%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET769+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.38s 0.63s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET769+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 05:41:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.38/0.63 % SZS status Theorem
% 0.38/0.63 % SZS output start Proof
% 0.38/0.63 tff(member_type, type, (
% 0.38/0.63 member: ( $i * $i ) > $o)).
% 0.38/0.63 tff(equivalence_class_type, type, (
% 0.38/0.63 equivalence_class: ( $i * $i * $i ) > $i)).
% 0.38/0.63 tff(tptp_fun_R_22_type, type, (
% 0.38/0.63 tptp_fun_R_22: $i)).
% 0.38/0.63 tff(tptp_fun_E_23_type, type, (
% 0.38/0.63 tptp_fun_E_23: $i)).
% 0.38/0.63 tff(tptp_fun_A_21_type, type, (
% 0.38/0.63 tptp_fun_A_21: $i)).
% 0.38/0.63 tff(tptp_fun_B_20_type, type, (
% 0.38/0.63 tptp_fun_B_20: $i)).
% 0.38/0.63 tff(apply_type, type, (
% 0.38/0.63 apply: ( $i * $i * $i ) > $o)).
% 0.38/0.63 tff(equivalence_type, type, (
% 0.38/0.63 equivalence: ( $i * $i ) > $o)).
% 0.38/0.63 tff(tptp_fun_Z_13_type, type, (
% 0.38/0.63 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.38/0.63 tff(tptp_fun_X_15_type, type, (
% 0.38/0.63 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.38/0.63 tff(tptp_fun_Y_14_type, type, (
% 0.38/0.63 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.38/0.63 tff(tptp_fun_X_12_type, type, (
% 0.38/0.63 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.38/0.63 tff(tptp_fun_Y_11_type, type, (
% 0.38/0.63 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.38/0.63 tff(tptp_fun_X_10_type, type, (
% 0.38/0.63 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.38/0.63 tff(equal_set_type, type, (
% 0.38/0.63 equal_set: ( $i * $i ) > $o)).
% 0.38/0.63 tff(disjoint_type, type, (
% 0.38/0.63 disjoint: ( $i * $i ) > $o)).
% 0.38/0.63 tff(subset_type, type, (
% 0.38/0.63 subset: ( $i * $i ) > $o)).
% 0.38/0.63 tff(tptp_fun_X_0_type, type, (
% 0.38/0.63 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.38/0.63 tff(tptp_fun_X_3_type, type, (
% 0.38/0.63 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.38/0.63 tff(1,plain,
% 0.38/0.63 (^[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)))))),
% 0.38/0.63 inference(bind,[status(th)],[])).
% 0.38/0.63 tff(2,plain,
% 0.38/0.63 (![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))))),
% 0.38/0.63 inference(quant_intro,[status(thm)],[1])).
% 0.38/0.63 tff(3,plain,
% 0.38/0.63 (^[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))))))),
% 0.38/0.63 inference(bind,[status(th)],[])).
% 0.38/0.63 tff(4,plain,
% 0.38/0.63 (![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))))),
% 0.38/0.63 inference(quant_intro,[status(thm)],[3])).
% 0.38/0.63 tff(5,plain,
% 0.38/0.63 (![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)))),
% 0.38/0.63 inference(rewrite,[status(thm)],[])).
% 0.38/0.63 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/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence_class')).
% 0.38/0.63 tff(7,plain,
% 0.38/0.63 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.38/0.63 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.38/0.63 tff(8,plain,(
% 0.38/0.63 ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.38/0.63 inference(skolemize,[status(sab)],[7])).
% 0.38/0.63 tff(9,plain,
% 0.38/0.63 (![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.38/0.63 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.38/0.63 tff(10,plain,
% 0.38/0.63 (![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))),
% 0.38/0.63 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.38/0.63 tff(11,plain,
% 0.38/0.63 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))) <=> member(B!20, equivalence_class(B!20, E!23, R!22))))),
% 0.38/0.63 inference(quant_inst,[status(thm)],[])).
