%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET770+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:26:18 AM UTC 2025
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET770+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:45:50 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(apply_type, type, (
% 0.22/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_X_0_type, type, (
% 0.22/0.40 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.22/0.40 tff(equivalence_class_type, type, (
% 0.22/0.40 equivalence_class: ( $i * $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_R_22_type, type, (
% 0.22/0.40 tptp_fun_R_22: $i)).
% 0.22/0.40 tff(tptp_fun_E_23_type, type, (
% 0.22/0.40 tptp_fun_E_23: $i)).
% 0.22/0.40 tff(tptp_fun_B_20_type, type, (
% 0.22/0.40 tptp_fun_B_20: $i)).
% 0.22/0.40 tff(tptp_fun_A_21_type, type, (
% 0.22/0.40 tptp_fun_A_21: $i)).
% 0.22/0.40 tff(tptp_fun_X_3_type, type, (
% 0.22/0.40 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.22/0.40 tff(member_type, type, (
% 0.22/0.40 member: ( $i * $i ) > $o)).
% 0.22/0.40 tff(subset_type, type, (
% 0.22/0.40 subset: ( $i * $i ) > $o)).
% 0.22/0.40 tff(disjoint_type, type, (
% 0.22/0.40 disjoint: ( $i * $i ) > $o)).
% 0.22/0.40 tff(equivalence_type, type, (
% 0.22/0.40 equivalence: ( $i * $i ) > $o)).
% 0.22/0.40 tff(equal_set_type, type, (
% 0.22/0.40 equal_set: ( $i * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_Z_13_type, type, (
% 0.22/0.40 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_X_15_type, type, (
% 0.22/0.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_Y_14_type, type, (
% 0.22/0.40 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_X_12_type, type, (
% 0.22/0.40 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_Y_11_type, type, (
% 0.22/0.40 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_X_10_type, type, (
% 0.22/0.40 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 (^[R: $i, E: $i, A: $i, X: $i] : refl((~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R)))) <=> (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 (![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R)))) <=> ![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 (^[R: $i, E: $i, A: $i, X: $i] : trans(trans(monotonicity(rewrite((member(X, E) & apply(R, A, X)) <=> (~((~member(X, E)) | (~apply(R, A, X))))), ((member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))))), rewrite((member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))) <=> (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))), ((member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R)))))), rewrite((~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R)))) <=> (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))), ((member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> ![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(6,axiom,(![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','equivalence_class')).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.40 tff(8,plain,(
% 0.22/0.40 ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[7])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (~(((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.40 tff(15,plain,
% 0.22/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.41 tff(23,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.22/0.41 tff(26,plain,(
% 0.22/0.41 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[25])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(30,plain,
% 0.22/0.41 (~((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 (((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))))) | (subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 (subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.22/0.41 tff(33,assumption,((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))), introduced(assumption)).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[34, 28, 33])).
% 0.22/0.41 tff(36,plain,(~((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 (((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 (~(((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[39, 10])).
% 0.22/0.41 tff(41,assumption,(~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))), introduced(assumption)).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(43,plain,
% 0.22/0.41 (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 ((((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 ((((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[45, 40])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (~(((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[47, 10])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[49, 41])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 ((((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 ((((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[52, 48])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 ((~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[56, 55, 46])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[58, 10])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[63, 61])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) <=> (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))), ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))), rewrite((disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))), ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((~(member(X, A) & member(X, B))) <=> (~(~((~member(X, A)) | (~member(X, B))))))), rewrite((~(~((~member(X, A)) | (~member(X, B))))) <=> ((~member(X, A)) | (~member(X, B)))), ((~(member(X, A) & member(X, B))) <=> ((~member(X, A)) | (~member(X, B)))))), (![X: $i] : (~(member(X, A) & member(X, B))) <=> ![X: $i] : ((~member(X, A)) | (~member(X, B))))), ((![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))) <=> (![X: $i] : ((~member(X, A)) | (~member(X, B))) | (~disjoint(A, B))))), rewrite((![X: $i] : ((~member(X, A)) | (~member(X, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))), ((![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))), (((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))) & ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))), rewrite(((disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))) & ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))), (((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 (![A: $i, B: $i] : ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 (^[A: $i, B: $i] : rewrite((((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) | disjoint(A, B)) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (![A: $i, B: $i] : (((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) | disjoint(A, B)) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B))) <=> ![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((~?[X: $i] : (member(X, A) & member(X, B))) <=> (~?[X: $i] : (member(X, A) & member(X, B)))), ((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))))), rewrite((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))), ((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B))))), rewrite((~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))), ((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> ![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.22/0.43 tff(72,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','disjoint')).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.22/0.43 tff(75,plain,(
% 0.22/0.43 ![A: $i, B: $i] : (((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) | disjoint(A, B)) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[74])).
