%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET772+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:26:19 AM UTC 2025
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SET772+4 : TPTP v9.0.0. Released v2.2.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:41:54 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(member_type, type, (
% 0.22/0.42 member: ( $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_Z_23_type, type, (
% 0.22/0.42 tptp_fun_Z_23: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_Y_14_type, type, (
% 0.22/0.42 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_E_21_type, type, (
% 0.22/0.42 tptp_fun_E_21: $i)).
% 0.22/0.42 tff(tptp_fun_R_20_type, type, (
% 0.22/0.42 tptp_fun_R_20: $i)).
% 0.22/0.42 tff(tptp_fun_Z_13_type, type, (
% 0.22/0.42 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_X_15_type, type, (
% 0.22/0.42 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_A_22_type, type, (
% 0.22/0.42 tptp_fun_A_22: $i)).
% 0.22/0.42 tff(apply_type, type, (
% 0.22/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_X_10_type, type, (
% 0.22/0.42 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_Y_4_type, type, (
% 0.22/0.42 tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.22/0.42 tff(subset_type, type, (
% 0.22/0.42 subset: ( $i * $i ) > $o)).
% 0.22/0.42 tff(partition_type, type, (
% 0.22/0.42 partition: ( $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_Y_7_type, type, (
% 0.22/0.42 tptp_fun_Y_7: $i > $i)).
% 0.22/0.42 tff(tptp_fun_X_8_type, type, (
% 0.22/0.42 tptp_fun_X_8: $i > $i)).
% 0.22/0.42 tff(tptp_fun_Z_9_type, type, (
% 0.22/0.42 tptp_fun_Z_9: $i > $i)).
% 0.22/0.42 tff(tptp_fun_X_5_type, type, (
% 0.22/0.42 tptp_fun_X_5: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_X_6_type, type, (
% 0.22/0.42 tptp_fun_X_6: ( $i * $i ) > $i)).
% 0.22/0.42 tff(equivalence_type, type, (
% 0.22/0.42 equivalence: ( $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_X_12_type, type, (
% 0.22/0.42 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_Y_11_type, type, (
% 0.22/0.42 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.22/0.42 tff(1,assumption,(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))), introduced(assumption)).
% 0.22/0.42 tff(2,plain,
% 0.22/0.42 (member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21))) <=> member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.22/0.42 tff(3,plain,
% 0.22/0.42 (member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) <=> member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))),
% 0.22/0.42 inference(symmetry,[status(thm)],[2])).
% 0.22/0.42 tff(4,plain,
% 0.22/0.42 ((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) <=> (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.22/0.42 tff(5,assumption,(~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))), introduced(assumption)).
% 0.22/0.42 tff(6,plain,
% 0.22/0.42 (((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | member(tptp_fun_X_10(R!20, E!21), E!21)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 (member(tptp_fun_X_10(R!20, E!21), E!21)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.22/0.42 tff(8,plain,
% 0.22/0.42 (^[A: $i, E: $i] : rewrite((~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(9,plain,
% 0.22/0.42 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.22/0.42 tff(10,plain,
% 0.22/0.42 (^[A: $i, E: $i] : refl((~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(11,plain,
% 0.22/0.42 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.42 tff(12,plain,
% 0.22/0.42 (^[A: $i, E: $i] : rewrite((~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(13,plain,
% 0.22/0.42 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.42 tff(14,plain,
% 0.22/0.42 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[13, 11])).
% 0.22/0.42 tff(15,plain,
% 0.22/0.42 (^[A: $i, E: $i] : trans(monotonicity(rewrite(((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) <=> ((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, A) & member(tptp_fun_X_6(E, A), Y)) <=> (~((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))), ((~(member(Y, A) & member(tptp_fun_X_6(E, A), Y))) <=> (~(~((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))), rewrite((~(~((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))) <=> ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))), ((~(member(Y, A) & member(tptp_fun_X_6(E, A), Y))) <=> ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))), (![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y))) <=> ![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))), ((member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) <=> (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))), rewrite((member(tptp_fun_X_6(E, A), E) & ![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))) <=> (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))), ((member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) <=> (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))))), rewrite(((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))) <=> (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))), ((partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))) <=> (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))), rewrite((partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))) <=> (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))), ((partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))) <=> (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))), ((((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) <=> (((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y)))))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))))), rewrite((((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y)))))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))), ((((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) <=> (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(16,plain,
% 0.22/0.43 (![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) <=> ![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 (^[A: $i, E: $i] : rewrite((((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | ((~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & (member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A)) & (member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))) <=> (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(18,plain,
% 0.22/0.43 (![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | ((~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & (member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A)) & (member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))))) <=> ![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 (![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y)))))) <=> ![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(20,plain,
% 0.22/0.43 (^[A: $i, E: $i] : rewrite((partition(A, E) <=> ((![X: $i] : (member(X, A) => subset(X, E)) & ![X: $i] : (member(X, E) => ?[Y: $i] : (member(Y, A) & member(X, Y)))) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (?[Z: $i] : (member(Z, X) & member(Z, Y)) => (X = Y))))) <=> (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y)))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(21,plain,
% 0.22/0.43 (![A: $i, E: $i] : (partition(A, E) <=> ((![X: $i] : (member(X, A) => subset(X, E)) & ![X: $i] : (member(X, E) => ?[Y: $i] : (member(Y, A) & member(X, Y)))) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (?[Z: $i] : (member(Z, X) & member(Z, Y)) => (X = Y))))) <=> ![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.43 tff(22,axiom,(![A: $i, E: $i] : (partition(A, E) <=> ((![X: $i] : (member(X, A) => subset(X, E)) & ![X: $i] : (member(X, E) => ?[Y: $i] : (member(Y, A) & member(X, Y)))) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (?[Z: $i] : (member(Z, X) & member(Z, Y)) => (X = Y)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','partition')).
