%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET771+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:19 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET771+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:41:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(member_type, type, (
% 0.19/0.40 member: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_A_57_type, type, (
% 0.19/0.40 tptp_fun_A_57: $i)).
% 0.19/0.40 tff(tptp_fun_X_46_type, type, (
% 0.19/0.40 tptp_fun_X_46: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_R_55_type, type, (
% 0.19/0.40 tptp_fun_R_55: $i)).
% 0.19/0.40 tff(apply_type, type, (
% 0.19/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_X_48_type, type, (
% 0.19/0.40 tptp_fun_X_48: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y_47_type, type, (
% 0.19/0.40 tptp_fun_Y_47: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y_59_type, type, (
% 0.19/0.40 tptp_fun_Y_59: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_F_58_type, type, (
% 0.19/0.40 tptp_fun_F_58: $i)).
% 0.19/0.40 tff(tptp_fun_B_56_type, type, (
% 0.19/0.40 tptp_fun_B_56: $i)).
% 0.19/0.40 tff(equivalence_type, type, (
% 0.19/0.40 equivalence: ( $i * $i ) > $o)).
% 0.19/0.40 tff(maps_type, type, (
% 0.19/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_Z_49_type, type, (
% 0.19/0.40 tptp_fun_Z_49: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_51_type, type, (
% 0.19/0.40 tptp_fun_X_51: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y_50_type, type, (
% 0.19/0.40 tptp_fun_Y_50: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_7_type, type, (
% 0.19/0.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_4_type, type, (
% 0.19/0.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(1,assumption,(~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | member(tptp_fun_X_48(R!55, A!57), A!57)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (member(tptp_fun_X_48(R!55, A!57), A!57)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | member(tptp_fun_Y_47(R!55, A!57), A!57)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (member(tptp_fun_Y_47(R!55, A!57), A!57)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (^[X1: $i, X2: $i] : refl(((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))) <=> ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))) <=> ![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (^[X1: $i, X2: $i] : rewrite(((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))) <=> ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))) <=> ![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))) <=> ![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X1, A!57) & member(X2, A!57)) <=> (~((~member(X1, A!57)) | (~member(X2, A!57))))), ((~(member(X1, A!57) & member(X2, A!57))) <=> (~(~((~member(X1, A!57)) | (~member(X2, A!57))))))), rewrite((~(~((~member(X1, A!57)) | (~member(X2, A!57))))) <=> ((~member(X1, A!57)) | (~member(X2, A!57)))), ((~(member(X1, A!57) & member(X2, A!57))) <=> ((~member(X1, A!57)) | (~member(X2, A!57))))), trans(monotonicity(rewrite(((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) <=> ((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))), rewrite((apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))) <=> (apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))), ((((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))) <=> (((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1)))))) & (apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))), rewrite((((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1)))))) & (apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))) <=> (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))), ((((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))) <=> (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))), (((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))))) <=> (((~member(X1, A!57)) | (~member(X2, A!57))) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))))), rewrite((((~member(X1, A!57)) | (~member(X2, A!57))) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y)))))))) <=> ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))), (((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))))) <=> ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))))) <=> ![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (((maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))))) & (~equivalence(R!55, A!57))) <=> (maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))))) & (~equivalence(R!55, A!57)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))))) <=> (maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (((maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))))) & (~equivalence(R!55, A!57))) <=> ((maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))))) & (~equivalence(R!55, A!57)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (((maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))))) & (~equivalence(R!55, A!57))) <=> (maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))))) & (~equivalence(R!55, A!57)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~![F: $i, A: $i, B: $i, R: $i] : ((~(maps(F, A, B) & ![X1: $i, X2: $i] : ((~(member(X1, A) & member(X2, A))) | (apply(R, X1, X2) <=> ?