% 0.38/0.63 tff(12,plain,
% 0.38/0.63 (~(((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))) <=> member(B!20, equivalence_class(B!20, E!23, R!22)))),
% 0.38/0.63 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.38/0.63 tff(13,plain,
% 0.38/0.63 (^[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)))))))))))),
% 0.38/0.63 inference(bind,[status(th)],[])).
% 0.38/0.63 tff(14,plain,
% 0.38/0.63 (![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))))))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[13])).
% 0.47/0.63 tff(15,plain,
% 0.47/0.63 (^[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)))))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(16,plain,
% 0.47/0.63 (![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))))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[15])).
% 0.47/0.63 tff(17,plain,
% 0.47/0.63 (^[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)))))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(18,plain,
% 0.47/0.63 (![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))))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[17])).
% 0.47/0.63 tff(19,plain,
% 0.47/0.63 (![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))))))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[18, 16])).
% 0.47/0.63 tff(20,plain,
% 0.47/0.63 (^[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))))))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(21,plain,
% 0.47/0.63 (![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))))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[20])).
% 0.47/0.63 tff(22,plain,
% 0.47/0.63 (^[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))))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(23,plain,
% 0.47/0.63 (![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)))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[22])).
% 0.47/0.63 tff(24,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(25,plain,
% 0.47/0.63 (^[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)))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(26,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[25])).
% 0.47/0.63 tff(27,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/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.47/0.63 tff(28,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.47/0.63 tff(29,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.47/0.63 tff(30,plain,(
% 0.47/0.63 ![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))))))))),
% 0.47/0.63 inference(skolemize,[status(sab)],[29])).
% 0.47/0.63 tff(31,plain,
% 0.47/0.63 (![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)))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.47/0.63 tff(32,plain,
% 0.47/0.63 (![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))))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.47/0.63 tff(33,plain,
% 0.47/0.63 (![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))))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[32, 19])).
% 0.47/0.64 tff(34,plain,
% 0.47/0.64 (![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))))))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[33, 14])).
% 0.47/0.64 tff(35,plain,
% 0.47/0.64 (((~![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)))))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(36,plain,
% 0.47/0.64 ((~((~(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))))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(37,plain,
% 0.47/0.64 (((~![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)))))))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[36])).
% 0.47/0.64 tff(38,plain,
% 0.47/0.64 (((~![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)))))))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[37, 35])).
% 0.47/0.64 tff(39,plain,
% 0.47/0.64 ((~![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))))))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(40,plain,
% 0.47/0.64 ((~![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))))))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.47/0.65 tff(41,plain,
% 0.47/0.65 (~((~(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)))))))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.47/0.65 tff(42,plain,
% 0.47/0.65 (((~(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)))))))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(43,plain,
% 0.47/0.65 ((~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))))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.47/0.65 tff(44,plain,
% 0.47/0.65 (((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> ((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(45,plain,
% 0.47/0.65 ((~((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))) <=> (~((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[44])).
% 0.47/0.65 tff(46,plain,
% 0.47/0.65 ((~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (~(disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)))))) <=> (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (~(disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(47,plain,
% 0.47/0.65 ((~![E: $i, R: $i, A: $i, B: $i] : (((equivalence(R, E) & member(A, E)) & member(B, E)) => (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))) <=> (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (~(disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(48,axiom,(~![E: $i, R: $i, A: $i, B: $i] : (((equivalence(R, E) & member(A, E)) & member(B, E)) => (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII05')).
% 0.47/0.65 tff(49,plain,
% 0.47/0.65 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (~(disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.47/0.65 tff(50,plain,
% 0.47/0.65 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (~(disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.47/0.65 tff(51,plain,
% 0.47/0.65 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (~(disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.47/0.65 tff(52,plain,
% 0.47/0.65 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (~(disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.47/0.65 tff(53,plain,(
% 0.47/0.65 ~((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.47/0.65 inference(skolemize,[status(sab)],[52])).
