%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET768+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET768+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:41:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(member_type, type, (
% 0.20/0.52 member: ( $i * $i ) > $o)).
% 0.20/0.52 tff(equivalence_class_type, type, (
% 0.20/0.52 equivalence_class: ( $i * $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_R_22_type, type, (
% 0.20/0.52 tptp_fun_R_22: $i)).
% 0.20/0.52 tff(tptp_fun_E_23_type, type, (
% 0.20/0.52 tptp_fun_E_23: $i)).
% 0.20/0.52 tff(tptp_fun_B_20_type, type, (
% 0.20/0.52 tptp_fun_B_20: $i)).
% 0.20/0.52 tff(tptp_fun_A_21_type, type, (
% 0.20/0.52 tptp_fun_A_21: $i)).
% 0.20/0.52 tff(apply_type, type, (
% 0.20/0.52 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_X_0_type, type, (
% 0.20/0.52 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.52 tff(subset_type, type, (
% 0.20/0.52 subset: ( $i * $i ) > $o)).
% 0.20/0.52 tff(equal_set_type, type, (
% 0.20/0.52 equal_set: ( $i * $i ) > $o)).
% 0.20/0.52 tff(equivalence_type, type, (
% 0.20/0.52 equivalence: ( $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_Z_13_type, type, (
% 0.20/0.52 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_X_15_type, type, (
% 0.20/0.52 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_Y_14_type, type, (
% 0.20/0.52 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_X_12_type, type, (
% 0.20/0.52 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_Y_11_type, type, (
% 0.20/0.52 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_X_10_type, type, (
% 0.20/0.52 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.20/0.52 tff(1,plain,
% 0.20/0.52 (^[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)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 (![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))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 (^[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))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(4,plain,
% 0.20/0.52 (![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))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.52 tff(5,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 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')).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.52 tff(8,plain,(
% 0.20/0.52 ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[7])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 (![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 ((~![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))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (~(((~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)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (^[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))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(14,plain,
% 0.20/0.52 (![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)))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.52 tff(15,plain,
% 0.20/0.52 (^[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))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(16,plain,
% 0.20/0.52 (![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)))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 (![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)))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.52 tff(18,plain,
% 0.20/0.52 (^[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)))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (![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)))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.52 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')).
% 0.20/0.52 tff(24,plain,
% 0.20/0.52 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.52 tff(26,plain,(
% 0.20/0.52 ![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)))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[25])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (![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)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 (![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)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 ((~![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))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 (~((~((~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)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 (((~((~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)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(32,plain,
% 0.20/0.52 (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))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.52 tff(33,assumption,(apply(R!22, A!21, B!20)), introduced(assumption)).
% 0.20/0.52 tff(34,plain,
% 0.20/0.52 ((~![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)) <=> apply(R, A, B)))) <=> (~![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)) <=> apply(R, A, B))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 ((~![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)) <=> apply(R, A, B)))) <=> (~![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)) <=> apply(R, A, B))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(36,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)) <=> apply(R, A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIII04')).
% 0.20/0.52 tff(37,plain,
% 0.20/0.52 (~![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)) <=> apply(R, A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.52 tff(38,plain,
% 0.20/0.52 (~![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)) <=> apply(R, A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.20/0.52 tff(39,plain,
% 0.20/0.52 (~![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)) <=> apply(R, A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.52 tff(40,plain,
% 0.20/0.52 (~![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)) <=> apply(R, A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.20/0.52 tff(41,plain,(
% 0.20/0.52 ~((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> apply(R!22, A!21, B!20)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[40])).
% 0.20/0.52 tff(42,plain,
% 0.20/0.52 (~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> apply(R!22, A!21, B!20))),
% 0.20/0.52 inference(or_elim,[status(thm)],[41])).
% 0.20/0.52 tff(43,plain,
% 0.20/0.52 ((equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> apply(R!22, A!21, B!20)) | (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, B!20))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(44,plain,
% 0.20/0.52 ((~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, B!20))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.52 tff(45,plain,
% 0.20/0.52 (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[44, 33])).
% 0.20/0.52 tff(46,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(47,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.52 tff(48,plain,
% 0.20/0.52 (^[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)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(49,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.52 tff(50,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(51,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')).
% 0.20/0.52 tff(52,plain,
% 0.20/0.52 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.52 tff(53,plain,(
% 0.20/0.52 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[52])).
