TSTP Solution File: SET732+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET732+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:47 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET732+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.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 07:38:10 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.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(apply_type, type, (
% 0.19/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y_20_type, type, (
% 0.19/0.41 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_G_42_type, type, (
% 0.19/0.41 tptp_fun_G_42: $i)).
% 0.19/0.41 tff(tptp_fun_A_41_type, type, (
% 0.19/0.41 tptp_fun_A_41: $i)).
% 0.19/0.41 tff(tptp_fun_C_39_type, type, (
% 0.19/0.41 tptp_fun_C_39: $i)).
% 0.19/0.41 tff(tptp_fun_X_23_type, type, (
% 0.19/0.41 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_F_43_type, type, (
% 0.19/0.41 tptp_fun_F_43: $i)).
% 0.19/0.41 tff(member_type, type, (
% 0.19/0.41 member: ( $i * $i ) > $o)).
% 0.19/0.41 tff(image2_type, type, (
% 0.19/0.41 image2: ( $i * $i ) > $i)).
% 0.19/0.41 tff(one_to_one_type, type, (
% 0.19/0.41 one_to_one: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(injective_type, type, (
% 0.19/0.41 injective: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_B_40_type, type, (
% 0.19/0.41 tptp_fun_B_40: $i)).
% 0.19/0.41 tff(subset_type, type, (
% 0.19/0.41 subset: ( $i * $i ) > $o)).
% 0.19/0.41 tff(maps_type, type, (
% 0.19/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(surjective_type, type, (
% 0.19/0.41 surjective: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_E_19_type, type, (
% 0.19/0.41 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y_16_type, type, (
% 0.19/0.41 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X2_17_type, type, (
% 0.19/0.41 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X1_18_type, type, (
% 0.19/0.41 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X_0_type, type, (
% 0.19/0.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[F: $i, A: $i, Y: $i] : refl((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[F: $i, A: $i, Y: $i] : rewrite((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (^[F: $i, A: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) <=> ((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))), rewrite((member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y))) <=> ![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(9,axiom,(![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','image2')).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.41 tff(11,plain,(
% 0.19/0.41 ![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))))) | (~(member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41)) | ![X: $i] : ((~member(X, A!41)) | (~apply(F!43, X, tptp_fun_Y_20(C!39, A!41, G!42))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (~((~((~member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))))) | (~(member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41)) | ![X: $i] : ((~member(X, A!41)) | (~apply(F!43, X, tptp_fun_Y_20(C!39, A!41, G!42)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (((~((~member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))))) | (~(member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41)) | ![X: $i] : ((~member(X, A!41)) | (~apply(F!43, X, tptp_fun_Y_20(C!39, A!41, G!42))))))) | ((~member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 ((~member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (((maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40)) & (~one_to_one(G!42, A!41, C!39))) <=> (maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40) & (~one_to_one(G!42, A!41, C!39)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 ((maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40)) <=> (maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (((maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40)) & (~one_to_one(G!42, A!41, C!39))) <=> ((maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40)) & (~one_to_one(G!42, A!41, C!39)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (((maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40)) & (~one_to_one(G!42, A!41, C!39))) <=> (maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40) & (~one_to_one(G!42, A!41, C!39)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : (((((maps(F, A, B) & subset(C, B)) & (image2(F, A) = C)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, C)) => (apply(G, X, Y) <=> apply(F, X, Y)))) & injective(F, A, B)) => one_to_one(G, A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(24,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : (((((maps(F, A, B) & subset(C, B)) & (image2(F, A) = C)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, C)) => (apply(G, X, Y) <=> apply(F, X, Y)))) & injective(F, A, B)) => one_to_one(G, A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII23')).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, B) & (image2(F, A) = C) & ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, C))) | (apply(G, X, Y) <=> apply(F, X, Y))) & injective(F, A, B))) | one_to_one(G, A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (maps(F!43, A!41, B!40) & subset(C!39, B!40) & (image2(F!43, A!41) = C!39) & ![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) & injective(F!43, A!41, B!40) & (~one_to_one(G!42, A!41, C!39))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (image2(F!43, A!41) = C!39),
% 0.19/0.42 inference(and_elim,[status(thm)],[32])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41)) <=> member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (member(tptp_fun_Y_20(C!39, A!41, G!42), C!39) <=> member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))),
% 0.19/0.42 inference(symmetry,[status(thm)],[34])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[39, 37])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.43 tff(48,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.43 tff(51,plain,(
% 0.19/0.43 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[50])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[53, 40])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(G!42, A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, G!42), A!41)) | (~apply(G!42, tptp_fun_E_19(Y, A!41, G!42), Y))))))) | (~(surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42)))))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (~((~((~surjective(G!42, A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, G!42), A!41)) | (~apply(G!42, tptp_fun_E_19(Y, A!41, G!42), Y))))))) | (~(surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (((~((~surjective(G!42, A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, G!42), A!41)) | (~apply(G!42, tptp_fun_E_19(Y, A!41, G!42), Y))))))) | (~(surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42)))))))))) | (surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.43 tff(59,assumption,((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))), introduced(assumption)).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.44 tff(70,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','injective')).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.44 tff(73,plain,(
% 0.19/0.44 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[72])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 ((~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))))) <=> (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[81, 75, 59])).