% 0.47/0.65 tff(54,plain,
% 0.47/0.65 (~((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[53, 45])).
% 0.47/0.65 tff(55,plain,
% 0.47/0.65 (equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23)),
% 0.47/0.65 inference(or_elim,[status(thm)],[54])).
% 0.47/0.65 tff(56,plain,
% 0.47/0.65 (equivalence(R!22, E!23)),
% 0.47/0.65 inference(and_elim,[status(thm)],[55])).
% 0.47/0.65 tff(57,plain,
% 0.47/0.65 ((~((~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))))))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(58,plain,
% 0.47/0.65 ((~((~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))))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.47/0.65 tff(59,plain,
% 0.47/0.65 (~((~![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)))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[58, 43])).
% 0.47/0.65 tff(60,plain,
% 0.47/0.65 (((~![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))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(61,plain,
% 0.47/0.65 (![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.47/0.65 tff(62,plain,
% 0.47/0.65 (member(B!20, E!23)),
% 0.47/0.65 inference(and_elim,[status(thm)],[55])).
% 0.47/0.65 tff(63,plain,
% 0.47/0.65 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | ((~member(B!20, E!23)) | apply(R!22, B!20, B!20))) <=> ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~member(B!20, E!23)) | apply(R!22, B!20, B!20))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(64,plain,
% 0.47/0.65 ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | ((~member(B!20, E!23)) | apply(R!22, B!20, B!20))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(65,plain,
% 0.47/0.65 ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~member(B!20, E!23)) | apply(R!22, B!20, B!20)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.47/0.65 tff(66,plain,
% 0.47/0.65 (apply(R!22, B!20, B!20)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[65, 62, 61])).
% 0.47/0.65 tff(67,plain,
% 0.47/0.65 ((~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))) | (~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(68,plain,
% 0.47/0.65 (~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[67, 62, 66])).
% 0.47/0.65 tff(69,plain,
% 0.47/0.65 ((((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))) <=> member(B!20, equivalence_class(B!20, E!23, R!22))) | ((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))) | member(B!20, equivalence_class(B!20, E!23, R!22))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(70,plain,
% 0.47/0.65 ((((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))) <=> member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(B!20, E!23, R!22))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.47/0.65 tff(71,plain,
% 0.47/0.65 (member(B!20, equivalence_class(B!20, E!23, R!22))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[70, 12])).
% 0.47/0.65 tff(72,plain,
% 0.47/0.65 (^[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))))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(73,plain,
% 0.47/0.65 (![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)))))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[72])).
% 0.47/0.65 tff(74,plain,
% 0.47/0.65 (^[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))))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(75,plain,
% 0.47/0.65 (![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)))))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[74])).
% 0.47/0.65 tff(76,plain,
% 0.47/0.65 (![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)))))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[75, 73])).
% 0.47/0.65 tff(77,plain,
% 0.47/0.65 (^[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)))))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(78,plain,
% 0.47/0.65 (![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)))))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[77])).
% 0.47/0.65 tff(79,plain,
% 0.47/0.65 (![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)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(80,plain,
% 0.47/0.65 (^[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))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(81,plain,
% 0.47/0.65 (![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)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[80])).
% 0.47/0.65 tff(82,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.47/0.65 tff(83,plain,
% 0.47/0.65 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.47/0.65 tff(84,plain,
% 0.47/0.65 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.47/0.65 tff(85,plain,(
% 0.47/0.65 ![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)))))),
% 0.47/0.65 inference(skolemize,[status(sab)],[84])).
