TSTP Solution File: SET771+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET771+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Tue Sep 20 05:07:57 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET771+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 07:47:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(member_type, type, (
% 0.19/0.42 member: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_A_57_type, type, (
% 0.19/0.42 tptp_fun_A_57: $i)).
% 0.19/0.42 tff(tptp_fun_X_46_type, type, (
% 0.19/0.42 tptp_fun_X_46: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_R_55_type, type, (
% 0.19/0.42 tptp_fun_R_55: $i)).
% 0.19/0.42 tff(apply_type, type, (
% 0.19/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_Y_47_type, type, (
% 0.19/0.42 tptp_fun_Y_47: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_48_type, type, (
% 0.19/0.42 tptp_fun_X_48: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y_59_type, type, (
% 0.19/0.42 tptp_fun_Y_59: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_F_58_type, type, (
% 0.19/0.42 tptp_fun_F_58: $i)).
% 0.19/0.42 tff(tptp_fun_B_56_type, type, (
% 0.19/0.42 tptp_fun_B_56: $i)).
% 0.19/0.42 tff(equivalence_type, type, (
% 0.19/0.42 equivalence: ( $i * $i ) > $o)).
% 0.19/0.42 tff(maps_type, type, (
% 0.19/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_Z_49_type, type, (
% 0.19/0.42 tptp_fun_Z_49: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y_50_type, type, (
% 0.19/0.42 tptp_fun_Y_50: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_51_type, type, (
% 0.19/0.42 tptp_fun_X_51: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_4_type, type, (
% 0.19/0.42 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.42 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.42 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_7_type, type, (
% 0.19/0.42 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(1,assumption,(~(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)))), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 ((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))) | member(tptp_fun_Y_47(R!55, A!57), A!57)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (member(tptp_fun_Y_47(R!55, A!57), A!57)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 ((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))) | member(tptp_fun_X_48(R!55, A!57), A!57)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (member(tptp_fun_X_48(R!55, A!57), A!57)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (^[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)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(7,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)))))))) <=> ![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))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (^[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)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(9,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)))))))) <=> ![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))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.43 tff(10,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)))))))) <=> ![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))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (^[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))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(12,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)))))) <=> ![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))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (((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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 ((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)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (((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)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (((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)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 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')).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (~![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.44 tff(28,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))))))),
% 0.19/0.44 inference(and_elim,[status(thm)],[27])).
% 0.19/0.44 tff(29,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))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[28, 12])).
% 0.19/0.44 tff(30,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))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[29, 10])).
% 0.19/0.44 tff(31,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_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))) | (~((~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))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(32,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_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))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(33,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_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)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (~((~((~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))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[33, 30, 5, 3])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (((~((~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)))))) | ((~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)))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((~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))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 ((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_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (apply(R!55, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_47(R!55, A!57))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[37, 1])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 ((~((~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))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 ((~((~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))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.44 tff(41,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_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)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[40, 36])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (((~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)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (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)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (((~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)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (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(unit_resolution,[status(thm)],[44, 41])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (((~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)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (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(unit_resolution,[status(thm)],[46, 41])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (((~![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_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_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(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))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (((~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_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(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))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 ((~((~((~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))) | (~((~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)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (((~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))) | (~((~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))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 (((~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_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(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))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (((~![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_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(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)))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (((~![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_X_48(R!55, A!57), A!57)) | (~member(tptp_fun_Y_47(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))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[53, 48])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 ((~![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))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 ((~![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_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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (~((~((~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))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[56, 30, 5, 3])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (((~((~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))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 ((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_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (~apply(R!55, tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[60, 1])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 ((~(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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 ((~(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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[63, 59])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (((~![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_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)))))) <=> ((~![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_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)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (((~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))))) <=> ((~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)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (((~![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)))) | ((~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))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 (((~![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)))) | (~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)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 ((~![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)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), Y)))) | (~member(tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_48(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_47(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_47(R!55, A!57), tptp_fun_X_48(R!55, A!57))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[70, 64, 47, 45, 43])).
