%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------ %----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 *) %------------------------------------------------------------------------------