% 0.47/0.65 tff(86,plain,
% 0.47/0.65 (![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)))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.47/0.65 tff(87,plain,
% 0.47/0.65 (![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)))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.47/0.65 tff(88,plain,
% 0.47/0.65 ((~![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))))))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(89,plain,
% 0.47/0.65 (~((~((~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)))))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.47/0.65 tff(90,plain,
% 0.47/0.65 (((~((~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))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(91,plain,
% 0.47/0.65 ((~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)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.47/0.65 tff(92,plain,
% 0.47/0.65 ((~![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))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(93,plain,
% 0.47/0.65 (~(((~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)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[92, 10])).
% 0.47/0.65 tff(94,plain,
% 0.47/0.65 (((~((~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)))))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(95,plain,
% 0.47/0.65 (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))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[94, 89])).
% 0.47/0.65 tff(96,assumption,(~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))), introduced(assumption)).
% 0.47/0.65 tff(97,plain,
% 0.47/0.65 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.47/0.65 inference(or_elim,[status(thm)],[54])).
% 0.47/0.65 tff(98,plain,
% 0.47/0.65 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(99,plain,
% 0.47/0.65 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.47/0.65 tff(100,plain,
% 0.47/0.65 (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.47/0.65 tff(101,plain,
% 0.47/0.65 (^[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))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(102,plain,
% 0.47/0.65 (![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)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[101])).
% 0.47/0.66 tff(103,plain,
% 0.47/0.66 (^[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)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(104,plain,
% 0.47/0.66 (![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)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[103])).
% 0.47/0.66 tff(105,plain,
% 0.47/0.66 (![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)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(106,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.47/0.66 tff(107,plain,
% 0.47/0.66 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.47/0.66 tff(108,plain,(
% 0.47/0.66 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[107])).
% 0.47/0.66 tff(109,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.47/0.66 tff(110,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.47/0.66 tff(111,plain,
% 0.47/0.66 ((~![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))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(112,plain,
% 0.47/0.66 (~(((~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)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.47/0.66 tff(113,plain,
% 0.47/0.66 ((((~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))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(114,plain,
% 0.47/0.66 (((~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))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.47/0.66 tff(115,plain,
% 0.47/0.66 ((~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)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[114, 100])).
% 0.47/0.66 tff(116,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)).
% 0.47/0.66 tff(117,plain,
% 0.47/0.66 ((~![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: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(118,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[117, 87, 116])).
% 0.47/0.66 tff(119,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,[]))).
% 0.47/0.66 tff(120,plain,
% 0.47/0.66 (((~((~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)))))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(121,plain,
% 0.47/0.66 (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))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.47/0.66 tff(122,plain,
% 0.47/0.66 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(123,plain,
% 0.47/0.66 (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[122, 10])).
% 0.47/0.66 tff(124,plain,
% 0.47/0.66 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(125,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[124])).
% 0.47/0.66 tff(126,plain,
% 0.47/0.66 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(127,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[126])).
% 0.47/0.66 tff(128,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[127, 125])).
% 0.47/0.66 tff(129,plain,
% 0.47/0.66 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) <=> (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))), ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))), rewrite((disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))), ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((~(member(X, A) & member(X, B))) <=> (~(~((~member(X, A)) | (~member(X, B))))))), rewrite((~(~((~member(X, A)) | (~member(X, B))))) <=> ((~member(X, A)) | (~member(X, B)))), ((~(member(X, A) & member(X, B))) <=> ((~member(X, A)) | (~member(X, B)))))), (![X: $i] : (~(member(X, A) & member(X, B))) <=> ![X: $i] : ((~member(X, A)) | (~member(X, B))))), ((![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))) <=> (![X: $i] : ((~member(X, A)) | (~member(X, B))) | (~disjoint(A, B))))), rewrite((![X: $i] : ((~member(X, A)) | (~member(X, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))), ((![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))), (((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))) & ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))))), rewrite(((disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))) & ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))), (((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(130,plain,
% 0.47/0.66 (![A: $i, B: $i] : ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[129])).
% 0.47/0.66 tff(131,plain,
% 0.47/0.66 (^[A: $i, B: $i] : rewrite((((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) | disjoint(A, B)) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(132,plain,
% 0.47/0.66 (![A: $i, B: $i] : (((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) | disjoint(A, B)) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[131])).