% 0.22/0.43 tff(76,plain,
% 0.22/0.43 (![A: $i, B: $i] : ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[77, 64])).
% 0.22/0.43 tff(79,plain,
% 0.22/0.43 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 ((~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))))) <=> (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(81,plain,
% 0.22/0.43 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.22/0.43 tff(82,plain,
% 0.22/0.43 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[81, 79])).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[84, 78])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 (((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))) | (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(87,plain,
% 0.22/0.44 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.22/0.44 tff(88,plain,
% 0.22/0.44 ((~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))))) <=> (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(89,plain,
% 0.22/0.44 ((~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))) <=> (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(90,plain,
% 0.22/0.44 ((~![E: $i, R: $i, A: $i, B: $i] : (((equivalence(R, E) & member(A, E)) & member(B, E)) => (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R))))) <=> (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(91,axiom,(~![E: $i, R: $i, A: $i, B: $i] : (((equivalence(R, E) & member(A, E)) & member(B, E)) => (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIII06')).
% 0.22/0.44 tff(92,plain,
% 0.22/0.44 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.22/0.44 tff(93,plain,
% 0.22/0.44 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.22/0.44 tff(94,plain,
% 0.22/0.44 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.22/0.44 tff(95,plain,
% 0.22/0.44 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[94, 89])).
% 0.22/0.44 tff(96,plain,(
% 0.22/0.44 ~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[95])).
% 0.22/0.44 tff(97,plain,
% 0.22/0.44 (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[96, 88])).
% 0.22/0.44 tff(98,plain,
% 0.22/0.44 (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.44 inference(or_elim,[status(thm)],[97])).
% 0.22/0.44 tff(99,plain,
% 0.22/0.44 ((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(100,plain,
% 0.22/0.44 ((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.22/0.44 tff(101,plain,
% 0.22/0.44 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[100, 87])).
% 0.22/0.44 tff(102,plain,
% 0.22/0.44 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(103,plain,
% 0.22/0.44 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.22/0.44 tff(104,plain,
% 0.22/0.44 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(105,plain,
% 0.22/0.44 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.22/0.44 tff(106,plain,
% 0.22/0.44 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[105, 59])).
% 0.22/0.44 tff(107,plain,
% 0.22/0.44 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(108,plain,
% 0.22/0.44 (apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.22/0.44 tff(109,plain,
% 0.22/0.44 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(110,plain,
% 0.22/0.44 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.22/0.44 tff(111,plain,
% 0.22/0.44 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(112,plain,
% 0.22/0.44 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[111])).
% 0.22/0.44 tff(113,plain,
% 0.22/0.44 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(114,plain,
% 0.22/0.44 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[113])).
% 0.22/0.45 tff(115,plain,
% 0.22/0.45 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(116,plain,
% 0.22/0.45 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.45 tff(117,plain,
% 0.22/0.45 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[116, 114])).
% 0.22/0.45 tff(118,plain,
% 0.22/0.45 (^[A: $i, R: $i] : trans(monotonicity(rewrite(((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) <=> (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A))))), rewrite((~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))) <=> (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), rewrite((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))), rewrite((((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(119,plain,
% 0.22/0.45 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[118])).
% 0.22/0.45 tff(120,plain,
% 0.22/0.45 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(121,plain,
% 0.22/0.45 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[120])).
% 0.22/0.45 tff(122,plain,
% 0.22/0.45 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(123,plain,
% 0.22/0.45 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(124,plain,
% 0.22/0.46 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[123])).
% 0.22/0.46 tff(125,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.22/0.46 tff(126,plain,
% 0.22/0.46 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.22/0.46 tff(127,plain,
% 0.22/0.46 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.22/0.46 tff(128,plain,(
% 0.22/0.46 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[127])).
% 0.22/0.46 tff(129,plain,
% 0.22/0.46 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.22/0.46 tff(130,plain,
% 0.22/0.46 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.22/0.46 tff(131,plain,
% 0.22/0.46 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[130, 117])).
% 0.22/0.46 tff(132,plain,
% 0.22/0.46 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[131, 112])).
% 0.22/0.46 tff(133,plain,
% 0.22/0.46 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(134,plain,
% 0.22/0.46 ((~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))) <=> (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(135,plain,
% 0.22/0.46 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[134])).
