TSTP Solution File: SEU089+1 by SuperZenon---0.0.1
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% File : SuperZenon---0.0.1
% Problem : SEU089+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 : Tue Jul 19 14:48:16 EDT 2022
% Result : Theorem 3.32s 3.51s
% Output : Proof 3.34s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % 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 : Sun Jun 19 04:18:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.32/3.51 % SZS status Theorem
% 3.32/3.51 (* PROOF-FOUND *)
% 3.32/3.51 (* BEGIN-PROOF *)
% 3.32/3.51 % SZS output start Proof
% 3.32/3.51 1. (finite T_0) (-. (finite T_0)) ### Axiom
% 3.32/3.51 2. (finite T_1) (-. (finite T_1)) ### Axiom
% 3.32/3.51 3. (-. (finite (cartesian_product2 T_0 T_1))) (finite (cartesian_product2 T_0 T_1)) ### Axiom
% 3.32/3.51 4. (((finite T_0) /\ (finite T_1)) => (finite (cartesian_product2 T_0 T_1))) (-. (finite (cartesian_product2 T_0 T_1))) (finite T_1) (finite T_0) ### DisjTree 1 2 3
% 3.32/3.51 5. (All B, (((finite T_0) /\ (finite B)) => (finite (cartesian_product2 T_0 B)))) (finite T_0) (finite T_1) (-. (finite (cartesian_product2 T_0 T_1))) ### All 4
% 3.32/3.51 6. (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (-. (finite (cartesian_product2 T_0 T_1))) (finite T_1) (finite T_0) ### All 5
% 3.32/3.51 7. (finite T_2) (-. (finite T_2)) ### Axiom
% 3.32/3.51 8. (-. (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2)) ### Axiom
% 3.32/3.51 9. (((finite (cartesian_product2 T_0 T_1)) /\ (finite T_2)) => (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) (-. (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) (finite T_2) (finite T_0) (finite T_1) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) ### DisjTree 6 7 8
% 3.32/3.51 10. (All B, (((finite (cartesian_product2 T_0 T_1)) /\ (finite B)) => (finite (cartesian_product2 (cartesian_product2 T_0 T_1) B)))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (finite T_1) (finite T_0) (finite T_2) (-. (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) ### All 9
% 3.32/3.51 11. (-. (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) (finite T_2) (finite T_0) (finite T_1) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) ### All 10
% 3.32/3.51 12. (-. (subset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) ### Refl(subset)
% 3.32/3.51 13. (-. (element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2)))) (element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) ### Axiom
% 3.32/3.51 14. ((element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) <=> (subset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) (-. (element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2)))) ### Equiv 12 13
% 3.32/3.51 15. (All B, ((element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) B))) (-. (element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2)))) ### All 14
% 3.32/3.51 16. ((cartesian_product2 (cartesian_product2 T_0 T_1) T_2) != (cartesian_product2 (cartesian_product2 T_0 T_1) T_2)) ### Refl(=)
% 3.34/3.51 17. ((cartesian_product2 (cartesian_product2 T_0 T_1) T_2) != (cartesian_product3 T_0 T_1 T_2)) ### Definition-Pseudo(cartesian_product3) 16
% 3.34/3.51 18. (-. (finite (cartesian_product3 T_0 T_1 T_2))) (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2)) ### P-NotP 17
% 3.34/3.51 19. ((element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) => (finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) (-. (finite (cartesian_product3 T_0 T_1 T_2))) (All B, ((element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) B))) ### Imply 15 18
% 3.34/3.51 20. (All B, ((element B (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) => (finite B))) (All B, ((element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) B))) (-. (finite (cartesian_product3 T_0 T_1 T_2))) ### All 19
% 3.34/3.51 21. ((finite (cartesian_product2 (cartesian_product2 T_0 T_1) T_2)) => (All B, ((element B (powerset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2))) => (finite B)))) (-. (finite (cartesian_product3 T_0 T_1 T_2))) (All B, ((element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) B))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (finite T_1) (finite T_0) (finite T_2) ### Imply 11 20
% 3.34/3.51 22. (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (finite T_2) (finite T_0) (finite T_1) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (All B, ((element (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) (powerset B)) <=> (subset (cartesian_product2 (cartesian_product2 T_0 T_1) T_2) B))) (-. (finite (cartesian_product3 T_0 T_1 T_2))) ### All 21
% 3.34/3.51 23. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (finite (cartesian_product3 T_0 T_1 T_2))) (All A, (All B, (((finite A) /\ (finite B)) => (finite (cartesian_product2 A B))))) (finite T_1) (finite T_0) (finite T_2) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) ### All 22
% 3.34/3.51 24. (-. (((finite T_0) /\ ((finite T_1) /\ (finite T_2))) => (finite (cartesian_product3 T_0 T_1 T_2)))) (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, ((element A (powerset B)) <=> (subset A B)))) ### ConjTree 23
% 3.34/3.51 25. (-. (All C, (((finite T_0) /\ ((finite T_1) /\ (finite C))) => (finite (cartesian_product3 T_0 T_1 C))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (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 24
% 3.34/3.51 26. (-. (All B, (All C, (((finite T_0) /\ ((finite B) /\ (finite C))) => (finite (cartesian_product3 T_0 B C)))))) (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, ((element A (powerset B)) <=> (subset A B)))) ### NotAllEx 25
% 3.34/3.51 27. (-. (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)))) (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
% 3.34/3.51 % SZS output end Proof
% 3.34/3.51 (* END-PROOF *)
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