% 0.47/0.66 tff(133,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B))) <=> ![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(134,plain,
% 0.47/0.66 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((~?[X: $i] : (member(X, A) & member(X, B))) <=> (~?[X: $i] : (member(X, A) & member(X, B)))), ((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))))), rewrite((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))), ((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B))))), rewrite((~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))), ((disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(135,plain,
% 0.47/0.66 (![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> ![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[134])).
% 0.47/0.66 tff(136,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','disjoint')).
% 0.47/0.66 tff(137,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.47/0.66 tff(138,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~(?[X: $i] : (member(X, A) & member(X, B)) <=> disjoint(A, B)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.47/0.66 tff(139,plain,(
% 0.47/0.66 ![A: $i, B: $i] : (((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) | disjoint(A, B)) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))))),
% 0.47/0.66 inference(skolemize,[status(sab)],[138])).
% 0.47/0.66 tff(140,plain,
% 0.47/0.66 (![A: $i, B: $i] : ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) & (![X: $i] : (~(member(X, A) & member(X, B))) | (~disjoint(A, B))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.47/0.66 tff(141,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.47/0.66 tff(142,plain,
% 0.47/0.66 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[141, 128])).
% 0.47/0.66 tff(143,plain,
% 0.47/0.66 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(144,plain,
% 0.47/0.66 ((~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))))) <=> (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(145,plain,
% 0.47/0.66 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[144])).
% 0.47/0.66 tff(146,plain,
% 0.47/0.66 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[145, 143])).
% 0.47/0.66 tff(147,plain,
% 0.47/0.66 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(148,plain,
% 0.47/0.67 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) | (~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.47/0.67 tff(149,plain,
% 0.47/0.67 (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[148, 142])).
% 0.47/0.67 tff(150,plain,
% 0.47/0.67 (((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))) | (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(151,plain,
% 0.47/0.67 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.47/0.67 tff(152,plain,
% 0.47/0.67 ((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(153,plain,
% 0.47/0.67 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.47/0.67 tff(154,plain,
% 0.47/0.67 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[153, 96])).
% 0.47/0.67 tff(155,plain,
% 0.47/0.67 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(156,plain,
% 0.47/0.67 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.47/0.67 tff(157,plain,
% 0.47/0.67 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(158,plain,
% 0.47/0.67 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.47/0.67 tff(159,plain,
% 0.47/0.67 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[158, 123])).
% 0.47/0.67 tff(160,plain,
% 0.47/0.67 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(161,plain,
% 0.47/0.67 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.47/0.67 tff(162,plain,
% 0.47/0.67 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(163,plain,
% 0.47/0.67 (apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.47/0.67 tff(164,plain,
% 0.47/0.67 ((~![R: $i, E: $i, A: $i, X: $i] : (~(((~member(X, E)) | (~apply(R, A, X))) <=> member(X, equivalence_class(A, E, R))))) | (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(165,plain,
% 0.47/0.67 (~(((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[164, 10])).
% 0.47/0.67 tff(166,plain,
% 0.47/0.67 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(167,plain,
% 0.47/0.67 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[166, 154])).
% 0.47/0.67 tff(168,plain,
% 0.47/0.67 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(169,plain,
% 0.47/0.67 ((((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) <=> member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.47/0.67 tff(170,plain,
% 0.47/0.67 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[169, 165])).
% 0.47/0.67 tff(171,plain,
% 0.47/0.67 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(172,plain,
% 0.47/0.67 (apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.47/0.67 tff(173,plain,
% 0.47/0.67 (((~![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))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(174,plain,
% 0.47/0.67 (![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[173, 59])).
% 0.47/0.67 tff(175,plain,
% 0.47/0.67 (member(A!21, E!23)),
% 0.47/0.67 inference(and_elim,[status(thm)],[55])).