% 0.19/0.47 tff(72,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(73,assumption,(~(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)))), introduced(assumption)).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 ((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))) | member(tptp_fun_Y_50(R!55, A!57), A!57)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 (member(tptp_fun_Y_50(R!55, A!57), A!57)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (^[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)))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 (![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))))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (^[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(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))))), 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)))))))), ((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, 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))))))))), rewrite((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, 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) | (~((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, 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)))))) <=> (((~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) | (~((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, 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))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 (![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)))))) <=> ![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))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.48 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')).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.48 tff(93,plain,(
% 0.19/0.48 ![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))))))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[92])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[95, 82])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (![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))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[96, 77])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (((~![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) | (~((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))))))))))) <=> ((~![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) | (~((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)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 ((~((~((~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) | (~((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))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 (((~![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) | (~((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)))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (((~![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) | (~((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)))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 ((~![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))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 ((~![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) | (~((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))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 (~((~(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)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (((~(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)) | (~((~![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)))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 ((~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))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 (maps(F!58, A!57, B!56)),
% 0.19/0.49 inference(and_elim,[status(thm)],[27])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 ((~((~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))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 ((~((~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))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (~((~![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)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (((~![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))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 (![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))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 (((~![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))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(114,plain,
% 0.19/0.50 ((~![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))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 ((~![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)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 (~((~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))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[115, 112, 75])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (((~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))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 (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))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 (((~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)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 (member(tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58), B!56)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 ((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))) | member(tptp_fun_Z_49(R!55, A!57), A!57)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 (member(tptp_fun_Z_49(R!55, A!57), A!57)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[121, 73])).
% 0.19/0.50 tff(123,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_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))) | (~((~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))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(124,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_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))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(125,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_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)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 (~((~((~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))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[125, 30, 75, 122])).
% 0.19/0.50 tff(127,plain,
% 0.19/0.50 (((~((~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)))))) | ((~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)))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(128,plain,
% 0.19/0.50 ((~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))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.50 tff(129,plain,
% 0.19/0.50 ((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))) | apply(R!55, tptp_fun_Y_50(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(130,plain,
% 0.19/0.50 (apply(R!55, tptp_fun_Y_50(R!55, A!57), tptp_fun_Z_49(R!55, A!57))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[129, 73])).
% 0.19/0.50 tff(131,plain,
% 0.19/0.50 ((~((~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))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(132,plain,
% 0.19/0.50 ((~((~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))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 (~((~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)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[132, 128])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 (((~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)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.50 tff(136,plain,
% 0.19/0.50 (((~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)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(137,plain,
% 0.19/0.50 (member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[136, 133])).
% 0.19/0.50 tff(138,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(139,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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[138, 110])).
% 0.19/0.50 tff(140,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)) | (~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_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)) | (~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_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))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(141,plain,
% 0.19/0.51 (((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)) | (~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_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))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(142,plain,
% 0.19/0.51 (((~![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)) | (~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_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)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[141])).
% 0.19/0.51 tff(143,plain,
% 0.19/0.51 (((~![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)) | (~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_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))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[142, 140])).
% 0.19/0.51 tff(144,plain,
% 0.19/0.51 ((~![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)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(145,plain,
% 0.19/0.51 ((~![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)) | (~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_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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.51 tff(146,plain,
% 0.19/0.51 (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))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[145, 139, 75, 137, 135, 120, 118])).
% 0.19/0.51 tff(147,plain,
% 0.19/0.51 ((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))) | member(tptp_fun_X_51(R!55, A!57), A!57)),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(148,plain,
% 0.19/0.51 (member(tptp_fun_X_51(R!55, A!57), A!57)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[147, 73])).
% 0.19/0.51 tff(149,plain,
% 0.19/0.51 (((~![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))) | (~((~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))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(150,plain,
% 0.19/0.51 ((~![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))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(151,plain,
% 0.19/0.51 ((~![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)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.51 tff(152,plain,
% 0.19/0.51 (~((~((~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))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[151, 30, 148, 75])).
% 0.19/0.51 tff(153,plain,
% 0.19/0.51 (((~((~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)))))) | ((~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)))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(154,plain,
% 0.19/0.51 ((~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))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.19/0.51 tff(155,plain,
% 0.19/0.51 ((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))) | apply(R!55, tptp_fun_X_51(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(156,plain,
% 0.19/0.51 (apply(R!55, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_50(R!55, A!57))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[155, 73])).