% 0.22/0.43 tff(23,plain,
% 0.22/0.43 (![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.22/0.43 tff(24,plain,
% 0.22/0.43 (![A: $i, E: $i] : (partition(A, E) <=> (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | ?[Y: $i] : (member(Y, A) & member(X, Y))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | (~?[Z: $i] : (member(Z, X) & member(Z, Y))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.22/0.43 tff(25,plain,(
% 0.22/0.43 ![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | ((~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & (member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A)) & (member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[24])).
% 0.22/0.43 tff(26,plain,
% 0.22/0.43 (![A: $i, E: $i] : (((~partition(A, E)) | (![X: $i] : ((~member(X, A)) | subset(X, E)) & ![X: $i] : ((~member(X, E)) | (member(tptp_fun_Y_4(X, A), A) & member(X, tptp_fun_Y_4(X, A)))) & ![X: $i, Y: $i] : ((X = Y) | (~(member(X, A) & member(Y, A))) | ![Z: $i] : (~(member(Z, X) & member(Z, Y)))))) & (partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (member(tptp_fun_X_6(E, A), E) & ![Y: $i] : (~(member(Y, A) & member(tptp_fun_X_6(E, A), Y)))) | ((~(tptp_fun_X_8(A) = tptp_fun_Y_7(A))) & member(tptp_fun_X_8(A), A) & member(tptp_fun_Y_7(A), A) & member(tptp_fun_Z_9(A), tptp_fun_X_8(A)) & member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.22/0.43 tff(27,plain,
% 0.22/0.43 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.22/0.43 tff(28,plain,
% 0.22/0.43 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y)))))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A)))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[27, 14])).
% 0.22/0.43 tff(29,plain,
% 0.22/0.43 (![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[28, 9])).
% 0.22/0.43 tff(30,plain,
% 0.22/0.43 (((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22))))))))) <=> ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(31,plain,
% 0.22/0.43 ((~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A!22)) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))))) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))))))) <=> (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22))))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A!22)) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))))) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y))))))))))) <=> ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)))))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[31])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 (((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A!22)) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))))) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y))))))))))) <=> ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[32, 30])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A!22)) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))))) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y))))))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(35,plain,
% 0.23/0.44 ((~![A: $i, E: $i] : (~((~((~partition(A, E)) | (~((~![X: $i] : ((~member(X, A)) | subset(X, E))) | (~![X: $i] : ((~member(X, E)) | (~((~member(tptp_fun_Y_4(X, A), A)) | (~member(X, tptp_fun_Y_4(X, A))))))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(X, A)) | (~member(Y, A)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))))))))) | (~(partition(A, E) | (~((~member(tptp_fun_X_5(E, A), A)) | subset(tptp_fun_X_5(E, A), E))) | (~((tptp_fun_X_8(A) = tptp_fun_Y_7(A)) | (~member(tptp_fun_X_8(A), A)) | (~member(tptp_fun_Y_7(A), A)) | (~member(tptp_fun_Z_9(A), tptp_fun_X_8(A))) | (~member(tptp_fun_Z_9(A), tptp_fun_Y_7(A))))) | (~((~member(tptp_fun_X_6(E, A), E)) | (~![Y: $i] : ((~member(Y, A)) | (~member(tptp_fun_X_6(E, A), Y))))))))))) | (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.44 tff(36,plain,
% 0.23/0.44 (~((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22)))))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[35, 29])).