% 0.20/0.52 tff(54,plain,
% 0.20/0.52 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.52 tff(55,plain,
% 0.20/0.52 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.20/0.52 tff(56,plain,
% 0.20/0.52 ((~![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))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(57,plain,
% 0.20/0.52 (~(((~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)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.53 tff(58,plain,
% 0.20/0.53 ((((~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))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(59,plain,
% 0.20/0.53 (((~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))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.53 tff(60,plain,
% 0.20/0.53 ((~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)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[59, 45])).
% 0.20/0.53 tff(61,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)).
% 0.20/0.53 tff(62,plain,
% 0.20/0.53 ((~![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: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(63,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[62, 28, 61])).
% 0.20/0.53 tff(64,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,[]))).
% 0.20/0.53 tff(65,plain,
% 0.20/0.53 (((~((~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)))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(66,plain,
% 0.20/0.53 (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))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.53 tff(67,plain,
% 0.20/0.53 (^[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)))))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(68,plain,
% 0.20/0.53 (![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))))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.53 tff(69,plain,
% 0.20/0.53 (^[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)))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(70,plain,
% 0.20/0.53 (![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))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.53 tff(71,plain,
% 0.20/0.53 (^[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)))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(72,plain,
% 0.20/0.53 (![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))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.53 tff(73,plain,
% 0.20/0.53 (![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))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.53 tff(74,plain,
% 0.20/0.53 (^[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))))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(75,plain,
% 0.20/0.53 (![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))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.53 tff(76,plain,
% 0.20/0.53 (^[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))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(77,plain,
% 0.20/0.53 (![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)))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.53 tff(78,plain,
% 0.20/0.53 (![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))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(79,plain,
% 0.20/0.53 (^[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)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(80,plain,
% 0.20/0.53 (![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))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.53 tff(81,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')).
% 0.20/0.53 tff(82,plain,
% 0.20/0.53 (![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))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.54 tff(83,plain,
% 0.20/0.54 (![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))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.54 tff(84,plain,(
% 0.20/0.54 ![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))))))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[83])).
% 0.20/0.54 tff(85,plain,
% 0.20/0.54 (![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)))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.54 tff(86,plain,
% 0.20/0.54 (![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))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.20/0.54 tff(87,plain,
% 0.20/0.54 (![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))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[86, 73])).
% 0.20/0.54 tff(88,plain,
% 0.20/0.54 (![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))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[87, 68])).
% 0.20/0.54 tff(89,plain,
% 0.20/0.54 (((~![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)))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(90,plain,
% 0.20/0.54 ((~((~(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))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(91,plain,
% 0.20/0.54 (((~![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)))))))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.54 tff(92,plain,
% 0.20/0.54 (((~![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)))))))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.54 tff(93,plain,
% 0.20/0.54 ((~![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))))))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(94,plain,
% 0.20/0.54 ((~![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))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.54 tff(95,plain,
% 0.20/0.54 (~((~(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)))))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.20/0.55 tff(96,plain,
% 0.20/0.55 (((~(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)))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(97,plain,
% 0.20/0.55 ((~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))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.55 tff(98,plain,
% 0.20/0.55 (equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23)),
% 0.20/0.55 inference(or_elim,[status(thm)],[41])).
% 0.20/0.55 tff(99,plain,
% 0.20/0.55 (equivalence(R!22, E!23)),
% 0.20/0.55 inference(and_elim,[status(thm)],[98])).
% 0.20/0.55 tff(100,plain,
% 0.20/0.55 ((~((~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))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(101,plain,
% 0.20/0.55 ((~((~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))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.55 tff(102,plain,
% 0.20/0.55 (~((~![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)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.20/0.55 tff(103,plain,
% 0.20/0.55 (((~![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))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(104,plain,
% 0.20/0.55 (![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.55 tff(105,plain,
% 0.20/0.55 (member(B!20, E!23)),
% 0.20/0.55 inference(and_elim,[status(thm)],[98])).
% 0.20/0.55 tff(106,plain,
% 0.20/0.55 (member(A!21, E!23)),
% 0.20/0.55 inference(and_elim,[status(thm)],[98])).
% 0.20/0.55 tff(107,plain,
% 0.20/0.55 (((~![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, B!20)) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | apply(R!22, B!20, A!21))) <=> ((~![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, B!20)) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | apply(R!22, B!20, A!21))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(108,plain,
% 0.20/0.55 ((~![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, B!20)) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | apply(R!22, B!20, A!21))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(109,plain,
% 0.20/0.55 ((~![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, B!20)) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | apply(R!22, B!20, A!21)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.55 tff(110,plain,
% 0.20/0.55 ((~apply(R!22, A!21, B!20)) | apply(R!22, B!20, A!21)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[109, 106, 105, 104])).