% 0.22/0.47 tff(136,plain,
% 0.22/0.47 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[135, 133])).
% 0.22/0.47 tff(137,plain,
% 0.22/0.47 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(138,plain,
% 0.22/0.47 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.22/0.47 tff(139,plain,
% 0.22/0.47 (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.22/0.47 tff(140,plain,
% 0.22/0.47 (((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~((~member(tptp_fun_Y_11(R!22, E!23), E!23)) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)))) | (~((~member(tptp_fun_Z_13(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))) | ((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(141,plain,
% 0.22/0.47 ((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.22/0.47 tff(142,plain,
% 0.22/0.47 (equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23)),
% 0.22/0.47 inference(or_elim,[status(thm)],[97])).
% 0.22/0.47 tff(143,plain,
% 0.22/0.47 (equivalence(R!22, E!23)),
% 0.22/0.47 inference(and_elim,[status(thm)],[142])).
% 0.22/0.47 tff(144,plain,
% 0.22/0.47 ((~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))) | (~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(145,plain,
% 0.22/0.47 ((~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.22/0.47 tff(146,plain,
% 0.22/0.47 (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[145, 141])).
% 0.22/0.47 tff(147,plain,
% 0.22/0.47 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))) | ![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(148,plain,
% 0.22/0.47 (![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.22/0.47 tff(149,plain,
% 0.22/0.47 (member(B!20, E!23)),
% 0.22/0.47 inference(and_elim,[status(thm)],[142])).
% 0.22/0.47 tff(150,plain,
% 0.22/0.47 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(151,plain,
% 0.22/0.48 ((apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23))) <=> ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(152,plain,
% 0.22/0.48 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[151])).
% 0.22/0.48 tff(153,plain,
% 0.22/0.48 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[152, 150])).
% 0.22/0.48 tff(154,plain,
% 0.22/0.48 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(155,plain,
% 0.22/0.48 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.48 tff(156,plain,
% 0.22/0.48 (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[155, 149, 148, 110, 108, 55, 57])).
% 0.22/0.48 tff(157,plain,
% 0.22/0.48 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(158,plain,
% 0.22/0.48 (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[157, 53])).
% 0.22/0.48 tff(159,plain,
% 0.22/0.48 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(160,plain,
% 0.22/0.48 (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[159, 10])).
% 0.22/0.48 tff(161,plain,
% 0.22/0.48 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(162,plain,
% 0.22/0.48 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[161, 101])).
% 0.22/0.48 tff(163,plain,
% 0.22/0.48 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(164,plain,
% 0.22/0.48 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.22/0.48 tff(165,plain,
% 0.22/0.48 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[164, 160])).
% 0.22/0.48 tff(166,plain,
% 0.22/0.48 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(167,plain,
% 0.22/0.48 (apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.22/0.48 tff(168,plain,
% 0.22/0.48 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))) | ![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(169,plain,
% 0.22/0.48 (![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[168, 146])).
% 0.22/0.48 tff(170,plain,
% 0.22/0.48 (member(A!21, E!23)),
% 0.22/0.48 inference(and_elim,[status(thm)],[142])).
% 0.22/0.48 tff(171,plain,
% 0.22/0.48 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(172,plain,
% 0.22/0.48 (((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) <=> ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(173,plain,
% 0.22/0.48 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[172])).
% 0.22/0.48 tff(174,plain,
% 0.22/0.48 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.22/0.49 inference(transitivity,[status(thm)],[173, 171])).
% 0.22/0.49 tff(175,plain,
% 0.22/0.49 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(176,plain,
% 0.22/0.49 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.22/0.49 tff(177,plain,
% 0.22/0.49 (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[176, 170, 169, 110, 167])).
% 0.22/0.49 tff(178,plain,
% 0.22/0.49 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(179,plain,
% 0.22/0.49 ((apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23))) <=> ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(180,plain,
% 0.22/0.49 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[179])).
% 0.22/0.49 tff(181,plain,
% 0.22/0.49 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.22/0.49 inference(transitivity,[status(thm)],[180, 178])).
% 0.22/0.49 tff(182,plain,
% 0.22/0.49 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(183,plain,
% 0.22/0.49 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.22/0.49 tff(184,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[183, 170, 148, 110, 177, 55, 158, 156])).
% 0.22/0.49 tff(185,plain,((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.49 tff(186,plain,
% 0.22/0.49 ((~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))) | subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(187,plain,
% 0.22/0.49 ((~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))) | subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.22/0.49 tff(188,plain,
% 0.22/0.49 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[187, 38])).