% 0.23/0.44 tff(37,plain,
% 0.23/0.44 (((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~(partition(A!22, E!21) | (~((~member(tptp_fun_X_6(E!21, A!22), E!21)) | (~![Y: $i] : ((~member(Y, A!22)) | (~member(tptp_fun_X_6(E!21, A!22), Y)))))) | (~((~member(tptp_fun_X_5(E!21, A!22), A!22)) | subset(tptp_fun_X_5(E!21, A!22), E!21))) | (~((~member(tptp_fun_Z_9(A!22), tptp_fun_Y_7(A!22))) | (~member(tptp_fun_Z_9(A!22), tptp_fun_X_8(A!22))) | (~member(tptp_fun_Y_7(A!22), A!22)) | (~member(tptp_fun_X_8(A!22), A!22)) | (tptp_fun_X_8(A!22) = tptp_fun_Y_7(A!22))))))) | ((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(38,plain,
% 0.23/0.45 ((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.23/0.45 tff(39,plain,
% 0.23/0.45 (((~equivalence(R!20, E!21)) & ![X: $i, Y: $i] : ((~(member(X, E!21) & member(Y, E!21))) | (((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z)))))) & partition(A!22, E!21)) <=> ((~equivalence(R!20, E!21)) & ![X: $i, Y: $i] : ((~(member(X, E!21) & member(Y, E!21))) | (((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z)))))) & partition(A!22, E!21))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(40,plain,
% 0.23/0.45 ((~![A: $i, E: $i, R: $i] : (equivalence(R, E) | (~![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (apply(R, X, Y) <=> ?[Z: $i] : (member(Z, A) & member(X, Z) & member(Y, Z))))) | (~partition(A, E)))) <=> (~![A: $i, E: $i, R: $i] : (equivalence(R, E) | (~![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (apply(R, X, Y) <=> ?[Z: $i] : (member(Z, A) & member(X, Z) & member(Y, Z))))) | (~partition(A, E))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(41,plain,
% 0.23/0.45 ((~![A: $i, E: $i, R: $i] : (partition(A, E) => (![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (apply(R, X, Y) <=> ?[Z: $i] : ((member(Z, A) & member(X, Z)) & member(Y, Z)))) => equivalence(R, E)))) <=> (~![A: $i, E: $i, R: $i] : (equivalence(R, E) | (~![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (apply(R, X, Y) <=> ?[Z: $i] : (member(Z, A) & member(X, Z) & member(Y, Z))))) | (~partition(A, E))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(42,axiom,(~![A: $i, E: $i, R: $i] : (partition(A, E) => (![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (apply(R, X, Y) <=> ?[Z: $i] : ((member(Z, A) & member(X, Z)) & member(Y, Z)))) => equivalence(R, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII08')).
% 0.23/0.45 tff(43,plain,
% 0.23/0.45 (~![A: $i, E: $i, R: $i] : (equivalence(R, E) | (~![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (apply(R, X, Y) <=> ?[Z: $i] : (member(Z, A) & member(X, Z) & member(Y, Z))))) | (~partition(A, E)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.23/0.45 tff(44,plain,
% 0.23/0.45 (~![A: $i, E: $i, R: $i] : (equivalence(R, E) | (~![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (apply(R, X, Y) <=> ?[Z: $i] : (member(Z, A) & member(X, Z) & member(Y, Z))))) | (~partition(A, E)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.23/0.45 tff(45,plain,
% 0.23/0.45 (~![A: $i, E: $i, R: $i] : (equivalence(R, E) | (~![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (apply(R, X, Y) <=> ?[Z: $i] : (member(Z, A) & member(X, Z) & member(Y, Z))))) | (~partition(A, E)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.23/0.45 tff(46,plain,
% 0.23/0.45 (~![A: $i, E: $i, R: $i] : (equivalence(R, E) | (~![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (apply(R, X, Y) <=> ?[Z: $i] : (member(Z, A) & member(X, Z) & member(Y, Z))))) | (~partition(A, E)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.23/0.45 tff(47,plain,
% 0.23/0.45 ((~equivalence(R!20, E!21)) & ![X: $i, Y: $i] : ((~(member(X, E!21) & member(Y, E!21))) | (((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z)))))) & partition(A!22, E!21)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.23/0.45 tff(48,plain,
% 0.23/0.45 (partition(A!22, E!21)),
% 0.23/0.45 inference(and_elim,[status(thm)],[47])).
% 0.23/0.45 tff(49,plain,
% 0.23/0.45 ((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22))))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(50,plain,
% 0.23/0.45 ((~((~partition(A!22, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))))) | (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.23/0.45 tff(51,plain,
% 0.23/0.45 (~((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[50, 38])).
% 0.23/0.45 tff(52,plain,
% 0.23/0.45 (((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22))))) | ![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(53,plain,
% 0.23/0.45 (![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.23/0.45 tff(54,plain,
% 0.23/0.45 (((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))))))) <=> ((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(55,plain,
% 0.23/0.45 ((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(56,plain,
% 0.23/0.45 ((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22)))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.23/0.45 tff(57,plain,
% 0.23/0.45 (~((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[56, 53, 7])).