% 0.47/0.67 tff(176,plain,
% 0.47/0.67 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(177,plain,
% 0.47/0.67 (((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) <=> ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(178,plain,
% 0.47/0.67 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[177])).
% 0.47/0.67 tff(179,plain,
% 0.47/0.67 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.47/0.68 inference(transitivity,[status(thm)],[178, 176])).
% 0.47/0.68 tff(180,plain,
% 0.47/0.68 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(181,plain,
% 0.47/0.68 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.47/0.68 tff(182,plain,
% 0.47/0.68 (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[181, 175, 174, 161, 172])).
% 0.47/0.68 tff(183,plain,
% 0.47/0.68 ((~![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))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(184,plain,
% 0.47/0.68 (~(((~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)))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[183, 10])).
% 0.47/0.68 tff(185,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)).
% 0.47/0.68 tff(186,plain,
% 0.47/0.68 (((~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)))),
% 0.47/0.68 inference(tautology,[status(thm)],[])).
% 0.47/0.68 tff(187,plain,
% 0.47/0.68 (~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))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.47/0.68 tff(188,plain,
% 0.47/0.68 ((((~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))),
% 0.47/0.68 inference(tautology,[status(thm)],[])).
% 0.47/0.68 tff(189,plain,
% 0.47/0.68 ((((~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)))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.47/0.68 tff(190,plain,
% 0.47/0.68 ((~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))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[189, 184])).
% 0.47/0.68 tff(191,plain,
% 0.47/0.68 ((~![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))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(192,plain,
% 0.47/0.68 (~(((~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)))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[191, 10])).
% 0.47/0.68 tff(193,plain,
% 0.47/0.68 (((~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))),
% 0.47/0.68 inference(tautology,[status(thm)],[])).
% 0.47/0.68 tff(194,plain,
% 0.47/0.68 (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))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[193, 185])).
% 0.47/0.68 tff(195,plain,
% 0.47/0.68 ((((~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)))),
% 0.47/0.68 inference(tautology,[status(thm)],[])).
% 0.47/0.68 tff(196,plain,
% 0.47/0.68 ((((~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))))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.47/0.68 tff(197,plain,
% 0.47/0.68 (~((~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)))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[196, 192])).
% 0.47/0.68 tff(198,plain,
% 0.47/0.68 (((~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)),
% 0.47/0.68 inference(tautology,[status(thm)],[])).
% 0.47/0.68 tff(199,plain,
% 0.47/0.68 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.47/0.68 tff(200,plain,
% 0.47/0.68 ((~((~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))))),
% 0.47/0.68 inference(tautology,[status(thm)],[])).
% 0.47/0.68 tff(201,plain,
% 0.47/0.68 (~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)))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[200, 199, 190])).
% 0.47/0.68 tff(202,assumption,(apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))), introduced(assumption)).
% 0.47/0.68 tff(203,assumption,(member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)), introduced(assumption)).
% 0.47/0.68 tff(204,plain,
% 0.47/0.68 (((~![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)))),
% 0.47/0.68 inference(tautology,[status(thm)],[])).
% 0.47/0.68 tff(205,plain,
% 0.47/0.68 (![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)))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[204, 59])).
% 0.47/0.68 tff(206,plain,
% 0.47/0.68 (((~![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(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(207,plain,
% 0.47/0.68 ((apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23))) <=> ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(208,plain,
% 0.47/0.68 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[207])).
% 0.47/0.68 tff(209,plain,
% 0.47/0.68 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[208, 206])).
% 0.47/0.69 tff(210,plain,
% 0.47/0.69 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(211,plain,
% 0.47/0.69 ((~![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(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.47/0.69 tff(212,plain,
% 0.47/0.69 (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[211, 62, 205, 203, 202, 199, 201])).
% 0.47/0.69 tff(213,plain,
% 0.47/0.69 (((~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)))),
% 0.47/0.69 inference(tautology,[status(thm)],[])).