[Y: $i] : (member(Y, B) & apply(F, X1, Y) & apply(F, X2, Y)))))) | equivalence(R, A))) <=> (~![F: $i, A: $i, B: $i, R: $i] : ((~(maps(F, A, B) & ![X1: $i, X2: $i] : ((~(member(X1, A) & member(X2, A))) | (apply(R, X1, X2) <=> ?[Y: $i] : (member(Y, B) & apply(F, X1, Y) & apply(F, X2, Y)))))) | equivalence(R, A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~![F: $i, A: $i, B: $i, R: $i] : ((maps(F, A, B) & ![X1: $i, X2: $i] : ((member(X1, A) & member(X2, A)) => (apply(R, X1, X2) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X1, Y)) & apply(F, X2, Y))))) => equivalence(R, A))) <=> (~![F: $i, A: $i, B: $i, R: $i] : ((~(maps(F, A, B) & ![X1: $i, X2: $i] : ((~(member(X1, A) & member(X2, A))) | (apply(R, X1, X2) <=> ?[Y: $i] : (member(Y, B) & apply(F, X1, Y) & apply(F, X2, Y)))))) | equivalence(R, A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(19,axiom,(~![F: $i, A: $i, B: $i, R: $i] : ((maps(F, A, B) & ![X1: $i, X2: $i] : ((member(X1, A) & member(X2, A)) => (apply(R, X1, X2) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X1, Y)) & apply(F, X2, Y))))) => equivalence(R, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIII07')).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (~![F: $i, A: $i, B: $i, R: $i] : ((~(maps(F, A, B) & ![X1: $i, X2: $i] : ((~(member(X1, A) & member(X2, A))) | (apply(R, X1, X2) <=> ?[Y: $i] : (member(Y, B) & apply(F, X1, Y) & apply(F, X2, Y)))))) | equivalence(R, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (~![F: $i, A: $i, B: $i, R: $i] : ((~(maps(F, A, B) & ![X1: $i, X2: $i] : ((~(member(X1, A) & member(X2, A))) | (apply(R, X1, X2) <=> ?[Y: $i] : (member(Y, B) & apply(F, X1, Y) & apply(F, X2, Y)))))) | equivalence(R, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (~![F: $i, A: $i, B: $i, R: $i] : ((~(maps(F, A, B) & ![X1: $i, X2: $i] : ((~(member(X1, A) & member(X2, A))) | (apply(R, X1, X2) <=> ?[Y: $i] : (member(Y, B) & apply(F, X1, Y) & apply(F, X2, Y)))))) | equivalence(R, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (~![F: $i, A: $i, B: $i, R: $i] : ((~(maps(F, A, B) & ![X1: $i, X2: $i] : ((~(member(X1, A) & member(X2, A))) | (apply(R, X1, X2) <=> ?[Y: $i] : (member(Y, B) & apply(F, X1, Y) & apply(F, X2, Y)))))) | equivalence(R, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (maps(F!58, A!57, B!56) & ![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y)))))) & (~equivalence(R!55, A!57))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![X1: $i, X2: $i] : ((~(member(X1, A!57) & member(X2, A!57))) | (((~apply(R!55, X1, X2)) | (member(tptp_fun_Y_59(X2, X1), B!56) & apply(F!58, X1, tptp_fun_Y_59(X2, X1)) & apply(F!58, X2, tptp_fun_Y_59(X2, X1)))) & (apply(R!55, X1, X2) | ![Y: $i] : (~(member(Y, B!56) & apply(F!58, X1, Y) & apply(F!58, X2, Y))))))),
% 0.19/0.41 inference(and_elim,[status(thm)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 12])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 10])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (((~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (~((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[33, 27, 5, 3])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (((~(apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))))))) | ((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[37, 1])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 ((~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 ((~((~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (~((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[40, 36])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))) | apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))) | apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))) | member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[46, 41])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56))))))))) <=> ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 ((~((~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))))) <=> (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[53, 48])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (~((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56)))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[56, 27, 5, 3])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57)), B!56))))))) | (apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 (((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))) | (~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[60, 1])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 ((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 ((~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y))))) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[63, 59])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | ((~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)))) <=> ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 (((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))) <=> ((~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | ((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))) <=> ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | ((~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | ((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))) <=> ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | ((~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[70, 64, 47, 45, 43])).