% 0.23/0.45 tff(58,plain,
% 0.23/0.45 (((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22)))) | member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(59,plain,
% 0.23/0.45 (member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.23/0.45 tff(60,plain,
% 0.23/0.45 (((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22)))) | member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(61,plain,
% 0.23/0.45 (member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.23/0.45 tff(62,plain,
% 0.23/0.45 (^[X: $i, Y: $i] : refl(((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))) <=> ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(63,plain,
% 0.23/0.45 (![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))) <=> ![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[62])).
% 0.23/0.45 tff(64,plain,
% 0.23/0.45 (^[X: $i, Y: $i] : rewrite(((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))) <=> ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(65,plain,
% 0.23/0.45 (![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))) <=> ![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.23/0.46 tff(66,plain,
% 0.23/0.46 (![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))) <=> ![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[65, 63])).
% 0.23/0.46 tff(67,plain,
% 0.23/0.46 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, E!21) & member(Y, E!21)) <=> (~((~member(X, E!21)) | (~member(Y, E!21))))), ((~(member(X, E!21) & member(Y, E!21))) <=> (~(~((~member(X, E!21)) | (~member(Y, E!21))))))), rewrite((~(~((~member(X, E!21)) | (~member(Y, E!21))))) <=> ((~member(X, E!21)) | (~member(Y, E!21)))), ((~(member(X, E!21) & member(Y, E!21))) <=> ((~member(X, E!21)) | (~member(Y, E!21))))), trans(monotonicity(rewrite(((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) <=> ((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))), rewrite((apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z)))) <=> (apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))), ((((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z))))) <=> (((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X)))))) & (apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))), rewrite((((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X)))))) & (apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))) <=> (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))), ((((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z))))) <=> (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))), (((~(member(X, E!21) & member(Y, E!21))) | (((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z)))))) <=> (((~member(X, E!21)) | (~member(Y, E!21))) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))))), rewrite((((~member(X, E!21)) | (~member(Y, E!21))) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z)))))))) <=> ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))), (((~(member(X, E!21) & member(Y, E!21))) | (((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z)))))) <=> ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(68,plain,
% 0.23/0.46 (![X: $i, Y: $i] : ((~(member(X, E!21) & member(Y, E!21))) | (((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z)))))) <=> ![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[67])).
% 0.23/0.46 tff(69,plain,
% 0.23/0.46 (![X: $i, Y: $i] : ((~(member(X, E!21) & member(Y, E!21))) | (((~apply(R!20, X, Y)) | (member(tptp_fun_Z_23(Y, X), A!22) & member(X, tptp_fun_Z_23(Y, X)) & member(Y, tptp_fun_Z_23(Y, X)))) & (apply(R!20, X, Y) | ![Z: $i] : (~(member(Z, A!22) & member(X, Z) & member(Y, Z))))))),
% 0.23/0.46 inference(and_elim,[status(thm)],[47])).
% 0.23/0.46 tff(70,plain,
% 0.23/0.46 (![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.23/0.46 tff(71,plain,
% 0.23/0.46 (![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.23/0.46 tff(72,plain,
% 0.23/0.46 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(73,plain,
% 0.23/0.46 (((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(74,plain,
% 0.23/0.46 ((~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_10(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))) <=> (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(75,plain,
% 0.23/0.46 (((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_10(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[74])).
% 0.23/0.46 tff(76,plain,
% 0.23/0.46 (((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_10(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[75, 73])).
% 0.23/0.47 tff(77,plain,
% 0.23/0.47 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_10(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[76])).
% 0.23/0.47 tff(78,plain,
% 0.23/0.47 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_10(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[77, 72])).
% 0.23/0.47 tff(79,plain,
% 0.23/0.47 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_10(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(80,plain,
% 0.23/0.47 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_10(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.23/0.47 tff(81,plain,
% 0.23/0.47 (~((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[80, 71, 7])).
% 0.23/0.47 tff(82,plain,
% 0.23/0.47 (((~((~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~((~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))))) | (apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(83,plain,
% 0.23/0.47 (apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.23/0.47 tff(84,plain,
% 0.23/0.47 (((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))) | (~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(85,plain,
% 0.23/0.48 (~apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[84, 5])).
% 0.23/0.48 tff(86,plain,
% 0.23/0.48 ((~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(87,plain,
% 0.23/0.48 ((~(apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z))))) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.23/0.48 tff(88,plain,
% 0.23/0.48 (![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[87, 83])).
