%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n009.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 05:37:59 EDT 2022 % Result : Theorem 0.20s 0.44s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0. % 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n009.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 % 0.13/0.34 % DateTime : Sun Jul 10 13:11:52 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.44 % SZS status Theorem % 0.20/0.44 (* PROOF-FOUND *) % 0.20/0.44 (* BEGIN-PROOF *) % 0.20/0.44 % SZS output start Proof % 0.20/0.44 1. (T_0 != T_0) ### Refl(=) % 0.20/0.44 2. ((union T_1 T_2) = (union T_2 T_1)) ((union T_2 T_1) != (union T_1 T_2)) ### Sym(=) % 0.20/0.44 3. (-. (member T_0 (union T_1 T_2))) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) ### P-NotP 1 2 % 0.20/0.44 4. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom % 0.20/0.44 5. (-. (member T_0 T_2)) (member T_0 T_2) ### Axiom % 0.20/0.44 6. ((member T_0 T_1) \/ (member T_0 T_2)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) ### Or 4 5 % 0.20/0.44 7. ((member T_0 (union T_1 T_2)) <=> ((member T_0 T_1) \/ (member T_0 T_2))) (-. (member T_0 T_1)) (-. (member T_0 T_2)) ((union T_1 T_2) = (union T_2 T_1)) (member T_0 (union T_2 T_1)) ### Equiv 3 6 % 0.20/0.44 8. (All D, ((member D (union T_1 T_2)) <=> ((member D T_1) \/ (member D T_2)))) (member T_0 (union T_2 T_1)) ((union T_1 T_2) = (union T_2 T_1)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) ### All 7 % 0.20/0.44 9. (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 T_1)) (-. (member T_0 T_2)) (member T_0 (union T_2 T_1)) (All D, ((member D (union T_1 T_2)) <=> ((member D T_1) \/ (member D T_2)))) ### All 8 % 0.20/0.44 10. (All C, (All D, ((member D (union T_1 C)) <=> ((member D T_1) \/ (member D C))))) (member T_0 (union T_2 T_1)) (-. (member T_0 T_2)) (-. (member T_0 T_1)) (All C, ((union T_1 C) = (union C T_1))) ### All 9 % 0.20/0.44 11. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 T_1)) (-. (member T_0 T_2)) (member T_0 (union T_2 T_1)) ### All 10 % 0.20/0.44 12. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 0.20/0.44 13. ((member T_0 T_1) => (member T_0 T_3)) (-. (member T_0 T_3)) (member T_0 (union T_2 T_1)) (-. (member T_0 T_2)) (All C, ((union T_1 C) = (union C T_1))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### Imply 11 12 % 0.20/0.44 14. (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All C, ((union T_1 C) = (union C T_1))) (-. (member T_0 T_2)) (member T_0 (union T_2 T_1)) (-. (member T_0 T_3)) ### All 13 % 0.20/0.44 15. (All B, (All C, ((union B C) = (union C B)))) (-. (member T_0 T_3)) (member T_0 (union T_2 T_1)) (-. (member T_0 T_2)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_1) => (member D T_3))) ### All 14 % 0.20/0.44 16. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 0.20/0.44 17. ((member T_0 T_2) => (member T_0 T_3)) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (member T_0 (union T_2 T_1)) (-. (member T_0 T_3)) (All B, (All C, ((union B C) = (union C B)))) ### Imply 15 16 % 0.20/0.44 18. (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((union B C) = (union C B)))) (-. (member T_0 T_3)) (member T_0 (union T_2 T_1)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_1) => (member D T_3))) ### All 17 % 0.20/0.44 19. (-. ((member T_0 (union T_2 T_1)) => (member T_0 T_3))) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) (All D, ((member D T_2) => (member D T_3))) ### NotImply 18 % 0.20/0.44 20. (-. (All D, ((member D (union T_2 T_1)) => (member D T_3)))) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_1) => (member D T_3))) ### NotAllEx 19 % 0.20/0.44 21. (-. (subset (union T_2 T_1) T_3)) (All D, ((member D T_1) => (member D T_3))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) (All D, ((member D T_2) => (member D T_3))) ### Definition-Pseudo(subset) 20 % 0.20/0.44 22. (subset T_1 T_3) (All D, ((member D T_2) => (member D T_3))) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (subset (union T_2 T_1) T_3)) ### Definition-Pseudo(subset) 21 % 0.20/0.44 23. (subset T_2 T_3) (-. (subset (union T_2 T_1) T_3)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) (subset T_1 T_3) ### Definition-Pseudo(subset) 22 % 0.20/0.44 24. (-. (((subset T_2 T_3) /\ (subset T_1 T_3)) => (subset (union T_2 T_1) T_3))) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### ConjTree 23 % 0.20/0.44 25. (-. (All D, (((subset T_2 T_3) /\ (subset D T_3)) => (subset (union T_2 D) T_3)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) ### NotAllEx 24 % 0.20/0.44 26. (-. (All C, (All D, (((subset T_2 C) /\ (subset D C)) => (subset (union T_2 D) C))))) (All B, (All C, ((union B C) = (union C B)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 25 % 0.20/0.44 27. (-. (All B, (All C, (All D, (((subset B C) /\ (subset D C)) => (subset (union B D) C)))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, ((union B C) = (union C B)))) ### NotAllEx 26 % 0.20/0.44 % SZS output end Proof % 0.20/0.44 (* END-PROOF *) %------------------------------------------------------------------------------