% 0.22/0.49 tff(189,plain,
% 0.22/0.49 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(190,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[189])).
% 0.22/0.49 tff(191,plain,
% 0.22/0.49 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(192,plain,
% 0.22/0.49 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[191])).
% 0.22/0.49 tff(193,plain,
% 0.22/0.49 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(194,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.22/0.49 tff(195,plain,
% 0.22/0.49 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.22/0.49 tff(196,plain,(
% 0.22/0.49 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.49 inference(skolemize,[status(sab)],[195])).
% 0.22/0.49 tff(197,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.22/0.49 tff(198,plain,
% 0.22/0.49 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.22/0.49 tff(199,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(200,plain,
% 0.22/0.49 (~(((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.22/0.49 tff(201,plain,
% 0.22/0.49 (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.49 inference(or_elim,[status(thm)],[97])).
% 0.22/0.49 tff(202,plain,
% 0.22/0.49 ((((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(203,plain,
% 0.22/0.49 ((((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.22/0.49 tff(204,plain,
% 0.22/0.49 ((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[203, 200])).
% 0.22/0.49 tff(205,plain,
% 0.22/0.49 ((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | (~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(206,plain,
% 0.22/0.49 ((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.22/0.49 tff(207,plain,
% 0.22/0.49 (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[206, 188])).
% 0.22/0.49 tff(208,plain,
% 0.22/0.49 ((~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))) | subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(209,plain,
% 0.22/0.49 ((~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.22/0.49 tff(210,plain,
% 0.22/0.49 (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[209, 32])).
% 0.22/0.50 tff(211,plain,
% 0.22/0.50 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(212,plain,
% 0.22/0.50 (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.22/0.50 tff(213,plain,
% 0.22/0.50 ((((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(214,plain,
% 0.22/0.50 ((((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.22/0.50 tff(215,plain,
% 0.22/0.50 ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[214, 12])).
% 0.22/0.50 tff(216,plain,
% 0.22/0.50 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(217,plain,
% 0.22/0.50 (~(((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[216, 10])).
% 0.22/0.50 tff(218,plain,
% 0.22/0.50 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(219,plain,
% 0.22/0.50 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[218, 210])).
% 0.22/0.50 tff(220,plain,
% 0.22/0.50 ((((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(221,plain,
% 0.22/0.50 ((((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.22/0.50 tff(222,plain,
% 0.22/0.50 (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[221, 217])).
% 0.22/0.50 tff(223,plain,
% 0.22/0.50 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(224,plain,
% 0.22/0.50 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.22/0.50 tff(225,plain,
% 0.22/0.50 ((~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(226,plain,
% 0.22/0.50 (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[225, 224, 215])).
% 0.22/0.50 tff(227,plain,
% 0.22/0.50 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(228,plain,
% 0.22/0.50 ((apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23))) <=> ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(229,plain,
% 0.22/0.50 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[228])).
% 0.22/0.50 tff(230,plain,
% 0.22/0.50 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[229, 227])).
% 0.22/0.50 tff(231,plain,
% 0.22/0.50 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(232,plain,
% 0.22/0.50 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.22/0.50 tff(233,plain,
% 0.22/0.50 (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[232, 170, 148, 110, 167, 224, 226])).
% 0.22/0.50 tff(234,plain,
% 0.22/0.50 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(235,plain,
% 0.22/0.50 (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[234, 222])).
% 0.22/0.50 tff(236,plain,
% 0.22/0.50 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(237,plain,
% 0.22/0.50 (((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) <=> ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(238,plain,
% 0.22/0.51 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[237])).
% 0.22/0.51 tff(239,plain,
% 0.22/0.51 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.22/0.51 inference(transitivity,[status(thm)],[238, 236])).
% 0.22/0.51 tff(240,plain,
% 0.22/0.51 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(241,plain,
% 0.22/0.51 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.22/0.51 tff(242,plain,
% 0.22/0.51 (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[241, 149, 169, 110, 108])).
% 0.22/0.51 tff(243,plain,
% 0.22/0.51 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(244,plain,
% 0.22/0.51 ((apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23))) <=> ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(245,plain,
% 0.22/0.51 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[244])).
% 0.22/0.51 tff(246,plain,
% 0.22/0.51 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[245, 243])).
% 0.22/0.51 tff(247,plain,
% 0.22/0.51 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(248,plain,
% 0.22/0.51 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.22/0.51 tff(249,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[248, 149, 148, 110, 242, 224, 235, 233])).
% 0.22/0.51 % SZS output end Proof
% 0.22/0.52 % E exiting
%------------------------------------------------------------------------------