% 0.23/0.48 tff(89,plain,
% 0.23/0.48 (((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))) | ((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))))) <=> ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))) | (~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(90,plain,
% 0.23/0.48 ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))) | ((~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(91,plain,
% 0.23/0.48 ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_10(R!20, E!21), Z)))) | (~member(tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22), A!22)) | (~member(tptp_fun_X_10(R!20, E!21), tptp_fun_Y_4(tptp_fun_X_10(R!20, E!21), A!22)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.23/0.48 tff(92,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[91, 88, 61, 59])).
% 0.23/0.48 tff(93,plain,((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(94,assumption,(~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))), introduced(assumption)).
% 0.23/0.48 tff(95,plain,
% 0.23/0.48 (((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | member(tptp_fun_X_12(R!20, E!21), E!21)),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(96,plain,
% 0.23/0.48 (member(tptp_fun_X_12(R!20, E!21), E!21)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.23/0.48 tff(97,plain,
% 0.23/0.48 (((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | member(tptp_fun_Y_11(R!20, E!21), E!21)),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(98,plain,
% 0.23/0.48 (member(tptp_fun_Y_11(R!20, E!21), E!21)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.23/0.48 tff(99,plain,
% 0.23/0.48 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(100,plain,
% 0.23/0.48 (((~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_12(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(101,plain,
% 0.23/0.48 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_12(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))))))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[100])).
% 0.23/0.48 tff(102,plain,
% 0.23/0.48 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_12(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[101, 99])).
% 0.23/0.48 tff(103,plain,
% 0.23/0.48 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_12(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z))))))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(104,plain,
% 0.23/0.48 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.23/0.49 tff(105,plain,
% 0.23/0.49 (~((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[104, 71, 98, 96])).
% 0.23/0.49 tff(106,plain,
% 0.23/0.49 (((~(apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | (~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))))))) | ((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(107,plain,
% 0.23/0.49 ((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.23/0.49 tff(108,plain,
% 0.23/0.49 (((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(109,plain,
% 0.23/0.49 (apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[108, 94])).
% 0.23/0.49 tff(110,plain,
% 0.23/0.49 ((~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(111,plain,
% 0.23/0.49 ((~((~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))))) | (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.23/0.49 tff(112,plain,
% 0.23/0.49 (~((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.23/0.49 tff(113,plain,
% 0.23/0.49 (((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))) | member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(114,plain,
% 0.23/0.49 (member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.23/0.49 tff(115,plain,
% 0.23/0.49 (((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))) | member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(116,plain,
% 0.23/0.49 (member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.23/0.49 tff(117,plain,
% 0.23/0.49 (((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))) | member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(118,plain,
% 0.23/0.49 (member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[117, 112])).
% 0.23/0.49 tff(119,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(120,plain,
% 0.23/0.49 (((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(121,plain,
% 0.23/0.49 ((~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))) <=> (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(122,plain,
% 0.23/0.49 (((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[121])).
% 0.23/0.49 tff(123,plain,
% 0.23/0.49 (((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[122, 120])).
% 0.23/0.49 tff(124,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))))))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[123])).
% 0.23/0.50 tff(125,plain,
% 0.23/0.50 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[124, 119])).
% 0.23/0.50 tff(126,plain,
% 0.23/0.50 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(127,plain,
% 0.23/0.50 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.23/0.50 tff(128,plain,
% 0.23/0.50 (~((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[127, 71, 98, 96])).
% 0.23/0.50 tff(129,plain,
% 0.23/0.50 (((~((~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~((~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))))) | (apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(130,plain,
% 0.23/0.50 (apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.23/0.50 tff(131,plain,
% 0.23/0.50 (((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))) | (~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(132,plain,
% 0.23/0.50 (~apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[131, 94])).
% 0.23/0.50 tff(133,plain,
% 0.23/0.50 ((~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(134,plain,
% 0.23/0.50 ((~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z))))) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.23/0.50 tff(135,plain,
% 0.23/0.50 (![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.23/0.50 tff(136,plain,
% 0.23/0.50 (((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | ((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))) <=> ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(137,plain,
% 0.23/0.50 (((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))))) <=> ((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(138,plain,
% 0.23/0.50 (((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))))) <=> ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | ((~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[137])).
% 0.23/0.50 tff(139,plain,
% 0.23/0.50 (((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))))) <=> ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)))),
% 0.23/0.50 inference(transitivity,[status(thm)],[138, 136])).
% 0.23/0.50 tff(140,plain,
% 0.23/0.50 ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(141,plain,
% 0.23/0.50 ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Y_11(R!20, E!21), Z)) | (~member(tptp_fun_X_12(R!20, E!21), Z)))) | (~member(tptp_fun_Y_11(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_X_12(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)), A!22))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.23/0.50 tff(142,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[141, 135, 118, 116, 114])).
% 0.23/0.50 tff(143,plain,((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(144,plain,
% 0.23/0.50 (^[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)))))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(145,plain,
% 0.23/0.50 (![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))))))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[144])).