% 0.19/0.51 tff(157,plain,
% 0.19/0.51 ((~((~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))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(158,plain,
% 0.19/0.51 ((~((~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))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.19/0.51 tff(159,plain,
% 0.19/0.51 (~((~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)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[158, 154])).
% 0.19/0.51 tff(160,plain,
% 0.19/0.51 (((~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)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(161,plain,
% 0.19/0.51 (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)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.52 tff(162,plain,
% 0.19/0.52 (((~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)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(163,plain,
% 0.19/0.52 (member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.19/0.52 tff(164,plain,
% 0.19/0.52 (((~![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)) | (~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_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)) | (~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_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))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(165,plain,
% 0.19/0.52 (((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)) | (~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_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))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(166,plain,
% 0.19/0.52 (((~![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)) | (~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_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)))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.52 tff(167,plain,
% 0.19/0.52 (((~![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)) | (~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_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))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[166, 164])).
% 0.19/0.52 tff(168,plain,
% 0.19/0.52 ((~![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)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(169,plain,
% 0.19/0.52 ((~![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)) | (~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_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)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.52 tff(170,plain,
% 0.19/0.52 (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))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[169, 139, 75, 163, 161, 120, 118])).
% 0.19/0.52 tff(171,plain,
% 0.19/0.52 (tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)) = tptp_fun_Y_3(tptp_fun_Y_50(R!55, A!57), B!56, F!58)),
% 0.19/0.52 inference(symmetry,[status(thm)],[170])).
% 0.19/0.52 tff(172,plain,
% 0.19/0.52 (tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)) = tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))),
% 0.19/0.52 inference(transitivity,[status(thm)],[171, 146])).
% 0.19/0.52 tff(173,plain,
% 0.19/0.52 (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_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.52 tff(174,plain,
% 0.19/0.52 (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_Y_50(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)))),
% 0.19/0.52 inference(symmetry,[status(thm)],[173])).
% 0.19/0.52 tff(175,plain,
% 0.19/0.52 ((~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_Y_50(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))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.52 tff(176,plain,
% 0.19/0.52 (((~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)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(177,plain,
% 0.19/0.52 (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)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[176, 133])).
% 0.19/0.52 tff(178,plain,
% 0.19/0.52 (((~![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))) | (~((~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))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(179,plain,
% 0.19/0.52 ((~![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))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(180,plain,
% 0.19/0.52 ((~![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)))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.52 tff(181,plain,
% 0.19/0.52 (~((~((~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))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[180, 30, 148, 122])).
% 0.19/0.52 tff(182,plain,
% 0.19/0.52 (((~((~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)))))) | (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))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(183,plain,
% 0.19/0.52 (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)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.19/0.52 tff(184,plain,
% 0.19/0.52 ((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))) | (~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(185,plain,
% 0.19/0.53 (~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)],[184, 73])).
% 0.19/0.53 tff(186,plain,
% 0.19/0.53 ((~(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)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(187,plain,
% 0.19/0.53 ((~(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)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.19/0.53 tff(188,plain,
% 0.19/0.53 (![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)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[187, 183])).
% 0.19/0.53 tff(189,plain,
% 0.19/0.53 (((~![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_Z_49(R!55, A!57), tptp_fun_Y_50(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_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)))))) <=> ((~![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_Z_49(R!55, A!57), tptp_fun_Y_50(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_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)))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(190,plain,
% 0.19/0.53 ((~![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_Z_49(R!55, A!57), tptp_fun_Y_50(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_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)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(191,plain,
% 0.19/0.53 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), Y)) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), Y)))) | (~member(tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))) | (~apply(F!58, tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.53 tff(192,plain,
% 0.19/0.53 (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Z_49(R!55, A!57), tptp_fun_Y_50(R!55, A!57)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[191, 188, 137, 177])).
% 0.19/0.53 tff(193,plain,
% 0.19/0.53 (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[192, 175])).