% 0.47/0.69 tff(214,plain,
% 0.47/0.69 (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)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[213, 197])).
% 0.47/0.69 tff(215,assumption,(apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)), introduced(assumption)).
% 0.47/0.69 tff(216,plain,
% 0.47/0.69 (((~![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(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(217,plain,
% 0.47/0.69 ((apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23))) <=> ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(218,plain,
% 0.47/0.69 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[217])).
% 0.53/0.69 tff(219,plain,
% 0.53/0.69 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.53/0.69 inference(transitivity,[status(thm)],[218, 216])).
% 0.53/0.69 tff(220,plain,
% 0.53/0.69 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))),
% 0.53/0.69 inference(quant_inst,[status(thm)],[])).
% 0.53/0.69 tff(221,plain,
% 0.53/0.69 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.53/0.69 tff(222,plain,
% 0.53/0.69 ($false),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[221, 175, 205, 203, 215, 199, 214, 212])).
% 0.53/0.69 tff(223,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))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.69 tff(224,plain,
% 0.53/0.69 ((~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))),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[223, 182, 163, 161])).
% 0.53/0.69 tff(225,plain,
% 0.53/0.69 ((~(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))))),
% 0.53/0.69 inference(tautology,[status(thm)],[])).
% 0.53/0.69 tff(226,plain,
% 0.53/0.69 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[225, 224, 121])).
% 0.53/0.69 tff(227,plain,
% 0.53/0.69 ((~((~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)))),
% 0.53/0.69 inference(tautology,[status(thm)],[])).
% 0.53/0.69 tff(228,plain,
% 0.53/0.69 (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[227, 226, 115])).
% 0.53/0.69 tff(229,plain,
% 0.53/0.69 ((~(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))))),
% 0.53/0.69 inference(tautology,[status(thm)],[])).
% 0.53/0.69 tff(230,plain,
% 0.53/0.69 ((~(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))))),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.53/0.69 tff(231,plain,
% 0.53/0.69 (~((~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)))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[230, 95])).
% 0.53/0.70 tff(232,plain,
% 0.53/0.70 (((~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)))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(233,plain,
% 0.53/0.70 (~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))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.53/0.70 tff(234,plain,
% 0.53/0.70 ((((~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))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(235,plain,
% 0.53/0.70 ((((~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)))))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.53/0.70 tff(236,plain,
% 0.53/0.70 ((~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))))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[235, 93])).
% 0.53/0.70 tff(237,plain,
% 0.53/0.70 ((~![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))))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(238,plain,
% 0.53/0.70 (~(((~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)))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[237, 10])).
% 0.53/0.70 tff(239,plain,
% 0.53/0.70 (((~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))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(240,plain,
% 0.53/0.70 (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))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[239, 231])).
% 0.53/0.70 tff(241,plain,
% 0.53/0.70 ((((~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)))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(242,plain,
% 0.53/0.70 ((((~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))))))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.53/0.70 tff(243,plain,
% 0.53/0.70 (~((~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)))))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[242, 238])).
% 0.53/0.70 tff(244,plain,
% 0.53/0.70 (((~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)),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(245,plain,
% 0.53/0.70 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.53/0.70 tff(246,plain,
% 0.53/0.70 ((~((~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))))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(247,plain,
% 0.53/0.70 (~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)))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[246, 245, 236])).
% 0.53/0.70 tff(248,plain,
% 0.53/0.70 (((~![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(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(249,plain,
% 0.53/0.70 ((apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23))) <=> ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(250,plain,
% 0.53/0.70 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[249])).
% 0.53/0.70 tff(251,plain,
% 0.53/0.70 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.53/0.70 inference(transitivity,[status(thm)],[250, 248])).
% 0.53/0.70 tff(252,plain,
% 0.53/0.70 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(253,plain,
% 0.53/0.70 ((~![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(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.53/0.70 tff(254,plain,
% 0.53/0.70 (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[253, 175, 205, 161, 172, 245, 247])).