% 0.19/0.45 tff(72,plain,((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(73,assumption,(~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))), introduced(assumption)).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | member(tptp_fun_Y_50(R!55, A!57), A!57)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (member(tptp_fun_Y_50(R!55, A!57), A!57)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.45 tff(90,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.45 tff(93,plain,(
% 0.19/0.45 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[92])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[95, 82])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[96, 77])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 ((~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!58, X, Y1)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~member(Y1, B!56)) | (~member(Y2, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)))) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))))))) <=> (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!58, X, Y1)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~member(Y1, B!56)) | (~member(Y2, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)))) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!58, X, Y1)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~member(Y1, B!56)) | (~member(Y2, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)))) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!58, X, Y1)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~member(Y1, B!56)) | (~member(Y2, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)))) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 (~((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58)))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~(maps(F!58, A!57, B!56) | (~((~member(tptp_fun_X_4(B!56, A!57, F!58), A!57)) | (~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_4(B!56, A!57, F!58), Y)))))) | (~((~member(tptp_fun_Y2_5(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_Y1_6(B!56, A!57, F!58), B!56)) | (~member(tptp_fun_X_7(B!56, A!57, F!58), A!57)) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y2_5(B!56, A!57, F!58))) | (~apply(F!58, tptp_fun_X_7(B!56, A!57, F!58), tptp_fun_Y1_6(B!56, A!57, F!58))) | (tptp_fun_Y1_6(B!56, A!57, F!58) = tptp_fun_Y2_5(B!56, A!57, F!58))))))) | ((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 ((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (maps(F!58, A!57, B!56)),
% 0.19/0.47 inference(and_elim,[status(thm)],[24])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 ((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 ((~((~maps(F!58, A!57, B!56)) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))))) | (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (~((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56))))) | ![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))))))) <=> ((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 ((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 ((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 (~((~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[115, 112, 75])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58)))) | apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 (apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58)))) | member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 (member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | member(tptp_fun_X_51(R!55, A!57), A!57)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (member(tptp_fun_X_51(R!55, A!57), A!57)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[121, 73])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[125, 123])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[128, 27, 75, 122])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))))) | ((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 ((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 (((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 (apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[132, 73])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 ((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 ((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 (~((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[135, 131])).
% 0.19/0.48 tff(137,plain,
% 0.19/0.48 (((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))) | apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(138,plain,
% 0.19/0.48 (apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.48 tff(139,plain,
% 0.19/0.48 (((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))) | member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(140,plain,
% 0.19/0.48 (member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.19/0.48 tff(141,plain,
% 0.19/0.48 (((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(142,plain,
% 0.19/0.48 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[141, 110])).
% 0.19/0.48 tff(143,plain,
% 0.19/0.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 (((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56))) <=> ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(145,plain,
% 0.19/0.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.48 tff(146,plain,
% 0.19/0.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[145, 143])).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[148, 142, 75, 140, 138, 120, 118])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 (((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | member(tptp_fun_Z_49(R!55, A!57), A!57)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (member(tptp_fun_Z_49(R!55, A!57), A!57)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[150, 73])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(153,plain,
% 0.19/0.48 (((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[154, 152])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (~((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[157, 27, 151, 75])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 (((~(apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))))))) | ((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 ((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 (apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[161, 73])).
% 0.19/0.49 tff(163,plain,
% 0.19/0.49 ((~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 ((~((~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.19/0.49 tff(165,plain,
% 0.19/0.49 (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[164, 160])).
% 0.19/0.49 tff(166,plain,
% 0.19/0.49 (((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))) | apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(167,plain,
% 0.19/0.49 (apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.19/0.49 tff(168,plain,
% 0.19/0.49 (((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))) | member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(169,plain,
% 0.19/0.49 (member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[168, 165])).
% 0.19/0.49 tff(170,plain,
% 0.19/0.49 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(171,plain,
% 0.19/0.49 (((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56))) <=> ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(172,plain,
% 0.19/0.49 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[171])).
% 0.19/0.49 tff(173,plain,
% 0.19/0.49 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[172, 170])).
% 0.19/0.50 tff(174,plain,
% 0.19/0.50 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | ((tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(175,plain,
% 0.19/0.50 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!56)) | (~apply(F!58, X, Y2)) | (~member(X, A!57)) | (~apply(F!58, X, Y1)) | (~member(Y1, B!56)))) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58))) | (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.50 tff(176,plain,
% 0.19/0.50 (tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[175, 142, 75, 169, 167, 120, 118])).
% 0.19/0.50 tff(177,plain,
% 0.19/0.50 (tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) = tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58)),
% 0.19/0.50 inference(symmetry,[status(thm)],[176])).
