /\ ((finite C) /\ (finite D)))) => (finite (cartesian_product4 A B C D)))))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (All A, (All B, (All C, (((finite A) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 A B C)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### NotAllEx 29
% 75.21/75.41 % SZS output end Proof
% 75.21/75.41 (* END-PROOF *)
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