% 0.53/0.70 tff(255,plain,
% 0.53/0.70 (((~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)))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(256,plain,
% 0.53/0.70 (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)))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[255, 243])).
% 0.53/0.71 tff(257,plain,
% 0.53/0.71 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(258,plain,
% 0.53/0.71 (((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) <=> ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(259,plain,
% 0.53/0.71 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[258])).
% 0.53/0.71 tff(260,plain,
% 0.53/0.71 (((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))) <=> ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.53/0.71 inference(transitivity,[status(thm)],[259, 257])).
% 0.53/0.71 tff(261,plain,
% 0.53/0.71 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | ((~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(262,plain,
% 0.53/0.71 ((~![X: $i, Y: $i] : ((~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R!22, Y, X))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.53/0.71 tff(263,plain,
% 0.53/0.71 (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[262, 62, 174, 161, 163])).
% 0.53/0.71 tff(264,plain,
% 0.53/0.71 (((~![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(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(265,plain,
% 0.53/0.71 ((apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23))) <=> ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(266,plain,
% 0.53/0.71 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[265])).
% 0.53/0.71 tff(267,plain,
% 0.53/0.71 (((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.53/0.71 inference(transitivity,[status(thm)],[266, 264])).
% 0.53/0.71 tff(268,plain,
% 0.53/0.71 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(269,plain,
% 0.53/0.71 ((~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.53/0.71 tff(270,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[269, 62, 205, 161, 263, 245, 256, 254])).
% 0.53/0.71 tff(271,plain,(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(272,plain,
% 0.53/0.71 ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(273,plain,
% 0.53/0.71 ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[272, 97])).
% 0.53/0.71 tff(274,plain,
% 0.53/0.71 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[273, 271])).
% 0.53/0.71 tff(275,plain,
% 0.53/0.71 ((((~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)))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(276,plain,
% 0.53/0.71 ((~((~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)))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[275, 112])).
% 0.53/0.71 tff(277,plain,
% 0.53/0.71 (~((~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))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[276, 274])).
% 0.53/0.71 tff(278,plain,
% 0.53/0.71 (((~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(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(279,plain,
% 0.53/0.71 (subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.53/0.71 tff(280,plain,
% 0.53/0.71 ((~((~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))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(281,plain,
% 0.53/0.71 ((~((~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))))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.53/0.71 tff(282,plain,
% 0.53/0.71 (![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[281, 91])).
% 0.53/0.71 tff(283,plain,
% 0.53/0.71 (((~![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))) | ((~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, 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)))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(A!21, E!23, R!22)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(284,plain,
% 0.53/0.71 ((~![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))) | ((~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(A!21, E!23, R!22)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(285,plain,
% 0.53/0.71 ((~![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(A!21, E!23, R!22))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.53/0.71 tff(286,plain,
% 0.53/0.71 (member(B!20, equivalence_class(A!21, E!23, R!22))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[285, 282, 71])).
% 0.53/0.71 tff(287,plain,
% 0.53/0.71 (((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))) | ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(288,plain,
% 0.53/0.71 ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[287, 149])).
% 0.53/0.71 tff(289,plain,
% 0.53/0.71 ((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(290,plain,
% 0.53/0.71 ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.53/0.71 tff(291,plain,
% 0.53/0.71 (![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[290, 271])).
% 0.53/0.71 tff(292,plain,
% 0.53/0.71 (((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))) | ((~member(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, 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(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(293,plain,
% 0.53/0.72 ((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))) | ((~member(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(294,plain,
% 0.53/0.72 ((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))) | (~member(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, equivalence_class(B!20, E!23, R!22)))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.53/0.72 tff(295,plain,
% 0.53/0.72 ($false),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[294, 291, 71, 286])).
% 0.53/0.72 % SZS output end Proof
% 0.53/0.72 % E exiting
%------------------------------------------------------------------------------