%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET766+4 : 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 : n018.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 05:43:50 EDT 2022 % Result : Theorem 0.19s 0.48s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0. % 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n018.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 Jul 10 07:59:57 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.48 % SZS status Theorem % 0.19/0.48 (* PROOF-FOUND *) % 0.19/0.48 (* BEGIN-PROOF *) % 0.19/0.48 % SZS output start Proof % 0.19/0.48 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.19/0.48 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.19/0.48 3. (-. (apply T_2 T_0 T_0)) (apply T_2 T_0 T_0) ### Axiom % 0.19/0.48 4. ((member T_0 T_1) => (apply T_2 T_0 T_0)) (-. (apply T_2 T_0 T_0)) (member T_0 T_1) ### Imply 2 3 % 0.19/0.48 5. (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (-. (apply T_2 T_0 T_0)) ### All 4 % 0.19/0.48 6. (-. ((member T_0 T_1) /\ (apply T_2 T_0 T_0))) (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) ### NotAnd 1 5 % 0.19/0.48 7. (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 (equivalence_class T_0 T_1 T_2)) ### Axiom % 0.19/0.48 8. ((member T_0 (equivalence_class T_0 T_1 T_2)) <=> ((member T_0 T_1) /\ (apply T_2 T_0 T_0))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) (All X, ((member X T_1) => (apply T_2 X X))) ### Equiv 6 7 % 0.19/0.48 9. (All X, ((member X (equivalence_class T_0 T_1 T_2)) <=> ((member X T_1) /\ (apply T_2 T_0 X)))) (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) ### All 8 % 0.19/0.48 10. (All A, (All X, ((member X (equivalence_class A T_1 T_2)) <=> ((member X T_1) /\ (apply T_2 A X))))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) (All X, ((member X T_1) => (apply T_2 X X))) ### All 9 % 0.19/0.48 11. (All E, (All A, (All X, ((member X (equivalence_class A E T_2)) <=> ((member X E) /\ (apply T_2 A X)))))) (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) ### All 10 % 0.19/0.48 12. (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) (All X, ((member X T_1) => (apply T_2 X X))) ### All 11 % 0.19/0.48 13. ((All X, ((member X T_1) => (apply T_2 X X))) /\ ((All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) /\ (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))))) (member T_0 T_1) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### ConjTree 12 % 0.19/0.48 14. (equivalence T_2 T_1) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) ### Definition-Pseudo(equivalence) 13 % 0.19/0.48 15. (-. (((equivalence T_2 T_1) /\ (member T_0 T_1)) => (member T_0 (equivalence_class T_0 T_1 T_2)))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### ConjTree 14 % 0.19/0.48 16. (-. (All A, (((equivalence T_2 T_1) /\ (member A T_1)) => (member A (equivalence_class A T_1 T_2))))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### NotAllEx 15 % 0.19/0.48 17. (-. (All R, (All A, (((equivalence R T_1) /\ (member A T_1)) => (member A (equivalence_class A T_1 R)))))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### NotAllEx 16 % 0.19/0.48 18. (-. (All E, (All R, (All A, (((equivalence R E) /\ (member A E)) => (member A (equivalence_class A E R))))))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### NotAllEx 17 % 0.19/0.48 % SZS output end Proof % 0.19/0.48 (* END-PROOF *) %------------------------------------------------------------------------------