% 0.23/0.50 tff(146,plain,
% 0.23/0.50 (^[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)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(147,plain,
% 0.23/0.50 (![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))))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[146])).
% 0.23/0.50 tff(148,plain,
% 0.23/0.50 (^[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)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(149,plain,
% 0.23/0.50 (![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))))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[148])).
% 0.23/0.50 tff(150,plain,
% 0.23/0.50 (![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))))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[149, 147])).
% 0.23/0.50 tff(151,plain,
% 0.23/0.50 (^[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))))))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(152,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[151])).
% 0.23/0.51 tff(153,plain,
% 0.23/0.51 (^[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))))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(154,plain,
% 0.23/0.51 (![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)))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[153])).
% 0.23/0.51 tff(155,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(156,plain,
% 0.23/0.51 (^[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)))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(157,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[156])).
% 0.23/0.51 tff(158,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')).
% 0.23/0.51 tff(159,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.23/0.51 tff(160,plain,
% 0.23/0.51 (![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))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.23/0.51 tff(161,plain,(
% 0.23/0.51 ![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))))))))),
% 0.23/0.51 inference(skolemize,[status(sab)],[160])).
% 0.23/0.51 tff(162,plain,
% 0.23/0.51 (![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)))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.23/0.51 tff(163,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[162, 152])).
% 0.23/0.51 tff(164,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[163, 150])).
% 0.23/0.51 tff(165,plain,
% 0.23/0.51 (![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))))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[164, 145])).
% 0.23/0.51 tff(166,plain,
% 0.23/0.51 (((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z)))))))))) <=> ((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z))))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(167,plain,
% 0.23/0.51 ((~((~(equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!21)) | (~member(Y, E!21)) | (~member(Z, E!21)))))))))) <=> (~((~(equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z)))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(168,plain,
% 0.23/0.51 (((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!21)) | (~member(Y, E!21)) | (~member(Z, E!21))))))))))) <=> ((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z))))))))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[167])).
% 0.23/0.51 tff(169,plain,
% 0.23/0.51 (((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!21)) | (~member(Y, E!21)) | (~member(Z, E!21))))))))))) <=> ((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z))))))))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[168, 166])).
% 0.23/0.52 tff(170,plain,
% 0.23/0.52 ((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~member(tptp_fun_Y_11(R!20, E!21), E!21)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!21)) | (~member(Y, E!21)) | (~member(Z, E!21))))))))))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(171,plain,
% 0.23/0.52 ((~![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!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z)))))))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.23/0.52 tff(172,plain,
% 0.23/0.52 (~((~(equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z))))))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[171, 165])).
% 0.23/0.52 tff(173,plain,
% 0.23/0.52 (((~(equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~equivalence(R!20, E!21)) | (~((~![X: $i] : ((~member(X, E!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!20, X, Y)) | (~member(X, E!21)) | (~member(Y, E!21)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!20, Y, Z)) | (~member(Y, E!21)) | (~member(Z, E!21)) | (~apply(R!20, X, Y)) | (~member(X, E!21)) | apply(R!20, X, Z)))))))) | (equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))),
% 0.23/0.52 inference(tautology,[status(thm)],[])).
% 0.23/0.52 tff(174,plain,
% 0.23/0.52 (equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.23/0.52 tff(175,plain,
% 0.23/0.52 (~equivalence(R!20, E!21)),
% 0.23/0.52 inference(and_elim,[status(thm)],[47])).
% 0.23/0.52 tff(176,plain,
% 0.23/0.52 ((~(equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))))),
% 0.23/0.52 inference(tautology,[status(thm)],[])).
% 0.23/0.52 tff(177,plain,
% 0.23/0.52 ((~(equivalence(R!20, E!21) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))))) | (~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.23/0.52 tff(178,plain,
% 0.23/0.52 ((~((~member(tptp_fun_X_10(R!20, E!21), E!21)) | apply(R!20, tptp_fun_X_10(R!20, E!21), tptp_fun_X_10(R!20, E!21)))) | (~((~member(tptp_fun_Y_11(R!20, E!21), E!21)) | (~member(tptp_fun_X_12(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_X_12(R!20, E!21), tptp_fun_Y_11(R!20, E!21))) | apply(R!20, tptp_fun_Y_11(R!20, E!21), tptp_fun_X_12(R!20, E!21)))) | (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[177, 174])).
% 0.23/0.52 tff(179,plain,
% 0.23/0.52 (~((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[178, 143, 93])).