% 0.19/0.53 tff(194,plain,
% 0.19/0.53 (((~member(tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)), B!56)) | (~apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))) | (~apply(F!58, tptp_fun_Y_50(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57))))) | apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(195,plain,
% 0.19/0.53 (apply(F!58, tptp_fun_X_51(R!55, A!57), tptp_fun_Y_59(tptp_fun_Y_50(R!55, A!57), tptp_fun_X_51(R!55, A!57)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[194, 159])).
% 0.19/0.53 tff(196,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[195, 193])).
% 0.19/0.53 tff(197,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(198,plain,
% 0.19/0.53 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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)))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(199,plain,
% 0.19/0.53 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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))))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[198])).
% 0.19/0.53 tff(200,plain,
% 0.19/0.53 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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)))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(201,plain,
% 0.19/0.53 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[200])).
% 0.19/0.53 tff(202,plain,
% 0.19/0.53 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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)))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(203,plain,
% 0.19/0.53 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[202])).
% 0.19/0.53 tff(204,plain,
% 0.19/0.53 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[203, 201])).
% 0.19/0.53 tff(205,plain,
% 0.19/0.53 (^[A: $i, R: $i] : trans(monotonicity(rewrite(((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(206,plain,
% 0.19/0.53 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_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))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.53 tff(207,plain,
% 0.19/0.53 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_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))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(208,plain,
% 0.19/0.53 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_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)))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[207])).
% 0.19/0.53 tff(209,plain,
% 0.19/0.53 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(210,plain,
% 0.19/0.53 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(211,plain,
% 0.19/0.53 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.53 tff(212,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')).
% 0.19/0.54 tff(213,plain,
% 0.19/0.54 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.19/0.54 tff(214,plain,
% 0.19/0.54 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.19/0.54 tff(215,plain,(
% 0.19/0.54 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_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))))))))),
% 0.19/0.54 inference(skolemize,[status(sab)],[214])).
% 0.19/0.54 tff(216,plain,
% 0.19/0.54 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_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)))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.19/0.54 tff(217,plain,
% 0.19/0.54 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[216, 206])).
% 0.19/0.54 tff(218,plain,
% 0.19/0.54 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~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))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[217, 204])).
% 0.19/0.54 tff(219,plain,
% 0.19/0.54 (![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))))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[218, 199])).
% 0.19/0.54 tff(220,plain,
% 0.19/0.54 (((~![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, 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)))) | (~(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, 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))))))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(221,plain,
% 0.19/0.54 ((~((~(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)))) | (~(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, 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)))))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(222,plain,
% 0.19/0.54 (((~![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)))) | (~(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, 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))))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[221])).
% 0.19/0.54 tff(223,plain,
% 0.19/0.54 (((~![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)))) | (~(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, 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))))))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[222, 220])).
% 0.19/0.54 tff(224,plain,
% 0.19/0.54 ((~![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))))))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(225,plain,
% 0.19/0.54 ((~![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, 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)))))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.19/0.55 tff(226,plain,
% 0.19/0.55 (~((~(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, 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))))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[225, 219])).
% 0.19/0.55 tff(227,plain,
% 0.19/0.55 (((~(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, 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)))) | (~(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)))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(228,plain,
% 0.19/0.55 (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))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.41/0.55 tff(229,plain,
% 0.41/0.55 (~equivalence(R!55, A!57)),
% 0.41/0.55 inference(and_elim,[status(thm)],[27])).
% 0.41/0.55 tff(230,plain,
% 0.41/0.55 ((~(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) | (~((~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))))),
% 0.41/0.55 inference(tautology,[status(thm)],[])).
% 0.41/0.55 tff(231,plain,
% 0.41/0.55 ((~(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)))))) | (~((~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))))),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.41/0.55 tff(232,plain,
% 0.41/0.55 ((~((~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))))),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[231, 228])).
% 0.41/0.55 tff(233,plain,
% 0.41/0.55 (~((~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)))),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[232, 197, 72])).
% 0.41/0.55 tff(234,plain,
% 0.41/0.55 (((~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)),
% 0.41/0.55 inference(tautology,[status(thm)],[])).