% 0.19/0.50 tff(178,plain,
% 0.19/0.50 (tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)) = tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))),
% 0.19/0.50 inference(transitivity,[status(thm)],[177, 149])).
% 0.19/0.50 tff(179,plain,
% 0.19/0.50 (apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) <=> apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[178])).
% 0.19/0.50 tff(180,plain,
% 0.19/0.50 (apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))) <=> apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[179])).
% 0.19/0.50 tff(181,plain,
% 0.19/0.50 ((~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) <=> (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[180])).
% 0.19/0.50 tff(182,plain,
% 0.19/0.50 (((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))) | apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(183,plain,
% 0.19/0.50 (apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[182, 136])).
% 0.19/0.50 tff(184,plain,
% 0.19/0.50 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(185,plain,
% 0.19/0.50 (((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(186,plain,
% 0.19/0.50 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[185])).
% 0.19/0.50 tff(187,plain,
% 0.19/0.50 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[186, 184])).
% 0.19/0.50 tff(188,plain,
% 0.19/0.50 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(189,plain,
% 0.19/0.50 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.19/0.50 tff(190,plain,
% 0.19/0.50 (~((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[189, 27, 151, 122])).
% 0.19/0.50 tff(191,plain,
% 0.19/0.50 (((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | (~((~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_X_51(R!55, A!57))))))))) | (apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(192,plain,
% 0.19/0.50 (apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.19/0.50 tff(193,plain,
% 0.19/0.50 (((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(194,plain,
% 0.19/0.50 (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[193, 73])).
% 0.19/0.50 tff(195,plain,
% 0.19/0.50 ((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(196,plain,
% 0.19/0.50 ((~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y))))) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.19/0.50 tff(197,plain,
% 0.19/0.50 (![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[196, 192])).
% 0.19/0.50 tff(198,plain,
% 0.19/0.50 (((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))) | ((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))) <=> ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(199,plain,
% 0.19/0.50 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))) | ((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(200,plain,
% 0.19/0.51 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.51 tff(201,plain,
% 0.19/0.51 (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[200, 197, 140, 183])).
% 0.19/0.51 tff(202,plain,
% 0.19/0.51 (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[201, 181])).
% 0.19/0.51 tff(203,plain,
% 0.19/0.51 (((~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))) | apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(204,plain,
% 0.19/0.51 (apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[203, 165])).
% 0.19/0.51 tff(205,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[204, 202])).
% 0.19/0.51 tff(206,plain,((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(207,plain,
% 0.19/0.51 (^[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) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(208,plain,
% 0.19/0.51 (![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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[207])).
% 0.19/0.51 tff(209,plain,
% 0.19/0.51 (^[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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(210,plain,
% 0.19/0.51 (![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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[209])).
% 0.19/0.51 tff(211,plain,
% 0.19/0.51 (^[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) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(212,plain,
% 0.19/0.51 (![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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.51 tff(213,plain,
% 0.19/0.51 (![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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[212, 210])).
% 0.19/0.51 tff(214,plain,
% 0.19/0.51 (^[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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) <=> (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A))))), rewrite((~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(R, A), A))))) <=> (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))), rewrite((equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A)))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(215,plain,
% 0.19/0.51 (![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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[214])).
% 0.19/0.51 tff(216,plain,
% 0.19/0.51 (^[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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(217,plain,
% 0.19/0.51 (![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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(R, A), A)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[216])).
% 0.19/0.51 tff(218,plain,
% 0.19/0.51 (![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))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(219,plain,
% 0.19/0.51 (^[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)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(220,plain,
% 0.19/0.51 (![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))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[219])).
% 0.19/0.51 tff(221,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.19/0.51 tff(222,plain,
% 0.19/0.51 (![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))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.51 tff(223,plain,
% 0.19/0.51 (![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))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.19/0.51 tff(224,plain,(
% 0.19/0.51 ![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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[223])).
% 0.19/0.51 tff(225,plain,
% 0.19/0.51 (![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_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~(member(tptp_fun_X_48(R, A), A) & member(tptp_fun_Y_47(R, A), A))) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A)) & apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A)))) | (~(member(tptp_fun_X_51(R, A), A) & member(tptp_fun_Y_50(R, A), A) & member(tptp_fun_Z_49(R, A), A)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.19/0.51 tff(226,plain,
% 0.19/0.51 (![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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[225, 215])).