% 0.20/0.55 tff(111,plain,
% 0.20/0.55 (apply(R!22, B!20, A!21)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[110, 33])).
% 0.20/0.55 tff(112,plain,
% 0.20/0.55 ((~![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))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(113,plain,
% 0.20/0.55 (~(((~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)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[112, 10])).
% 0.20/0.55 tff(114,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)).
% 0.20/0.55 tff(115,plain,
% 0.20/0.55 (((~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))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(116,plain,
% 0.20/0.55 (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))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.55 tff(117,plain,
% 0.20/0.55 ((((~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)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(118,plain,
% 0.20/0.55 ((((~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))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.55 tff(119,plain,
% 0.20/0.55 (~((~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)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[118, 113])).
% 0.20/0.55 tff(120,plain,
% 0.20/0.55 (((~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)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(121,plain,
% 0.20/0.55 (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)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.55 tff(122,plain,
% 0.20/0.55 ((~![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))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(123,plain,
% 0.20/0.55 (~(((~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)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[122, 10])).
% 0.20/0.55 tff(124,plain,
% 0.20/0.55 (((~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)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(125,plain,
% 0.20/0.55 (~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))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[124, 114])).
% 0.20/0.55 tff(126,plain,
% 0.20/0.55 ((((~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))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(127,plain,
% 0.20/0.55 ((((~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)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.55 tff(128,plain,
% 0.20/0.55 ((~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))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[127, 123])).
% 0.20/0.55 tff(129,plain,
% 0.20/0.55 (((~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)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(130,plain,
% 0.20/0.55 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[129, 119])).
% 0.20/0.55 tff(131,plain,
% 0.20/0.55 ((~((~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))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(132,plain,
% 0.20/0.55 (~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)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[131, 130, 128])).
% 0.20/0.56 tff(133,assumption,(apply(R!22, B!20, A!21)), introduced(assumption)).
% 0.20/0.56 tff(134,plain,
% 0.20/0.56 (((~![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)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(135,plain,
% 0.20/0.56 (![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)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[134, 102])).
% 0.20/0.56 tff(136,plain,
% 0.20/0.56 (((~![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(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)) | (~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, A!21, 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(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)) | (~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, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(137,plain,
% 0.20/0.56 ((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, 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(B!20, 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(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)) | (~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, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(138,plain,
% 0.20/0.56 (((~![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, 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(B!20, 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(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)) | (~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, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.56 tff(139,plain,
% 0.20/0.56 (((~![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, 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(B!20, 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(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)) | (~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, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[138, 136])).
% 0.20/0.56 tff(140,plain,
% 0.20/0.56 ((~![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, 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(B!20, 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)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(141,plain,
% 0.20/0.56 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.56 tff(142,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[141, 106, 105, 135, 133, 130, 132, 121])).
% 0.20/0.56 tff(143,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))) | (~apply(R!22, B!20, A!21))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(144,plain,
% 0.20/0.56 ((~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))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[143, 111])).
% 0.20/0.56 tff(145,plain,
% 0.20/0.56 ((~(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))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(146,plain,
% 0.20/0.56 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[145, 144, 66])).
% 0.20/0.56 tff(147,plain,
% 0.20/0.56 ((~((~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)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(148,plain,
% 0.20/0.56 (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[147, 146, 60])).
% 0.20/0.56 tff(149,plain,
% 0.20/0.56 ((~(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))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(150,plain,
% 0.20/0.56 ((~(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))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.56 tff(151,plain,
% 0.20/0.56 (~((~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)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[150, 32])).
% 0.20/0.56 tff(152,plain,
% 0.20/0.56 (((~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))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(153,plain,
% 0.20/0.56 (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))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.56 tff(154,plain,
% 0.20/0.56 ((((~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)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(155,plain,
% 0.20/0.56 ((((~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))))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.56 tff(156,plain,
% 0.20/0.56 (~((~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)))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[155, 12])).
% 0.20/0.56 tff(157,plain,
% 0.20/0.56 (((~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)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(158,plain,
% 0.20/0.56 (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)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.20/0.56 tff(159,plain,
% 0.20/0.56 ((~![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))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(160,plain,
% 0.20/0.56 (~(((~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)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[159, 10])).
% 0.20/0.56 tff(161,plain,
% 0.20/0.56 (((~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)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(162,plain,
% 0.20/0.56 (~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))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[161, 151])).