% 0.23/0.52 tff(180,plain,
% 0.23/0.52 (((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | member(tptp_fun_Y_14(R!20, E!21), E!21)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(181,plain,
% 0.23/0.53 (member(tptp_fun_Y_14(R!20, E!21), E!21)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.23/0.53 tff(182,plain,
% 0.23/0.53 (((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | member(tptp_fun_Z_13(R!20, E!21), E!21)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(183,plain,
% 0.23/0.53 (member(tptp_fun_Z_13(R!20, E!21), E!21)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.23/0.53 tff(184,plain,
% 0.23/0.53 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(185,plain,
% 0.23/0.53 (((~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_14(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(186,plain,
% 0.23/0.53 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_14(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z)))))))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[185])).
% 0.23/0.53 tff(187,plain,
% 0.23/0.53 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_14(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))),
% 0.23/0.53 inference(transitivity,[status(thm)],[186, 184])).
% 0.23/0.53 tff(188,plain,
% 0.23/0.53 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_Y_14(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(189,plain,
% 0.23/0.53 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z)))))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.23/0.53 tff(190,plain,
% 0.23/0.53 (~((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[189, 71, 183, 181])).
% 0.23/0.53 tff(191,plain,
% 0.23/0.53 (((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z)))))) | ((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(192,plain,
% 0.23/0.53 ((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.23/0.53 tff(193,plain,
% 0.23/0.53 (((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(194,plain,
% 0.23/0.53 (apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[193, 179])).
% 0.23/0.53 tff(195,plain,
% 0.23/0.53 ((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(196,plain,
% 0.23/0.53 ((~((~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.23/0.53 tff(197,plain,
% 0.23/0.53 (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[196, 192])).
% 0.23/0.53 tff(198,plain,
% 0.23/0.53 (((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(199,plain,
% 0.23/0.53 (member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.23/0.53 tff(200,plain,
% 0.23/0.53 (((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(201,plain,
% 0.23/0.54 (member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[200, 197])).
% 0.23/0.54 tff(202,plain,
% 0.23/0.54 (((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | member(tptp_fun_X_15(R!20, E!21), E!21)),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(203,plain,
% 0.23/0.54 (member(tptp_fun_X_15(R!20, E!21), E!21)),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[202, 179])).
% 0.23/0.54 tff(204,plain,
% 0.23/0.54 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(205,plain,
% 0.23/0.54 (((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(206,plain,
% 0.23/0.54 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))))))))),
% 0.23/0.54 inference(monotonicity,[status(thm)],[205])).
% 0.23/0.54 tff(207,plain,
% 0.23/0.54 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[206, 204])).
% 0.23/0.54 tff(208,plain,
% 0.23/0.54 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))))),
% 0.23/0.54 inference(quant_inst,[status(thm)],[])).
% 0.23/0.54 tff(209,plain,
% 0.23/0.54 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.23/0.54 tff(210,plain,
% 0.23/0.54 (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[209, 71, 183, 203])).
% 0.23/0.54 tff(211,plain,
% 0.23/0.54 (((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))))) | (apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(212,plain,
% 0.23/0.54 (apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.23/0.54 tff(213,plain,
% 0.23/0.54 (((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)))),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(214,plain,
% 0.23/0.54 (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[213, 179])).
% 0.23/0.54 tff(215,plain,
% 0.23/0.54 ((~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(216,plain,
% 0.23/0.54 ((~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z))))) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.23/0.54 tff(217,plain,
% 0.23/0.54 (![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[216, 212])).
% 0.23/0.54 tff(218,plain,
% 0.23/0.54 (((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) <=> ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(219,plain,
% 0.23/0.54 (((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) <=> ((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(220,plain,
% 0.23/0.54 (((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) <=> ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))))),
% 0.23/0.54 inference(monotonicity,[status(thm)],[219])).
% 0.23/0.54 tff(221,plain,
% 0.23/0.54 (((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) <=> ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[220, 218])).
% 0.23/0.54 tff(222,plain,
% 0.23/0.54 ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | ((~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.23/0.54 inference(quant_inst,[status(thm)],[])).
% 0.23/0.54 tff(223,plain,
% 0.23/0.54 ((~![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Z_13(R!20, E!21), Z)))) | (~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.23/0.54 tff(224,plain,
% 0.23/0.54 (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[223, 217, 201, 199])).
% 0.23/0.54 tff(225,plain,
% 0.23/0.54 (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[224, 4])).
% 0.23/0.54 tff(226,plain,
% 0.23/0.54 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(227,plain,
% 0.23/0.55 (((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), Z)))))))) <=> ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(228,plain,
% 0.23/0.55 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z)))))))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[227])).
% 0.23/0.55 tff(229,plain,
% 0.23/0.55 (((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))),
% 0.40/0.55 inference(transitivity,[status(thm)],[228, 226])).