% 0.19/0.51 tff(227,plain,
% 0.19/0.51 (![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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(R, A), A))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[226, 213])).
% 0.19/0.51 tff(228,plain,
% 0.19/0.51 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[227, 208])).
% 0.19/0.51 tff(229,plain,
% 0.19/0.51 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z)))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(230,plain,
% 0.19/0.52 ((~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : (apply(R!55, Y, X) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!55, X, Z) | (~member(Y, A!57)) | (~member(X, A!57)) | (~member(Z, A!57)) | (~apply(R!55, Y, Z)) | (~apply(R!55, X, Y)))))))))) <=> (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z)))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(231,plain,
% 0.19/0.52 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : (apply(R!55, Y, X) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!55, X, Z) | (~member(Y, A!57)) | (~member(X, A!57)) | (~member(Z, A!57)) | (~apply(R!55, Y, Z)) | (~apply(R!55, X, Y))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z))))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[230])).
% 0.19/0.52 tff(232,plain,
% 0.19/0.52 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : (apply(R!55, Y, X) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!55, X, Z) | (~member(Y, A!57)) | (~member(X, A!57)) | (~member(Z, A!57)) | (~apply(R!55, Y, Z)) | (~apply(R!55, X, Y))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z))))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[231, 229])).
% 0.19/0.52 tff(233,plain,
% 0.19/0.52 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~(apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(R!55, A!57), A!57)))) | (~(apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_Z_49(R!55, A!57), A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : (apply(R!55, Y, X) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!55, X, Z) | (~member(Y, A!57)) | (~member(X, A!57)) | (~member(Z, A!57)) | (~apply(R!55, Y, Z)) | (~apply(R!55, X, Y))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(234,plain,
% 0.19/0.52 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_46(R, A), A)) | apply(R, tptp_fun_X_46(R, A), tptp_fun_X_46(R, A)))) | (~(apply(R, tptp_fun_Y_47(R, A), tptp_fun_X_48(R, A)) | (~apply(R, tptp_fun_X_48(R, A), tptp_fun_Y_47(R, A))) | (~member(tptp_fun_X_48(R, A), A)) | (~member(tptp_fun_Y_47(R, A), A)))) | (~(apply(R, tptp_fun_X_51(R, A), tptp_fun_Z_49(R, A)) | (~apply(R, tptp_fun_X_51(R, A), tptp_fun_Y_50(R, A))) | (~apply(R, tptp_fun_Y_50(R, A), tptp_fun_Z_49(R, A))) | (~member(tptp_fun_X_51(R, A), A)) | (~member(tptp_fun_Y_50(R, A), A)) | (~member(tptp_fun_Z_49(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) | (~member(Y, A)) | (~member(X, A)) | (~member(Z, A)) | (~apply(R, Y, Z)) | (~apply(R, X, Y))))))))))) | (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z)))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.19/0.52 tff(235,plain,
% 0.19/0.52 (~((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[234, 228])).
% 0.19/0.52 tff(236,plain,
% 0.19/0.52 (((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~equivalence(R!55, A!57)) | (~((~![X: $i] : ((~member(X, A!57)) | apply(R!55, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!55, X, Y)) | (~member(X, A!57)) | (~member(Y, A!57)) | apply(R!55, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R!55, Y, Z)) | (~member(Y, A!57)) | (~member(Z, A!57)) | (~apply(R!55, X, Y)) | (~member(X, A!57)) | apply(R!55, X, Z)))))))) | (equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(237,plain,
% 0.19/0.53 (equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.19/0.53 tff(238,plain,
% 0.19/0.53 (~equivalence(R!55, A!57)),
% 0.19/0.53 inference(and_elim,[status(thm)],[24])).
% 0.19/0.53 tff(239,plain,
% 0.19/0.53 ((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(240,plain,
% 0.19/0.53 ((~(equivalence(R!55, A!57) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57)))))) | (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.19/0.53 tff(241,plain,
% 0.19/0.53 ((~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~((~member(tptp_fun_Y_47(R!55, A!57), A!57)) | (~member(tptp_fun_X_48(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))) | apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~((~member(tptp_fun_Z_49(R!55, A!57), A!57)) | (~member(tptp_fun_Y_50(R!55, A!57), A!57)) | (~member(tptp_fun_X_51(R!55, A!57), A!57)) | (~apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))) | (~apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))) | apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Z_49(R!55, A!57))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[240, 237])).