% 0.20/0.56 tff(163,plain,
% 0.20/0.56 ((((~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))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(164,plain,
% 0.20/0.56 ((((~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)))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.20/0.57 tff(165,plain,
% 0.20/0.57 ((~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))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[164, 160])).
% 0.20/0.57 tff(166,plain,
% 0.20/0.57 (((~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)),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(167,plain,
% 0.20/0.57 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[166, 156])).
% 0.20/0.57 tff(168,plain,
% 0.20/0.57 ((~((~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))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(169,plain,
% 0.20/0.57 (~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)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[168, 167, 165])).
% 0.20/0.57 tff(170,plain,
% 0.20/0.57 (((~![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, B!20)) | (~member(A!21, 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, 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, B!20, 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)))) | (~apply(R!22, A!21, B!20)) | (~member(A!21, 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, 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, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(171,plain,
% 0.20/0.57 ((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, 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(A!21, 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, A!21, B!20)) | (~member(A!21, 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, 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, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(172,plain,
% 0.20/0.57 (((~![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, 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(A!21, 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)))) | ((~apply(R!22, A!21, B!20)) | (~member(A!21, 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, 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, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.57 tff(173,plain,
% 0.20/0.57 (((~![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, 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(A!21, 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)))) | (~apply(R!22, A!21, B!20)) | (~member(A!21, 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, 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, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.20/0.57 inference(transitivity,[status(thm)],[172, 170])).
% 0.20/0.57 tff(174,plain,
% 0.20/0.57 ((~![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, 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(A!21, 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)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(175,plain,
% 0.20/0.57 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~apply(R!22, A!21, B!20)) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.57 tff(176,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[175, 106, 105, 33, 135, 167, 169, 158])).
% 0.20/0.57 tff(177,plain,(~apply(R!22, A!21, B!20)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(178,plain,
% 0.20/0.57 (((~![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, B!20) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)))) <=> ((~![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, B!20) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(179,plain,
% 0.20/0.57 (((~apply(R!22, B!20, A!21)) | (~member(B!20, E!23)) | (~member(A!21, E!23)) | apply(R!22, A!21, B!20)) <=> (apply(R!22, A!21, B!20) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(180,plain,
% 0.20/0.57 (((~![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, A!21)) | (~member(B!20, E!23)) | (~member(A!21, E!23)) | apply(R!22, A!21, B!20))) <=> ((~![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, B!20) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.57 tff(181,plain,
% 0.20/0.57 (((~![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, A!21)) | (~member(B!20, E!23)) | (~member(A!21, E!23)) | apply(R!22, A!21, B!20))) <=> ((~![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, B!20) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.57 tff(182,plain,
% 0.20/0.57 ((~![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, A!21)) | (~member(B!20, E!23)) | (~member(A!21, E!23)) | apply(R!22, A!21, B!20))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(183,plain,
% 0.20/0.57 ((~![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, B!20) | (~member(A!21, E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, A!21))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.57 tff(184,plain,
% 0.20/0.57 (apply(R!22, A!21, B!20) | (~apply(R!22, B!20, A!21))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[183, 106, 105, 104])).
% 0.20/0.57 tff(185,plain,
% 0.20/0.57 (~apply(R!22, B!20, A!21)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[184, 177])).
% 0.20/0.57 tff(186,plain,
% 0.20/0.57 (((~member(A!21, E!23)) | (~apply(R!22, B!20, A!21))) | apply(R!22, B!20, A!21)),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(187,plain,
% 0.20/0.57 ((~member(A!21, E!23)) | (~apply(R!22, B!20, A!21))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.20/0.57 tff(188,plain,
% 0.20/0.57 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(A!21, E!23)) | (~apply(R!22, A!21, A!21))) <=> member(A!21, equivalence_class(A!21, E!23, R!22))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(189,plain,
% 0.20/0.57 (~(((~member(A!21, E!23)) | (~apply(R!22, A!21, A!21))) <=> member(A!21, equivalence_class(A!21, E!23, R!22)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[188, 10])).
% 0.20/0.57 tff(190,plain,
% 0.20/0.57 (((~![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))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(191,plain,
% 0.20/0.57 (![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[190, 102])).
% 0.20/0.57 tff(192,plain,
% 0.20/0.57 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | ((~member(A!21, E!23)) | apply(R!22, A!21, A!21))) <=> ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~member(A!21, E!23)) | apply(R!22, A!21, A!21))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(193,plain,
% 0.20/0.57 ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | ((~member(A!21, E!23)) | apply(R!22, A!21, A!21))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(194,plain,
% 0.20/0.57 ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~member(A!21, E!23)) | apply(R!22, A!21, A!21)),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.57 tff(195,plain,
% 0.20/0.57 (apply(R!22, A!21, A!21)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[194, 106, 191])).