% 0.40/0.55 tff(230,plain,
% 0.40/0.55 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | ((~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(Z, A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(231,plain,
% 0.40/0.55 ((~![X: $i, Y: $i] : ((~member(X, E!21)) | (~member(Y, E!21)) | (~((~((~apply(R!20, X, Y)) | (~((~member(tptp_fun_Z_23(Y, X), A!22)) | (~member(X, tptp_fun_Z_23(Y, X))) | (~member(Y, tptp_fun_Z_23(Y, X))))))) | (~(apply(R!20, X, Y) | ![Z: $i] : ((~member(X, Z)) | (~member(Z, A!22)) | (~member(Y, Z))))))))) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z)))))))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.40/0.55 tff(232,plain,
% 0.40/0.55 (~((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z))))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[231, 71, 181, 203])).
% 0.40/0.55 tff(233,plain,
% 0.40/0.55 (((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21)) | ![Z: $i] : ((~member(Z, A!22)) | (~member(tptp_fun_X_15(R!20, E!21), Z)) | (~member(tptp_fun_Y_14(R!20, E!21), Z)))))) | ((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(234,plain,
% 0.40/0.55 ((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.40/0.55 tff(235,plain,
% 0.40/0.55 (((~member(tptp_fun_Z_13(R!20, E!21), E!21)) | (~member(tptp_fun_Y_14(R!20, E!21), E!21)) | (~member(tptp_fun_X_15(R!20, E!21), E!21)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Z_13(R!20, E!21))) | apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(236,plain,
% 0.40/0.55 (apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[235, 179])).
% 0.40/0.55 tff(237,plain,
% 0.40/0.55 ((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22))))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(238,plain,
% 0.40/0.55 ((~((~apply(R!20, tptp_fun_X_15(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))))) | (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.40/0.55 tff(239,plain,
% 0.40/0.55 (~((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[238, 234])).
% 0.40/0.55 tff(240,plain,
% 0.40/0.55 (((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22))) | member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(241,plain,
% 0.40/0.55 (member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.40/0.55 tff(242,plain,
% 0.40/0.55 ($false),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[241, 225])).
% 0.40/0.55 tff(243,plain,(~(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55 tff(244,plain,
% 0.40/0.55 (((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22))) | member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(245,plain,
% 0.40/0.55 (member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[244, 239])).
% 0.40/0.55 tff(246,plain,
% 0.40/0.55 (((~![X: $i] : ((~member(X, E!21)) | (~((~member(tptp_fun_Y_4(X, A!22), A!22)) | (~member(X, tptp_fun_Y_4(X, A!22))))))) | (~![X: $i] : ((~member(X, A!22)) | subset(X, E!21))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22))))) | ![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(247,plain,
% 0.40/0.55 (![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[246, 51])).
% 0.40/0.55 tff(248,plain,
% 0.40/0.55 (((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | ((~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(249,plain,
% 0.40/0.55 (((tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22))) <=> ((~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(250,plain,
% 0.40/0.56 (((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | ((tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | ((~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[249])).
% 0.40/0.56 tff(251,plain,
% 0.40/0.56 (((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | ((tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))),
% 0.40/0.56 inference(transitivity,[status(thm)],[250, 248])).
% 0.40/0.56 tff(252,plain,
% 0.40/0.56 ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | ((tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(253,plain,
% 0.40/0.56 ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, A!22)) | ![Z: $i] : ((~member(Z, X)) | (~member(Z, Y))) | (~member(X, A!22)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22)) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | ![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.40/0.56 tff(254,plain,
% 0.40/0.56 (![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | (tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)) = tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[253, 247, 245, 199])).
% 0.40/0.56 tff(255,plain,
% 0.40/0.56 (![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[254, 243])).
% 0.40/0.56 tff(256,plain,
% 0.40/0.56 (((~member(tptp_fun_Z_13(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)), A!22)) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))) | member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(257,plain,
% 0.40/0.56 (member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[256, 197])).
% 0.40/0.56 tff(258,plain,
% 0.40/0.56 (((~member(tptp_fun_X_15(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)), A!22))) | member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(259,plain,
% 0.40/0.56 (member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[258, 239])).
% 0.40/0.56 tff(260,plain,
% 0.40/0.56 (((~![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) | ((~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) <=> ((~![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(261,plain,
% 0.40/0.56 ((~![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) | ((~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(262,plain,
% 0.40/0.56 ((~![Z: $i] : ((~member(Z, tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(Z, tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21)))))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Y_14(R!20, E!21), tptp_fun_X_15(R!20, E!21)))) | (~member(tptp_fun_Y_14(R!20, E!21), tptp_fun_Z_23(tptp_fun_Z_13(R!20, E!21), tptp_fun_Y_14(R!20, E!21))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.40/0.56 tff(263,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[262, 259, 257, 255])).
% 0.40/0.56 % SZS output end Proof
% 0.40/0.56 % E exiting
%------------------------------------------------------------------------------