% 0.41/0.55 tff(235,plain,
% 0.41/0.55 (member(tptp_fun_X_46(R!55, A!57), A!57)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.41/0.55 tff(236,plain,
% 0.41/0.55 (((~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)))),
% 0.41/0.55 inference(tautology,[status(thm)],[])).
% 0.41/0.55 tff(237,plain,
% 0.41/0.55 (~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[236, 233])).
% 0.41/0.55 tff(238,assumption,(member(tptp_fun_X_46(R!55, A!57), A!57)), introduced(assumption)).
% 0.41/0.55 tff(239,plain,
% 0.41/0.55 (((~![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))))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(240,plain,
% 0.41/0.55 ((~![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))))))),
% 0.41/0.55 inference(quant_inst,[status(thm)],[])).
% 0.41/0.55 tff(241,plain,
% 0.41/0.55 ((~![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)))))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.41/0.55 tff(242,plain,
% 0.41/0.55 (~((~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))))),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[241, 112, 238])).
% 0.41/0.55 tff(243,plain,
% 0.41/0.55 (((~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))),
% 0.41/0.55 inference(tautology,[status(thm)],[])).
% 0.41/0.55 tff(244,plain,
% 0.41/0.55 (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))),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.41/0.55 tff(245,plain,
% 0.41/0.55 (((~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)),
% 0.41/0.55 inference(tautology,[status(thm)],[])).
% 0.41/0.55 tff(246,plain,
% 0.41/0.55 (member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[245, 242])).
% 0.41/0.55 tff(247,plain,
% 0.41/0.55 (((~![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))) | (~((~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(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))) | (~((~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(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))))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(248,plain,
% 0.41/0.56 (((~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(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))) | (~((~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(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))))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(249,plain,
% 0.41/0.56 ((~((~((~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))) | (~((~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(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)))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(250,plain,
% 0.41/0.56 (((~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))) | (~((~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(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))))))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[249])).
% 0.41/0.56 tff(251,plain,
% 0.41/0.56 (((~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))) | (~((~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(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))))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[250, 248])).
% 0.41/0.56 tff(252,plain,
% 0.41/0.56 (((~![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_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))) | (~((~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(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)))))))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[251])).
% 0.41/0.56 tff(253,plain,
% 0.41/0.56 (((~![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_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))) | (~((~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(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))))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[252, 247])).
% 0.41/0.56 tff(254,plain,
% 0.41/0.56 ((~![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_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))))))))),
% 0.41/0.56 inference(quant_inst,[status(thm)],[])).
% 0.41/0.56 tff(255,plain,
% 0.41/0.56 ((~![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_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(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)))))))),
% 0.41/0.56 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.41/0.56 tff(256,plain,
% 0.41/0.56 (~((~((~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(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))))))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[255, 30, 238])).
% 0.41/0.57 tff(257,plain,
% 0.41/0.57 (((~((~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(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))))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(258,plain,
% 0.41/0.57 (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)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[257, 256])).
% 0.41/0.57 tff(259,assumption,(~apply(R!55, tptp_fun_X_46(R!55, A!57), tptp_fun_X_46(R!55, A!57))), introduced(assumption)).
% 0.41/0.57 tff(260,plain,
% 0.41/0.57 ((~(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(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)))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(261,plain,
% 0.41/0.57 ((~(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))))) | ![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.41/0.57 tff(262,plain,
% 0.41/0.57 (![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[261, 258])).
% 0.41/0.57 tff(263,plain,
% 0.41/0.57 (((~![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))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(264,plain,
% 0.41/0.57 ((~![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))))),
% 0.41/0.57 inference(quant_inst,[status(thm)],[])).
% 0.41/0.57 tff(265,plain,
% 0.41/0.57 ((~![Y: $i] : ((~member(Y, B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58), B!56)) | (~apply(F!58, tptp_fun_X_46(R!55, A!57), tptp_fun_Y_3(tptp_fun_X_46(R!55, A!57), B!56, F!58)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.41/0.57 tff(266,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[265, 262, 246, 244])).
% 0.41/0.57 tff(267,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,[]))).
% 0.41/0.57 tff(268,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[267, 237, 235])).
% 0.41/0.57 % SZS output end Proof
%------------------------------------------------------------------------------