% 0.19/0.53 tff(242,plain,
% 0.19/0.53 (~((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[241, 206, 72])).
% 0.19/0.53 tff(243,plain,
% 0.19/0.53 (((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | member(tptp_fun_X_46(R!55, A!57), A!57)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(244,plain,
% 0.19/0.53 (member(tptp_fun_X_46(R!55, A!57), A!57)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.19/0.53 tff(245,plain,
% 0.19/0.53 (((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(246,plain,
% 0.19/0.53 (~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[245, 242])).
% 0.19/0.53 tff(247,assumption,(member(tptp_fun_X_46(R!55, A!57), A!57)), introduced(assumption)).
% 0.19/0.53 tff(248,plain,
% 0.19/0.53 (((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))))))) <=> ((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(249,plain,
% 0.19/0.53 ((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(250,plain,
% 0.19/0.53 ((~![X: $i] : ((~member(X, A!57)) | (~((~member(tptp_fun_Y_3(X, B!56, F!58), B!56)) | (~apply(F!58, X, tptp_fun_Y_3(X, B!56, F!58))))))) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.19/0.53 tff(251,plain,
% 0.19/0.53 (~((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[250, 112, 247])).
% 0.19/0.53 tff(252,plain,
% 0.19/0.53 (((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58)))) | apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(253,plain,
% 0.19/0.53 (apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.19/0.53 tff(254,plain,
% 0.19/0.53 (((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58)))) | member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(255,plain,
% 0.19/0.53 (member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[254, 251])).
% 0.19/0.53 tff(256,plain,
% 0.19/0.53 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(257,plain,
% 0.19/0.53 (((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(258,plain,
% 0.19/0.53 ((~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))) <=> (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(259,plain,
% 0.19/0.53 (((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[258])).
% 0.19/0.53 tff(260,plain,
% 0.19/0.53 (((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))))))) <=> ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[259, 257])).
% 0.19/0.53 tff(261,plain,
% 0.19/0.53 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[260])).
% 0.19/0.54 tff(262,plain,
% 0.19/0.54 (((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))) <=> ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[261, 256])).
% 0.19/0.54 tff(263,plain,
% 0.19/0.54 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | ((~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(264,plain,
% 0.19/0.54 ((~![X1: $i, X2: $i] : ((~member(X1, A!57)) | (~member(X2, A!57)) | (~((~((~apply(R!55, X1, X2)) | (~((~member(tptp_fun_Y_59(X2, X1), B!56)) | (~apply(F!58, X1, tptp_fun_Y_59(X2, X1))) | (~apply(F!58, X2, tptp_fun_Y_59(X2, X1))))))) | (~(apply(R!55, X1, X2) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, X1, Y)) | (~apply(F!58, X2, Y))))))))) | (~member(tptp_fun_X_46(R!55, A!57), A!57)) | (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.19/0.54 tff(265,plain,
% 0.19/0.54 (~((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[264, 27, 247])).
% 0.19/0.54 tff(266,plain,
% 0.19/0.54 (((~((~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))) | (~((~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)))) | (~member(tptp_fun_Y_59(tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)), B!56)))))) | (~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))))) | (apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(267,plain,
% 0.19/0.54 (apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.19/0.54 tff(268,assumption,(~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))), introduced(assumption)).
% 0.19/0.54 tff(269,plain,
% 0.19/0.54 ((~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(270,plain,
% 0.19/0.54 ((~(apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57)) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y))))) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[269, 268])).
% 0.19/0.54 tff(271,plain,
% 0.19/0.54 (![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[270, 267])).
% 0.19/0.54 tff(272,plain,
% 0.19/0.54 (((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))))) <=> ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(273,plain,
% 0.19/0.54 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(274,plain,
% 0.19/0.54 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.54 tff(275,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[274, 271, 255, 253])).
% 0.19/0.54 tff(276,plain,((~member(tptp_fun_X_46(R!55, A!57), A!57)) | apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(277,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[276, 246, 244])).
% 0.19/0.54 % SZS output end Proof
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------