% 0.20/0.57 tff(196,plain,
% 0.20/0.57 ((~((~member(A!21, E!23)) | (~apply(R!22, A!21, A!21)))) | (~member(A!21, E!23)) | (~apply(R!22, A!21, A!21))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(197,plain,
% 0.20/0.57 (~((~member(A!21, E!23)) | (~apply(R!22, A!21, A!21)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[196, 106, 195])).
% 0.20/0.57 tff(198,plain,
% 0.20/0.57 ((((~member(A!21, E!23)) | (~apply(R!22, A!21, A!21))) <=> member(A!21, equivalence_class(A!21, E!23, R!22))) | ((~member(A!21, E!23)) | (~apply(R!22, A!21, A!21))) | member(A!21, equivalence_class(A!21, E!23, R!22))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(199,plain,
% 0.20/0.57 ((((~member(A!21, E!23)) | (~apply(R!22, A!21, A!21))) <=> member(A!21, equivalence_class(A!21, E!23, R!22))) | member(A!21, equivalence_class(A!21, E!23, R!22))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.57 tff(200,plain,
% 0.20/0.57 (member(A!21, equivalence_class(A!21, E!23, R!22))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[199, 189])).
% 0.20/0.57 tff(201,plain,
% 0.20/0.57 (((~((~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))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(202,plain,
% 0.20/0.57 ((~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)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[201, 64])).
% 0.20/0.57 tff(203,plain,
% 0.20/0.57 ((equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> apply(R!22, A!21, B!20)) | equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | apply(R!22, A!21, B!20)),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(204,plain,
% 0.20/0.57 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | apply(R!22, A!21, B!20)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[203, 42])).
% 0.20/0.57 tff(205,plain,
% 0.20/0.57 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[204, 177])).
% 0.20/0.57 tff(206,plain,
% 0.20/0.57 ((((~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)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(207,plain,
% 0.20/0.57 ((~((~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)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[206, 57])).
% 0.20/0.57 tff(208,plain,
% 0.20/0.57 (~((~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))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[207, 205])).
% 0.20/0.58 tff(209,plain,
% 0.20/0.58 (((~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))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(210,plain,
% 0.20/0.58 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.20/0.58 tff(211,plain,
% 0.20/0.58 ((~((~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))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22)))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(212,plain,
% 0.20/0.58 (![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22)))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[211, 210, 202])).
% 0.20/0.58 tff(213,plain,
% 0.20/0.58 (((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22)))) | ((~member(A!21, equivalence_class(A!21, E!23, R!22))) | member(A!21, 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)))) | (~member(A!21, equivalence_class(A!21, E!23, R!22))) | member(A!21, equivalence_class(B!20, E!23, R!22)))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(214,plain,
% 0.20/0.58 ((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22)))) | ((~member(A!21, equivalence_class(A!21, E!23, R!22))) | member(A!21, equivalence_class(B!20, E!23, R!22)))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(215,plain,
% 0.20/0.58 ((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, equivalence_class(A!21, E!23, R!22))) | member(A!21, equivalence_class(B!20, E!23, R!22))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.58 tff(216,plain,
% 0.20/0.58 (member(A!21, equivalence_class(B!20, E!23, R!22))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[215, 212, 200])).
% 0.20/0.58 tff(217,plain,
% 0.20/0.58 ((((~member(A!21, E!23)) | (~apply(R!22, B!20, A!21))) <=> member(A!21, equivalence_class(B!20, E!23, R!22))) | (~((~member(A!21, E!23)) | (~apply(R!22, B!20, A!21)))) | (~member(A!21, equivalence_class(B!20, E!23, R!22)))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(218,plain,
% 0.20/0.58 (((~member(A!21, E!23)) | (~apply(R!22, B!20, A!21))) <=> member(A!21, equivalence_class(B!20, E!23, R!22))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[217, 216, 187])).
% 0.20/0.58 tff(219,plain,
% 0.20/0.58 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(A!21, E!23)) | (~apply(R!22, B!20, A!21))) <=> member(A!21, equivalence_class(B!20, E!23, R!22))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(220,plain,
% 0.20/0.58 ($false),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[219, 10, 218])).
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % E exiting
%------------------------------------------------------------------------------