%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET027+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : 300s
% DateTime : Sat Jun 21 05:24:53 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET027+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.05/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:03:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(member_type, type, (
% 0.21/0.39 member: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_Y_8_type, type, (
% 0.21/0.39 tptp_fun_Y_8: $i)).
% 0.21/0.39 tff(tptp_fun_U_0_type, type, (
% 0.21/0.39 tptp_fun_U_0: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_X_9_type, type, (
% 0.21/0.39 tptp_fun_X_9: $i)).
% 0.21/0.39 tff(tptp_fun_Z_7_type, type, (
% 0.21/0.39 tptp_fun_Z_7: $i)).
% 0.21/0.39 tff(subclass_type, type, (
% 0.21/0.39 subclass: ( $i * $i ) > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : refl((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : rewrite((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))), rewrite((subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))) <=> (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))), rewrite((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : rewrite((subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.39 tff(11,axiom,(![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','subclass_defn')).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.39 tff(14,plain,(
% 0.21/0.39 ![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ((~![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))) | (~((~((~subclass(X!9, Z!7)) | ![U: $i] : ((~member(U, X!9)) | member(U, Z!7)))) | (~(subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~((~((~subclass(X!9, Z!7)) | ![U: $i] : ((~member(U, X!9)) | member(U, Z!7)))) | (~(subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (((~((~subclass(X!9, Z!7)) | ![U: $i] : ((~member(U, X!9)) | member(U, Z!7)))) | (~(subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)))))) | (subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~(subclass(X, Y) & subclass(Y, Z))) | subclass(X, Z))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(subclass(X, Y) & subclass(Y, Z))) | subclass(X, Z)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 ((~![X: $i, Y: $i, Z: $i] : ((subclass(X, Y) & subclass(Y, Z)) => subclass(X, Z))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(subclass(X, Y) & subclass(Y, Z))) | subclass(X, Z)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(23,axiom,(~![X: $i, Y: $i, Z: $i] : ((subclass(X, Y) & subclass(Y, Z)) => subclass(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(subclass(X, Y) & subclass(Y, Z))) | subclass(X, Z))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(subclass(X, Y) & subclass(Y, Z))) | subclass(X, Z))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(subclass(X, Y) & subclass(Y, Z))) | subclass(X, Z))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(subclass(X, Y) & subclass(Y, Z))) | subclass(X, Z))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.21/0.40 tff(28,plain,(
% 0.21/0.40 ~((~(subclass(X!9, Y!8) & subclass(Y!8, Z!7))) | subclass(X!9, Z!7))),
% 0.21/0.40 inference(skolemize,[status(sab)],[27])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (~subclass(X!9, Z!7)),
% 0.21/0.40 inference(or_elim,[status(thm)],[28])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~(subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))))) | subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~(subclass(X!9, Z!7) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))))) | (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (~((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)) | (~member(tptp_fun_U_0(Z!7, X!9), Z!7))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (~member(tptp_fun_U_0(Z!7, X!9), Z!7)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))) | (~((~((~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7)))) | (~(subclass(Y!8, Z!7) | (~((~member(tptp_fun_U_0(Z!7, Y!8), Y!8)) | member(tptp_fun_U_0(Z!7, Y!8), Z!7)))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (~((~((~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7)))) | (~(subclass(Y!8, Z!7) | (~((~member(tptp_fun_U_0(Z!7, Y!8), Y!8)) | member(tptp_fun_U_0(Z!7, Y!8), Z!7))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[35, 16])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (((~((~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7)))) | (~(subclass(Y!8, Z!7) | (~((~member(tptp_fun_U_0(Z!7, Y!8), Y!8)) | member(tptp_fun_U_0(Z!7, Y!8), Z!7)))))) | ((~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (subclass(X!9, Y!8) & subclass(Y!8, Z!7)),
% 0.21/0.40 inference(or_elim,[status(thm)],[28])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (subclass(Y!8, Z!7)),
% 0.21/0.40 inference(and_elim,[status(thm)],[39])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 ((~((~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7)))) | (~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 ((~((~subclass(Y!8, Z!7)) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7)))) | ![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (((~![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))) | ((~member(tptp_fun_U_0(Z!7, X!9), Y!8)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))) <=> ((~![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))) | (~member(tptp_fun_U_0(Z!7, X!9), Y!8)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 ((~![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))) | ((~member(tptp_fun_U_0(Z!7, X!9), Y!8)) | member(tptp_fun_U_0(Z!7, X!9), Z!7))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ((~![U: $i] : ((~member(U, Y!8)) | member(U, Z!7))) | (~member(tptp_fun_U_0(Z!7, X!9), Y!8)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (~member(tptp_fun_U_0(Z!7, X!9), Y!8)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[46, 43, 34])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Z!7)) | member(tptp_fun_U_0(Z!7, X!9), X!9)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (member(tptp_fun_U_0(Z!7, X!9), X!9)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[48, 32])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))) | (~((~((~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8)))) | (~(subclass(X!9, Y!8) | (~((~member(tptp_fun_U_0(Y!8, X!9), X!9)) | member(tptp_fun_U_0(Y!8, X!9), Y!8)))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (~((~((~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8)))) | (~(subclass(X!9, Y!8) | (~((~member(tptp_fun_U_0(Y!8, X!9), X!9)) | member(tptp_fun_U_0(Y!8, X!9), Y!8))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[50, 16])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (((~((~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8)))) | (~(subclass(X!9, Y!8) | (~((~member(tptp_fun_U_0(Y!8, X!9), X!9)) | member(tptp_fun_U_0(Y!8, X!9), Y!8)))))) | ((~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 ((~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (subclass(X!9, Y!8)),
% 0.21/0.40 inference(and_elim,[status(thm)],[39])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ((~((~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8)))) | (~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 ((~((~subclass(X!9, Y!8)) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8)))) | ![U: $i] : ((~member(U, X!9)) | member(U, Y!8))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (![U: $i] : ((~member(U, X!9)) | member(U, Y!8))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (((~![U: $i] : ((~member(U, X!9)) | member(U, Y!8))) | ((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Y!8))) <=> ((~![U: $i] : ((~member(U, X!9)) | member(U, Y!8))) | (~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Y!8))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 ((~![U: $i] : ((~member(U, X!9)) | member(U, Y!8))) | ((~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Y!8))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 ((~![U: $i] : ((~member(U, X!9)) | member(U, Y!8))) | (~member(tptp_fun_U_0(Z!7, X!9), X!9)) | member(tptp_fun_U_0(Z!7, X!9), Y!8)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[60, 57, 49, 47])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------