% 0.19/0.45 tff(83,plain,(~((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (((~((~injective(G!42, A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~member(Y, C!39)) | (~member(X1, A!41)) | (~apply(G!42, X1, Y)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))))) | (injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.45 tff(86,assumption,(~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))), introduced(assumption)).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 (((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) | member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 (((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) | member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 (member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : refl(((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39))) <=> ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39))) <=> ![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A!41) & member(Y, C!39)) <=> (~((~member(X, A!41)) | (~member(Y, C!39))))), ((~(member(X, A!41) & member(Y, C!39))) <=> (~(~((~member(X, A!41)) | (~member(Y, C!39))))))), rewrite((~(~((~member(X, A!41)) | (~member(Y, C!39))))) <=> ((~member(X, A!41)) | (~member(Y, C!39)))), ((~(member(X, A!41) & member(Y, C!39))) <=> ((~member(X, A!41)) | (~member(Y, C!39))))), (((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) <=> (((~member(X, A!41)) | (~member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))))), rewrite((((~member(X, A!41)) | (~member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) <=> ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))), (((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) <=> ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y))) <=> ![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[32])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (((apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) <=> ((~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[103, 97, 90, 88])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) | apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(106,plain,
% 0.19/0.46 (apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[105, 86])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 ((~(apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 ((~(apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))) | apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 (apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[108, 104])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 (((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) | member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 (member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[110, 86])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 (((apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) <=> ((~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[114, 112])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[117, 97, 111, 88])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) | apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 (apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[119, 86])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 ((~(apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 ((~(apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))) | apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[122, 118])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.47 tff(134,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.19/0.47 tff(137,plain,(
% 0.19/0.47 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[136])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[138, 128])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40)))) | (~(subset(C!39, B!40) | (~((~member(tptp_fun_X_0(B!40, C!39), C!39)) | member(tptp_fun_X_0(B!40, C!39), B!40)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 (~((~((~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40)))) | (~(subset(C!39, B!40) | (~((~member(tptp_fun_X_0(B!40, C!39), C!39)) | member(tptp_fun_X_0(B!40, C!39), B!40))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 (((~((~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40)))) | (~(subset(C!39, B!40) | (~((~member(tptp_fun_X_0(B!40, C!39), C!39)) | member(tptp_fun_X_0(B!40, C!39), B!40)))))) | ((~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 ((~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (subset(C!39, B!40)),
% 0.19/0.47 inference(and_elim,[status(thm)],[32])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 ((~((~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40)))) | (~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 ((~((~subset(C!39, B!40)) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40)))) | ![X: $i] : ((~member(X, C!39)) | member(X, B!40))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (![X: $i] : ((~member(X, C!39)) | member(X, B!40))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[146, 143])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (((~![X: $i] : ((~member(X, C!39)) | member(X, B!40))) | ((~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | member(tptp_fun_Y_16(C!39, A!41, G!42), B!40))) <=> ((~![X: $i] : ((~member(X, C!39)) | member(X, B!40))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | member(tptp_fun_Y_16(C!39, A!41, G!42), B!40))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 ((~![X: $i] : ((~member(X, C!39)) | member(X, B!40))) | ((~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | member(tptp_fun_Y_16(C!39, A!41, G!42), B!40))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 ((~![X: $i] : ((~member(X, C!39)) | member(X, B!40))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)) | member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 (member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[150, 147, 88])).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))) | (~(tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 (~(tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[152, 86])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 ((~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))) <=> (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.48 tff(158,plain,
% 0.19/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(159,plain,
% 0.19/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.48 tff(160,plain,
% 0.19/0.48 (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[159, 75])).
% 0.19/0.48 tff(161,plain,
% 0.19/0.48 (((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))) | ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(162,plain,
% 0.19/0.48 ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.19/0.48 tff(163,plain,
% 0.19/0.48 (injective(F!43, A!41, B!40)),
% 0.19/0.48 inference(and_elim,[status(thm)],[32])).
% 0.19/0.48 tff(164,plain,
% 0.19/0.48 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(165,plain,
% 0.19/0.48 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.19/0.48 tff(166,plain,
% 0.19/0.48 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[165, 162])).
% 0.19/0.48 tff(167,plain,
% 0.19/0.48 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | (tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(168,plain,
% 0.19/0.48 (((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42)))) <=> ((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(169,plain,
% 0.19/0.48 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.48 tff(170,plain,
% 0.19/0.48 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | (tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.48 tff(171,plain,
% 0.19/0.48 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y)))) | (tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), B!40))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.48 tff(173,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[172, 166, 153, 90, 111, 151, 123, 109])).
% 0.19/0.48 tff(174,plain,((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 ((~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))) | injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(176,plain,
% 0.19/0.48 ((~(injective(G!42, A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, G!42) = tptp_fun_X2_17(C!39, A!41, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, A!41, G!42), tptp_fun_Y_16(C!39, A!41, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, G!42), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, G!42), C!39)))))) | injective(G!42, A!41, C!39)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 (injective(G!42, A!41, C!39)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[176, 85])).
% 0.19/0.48 tff(178,plain,
% 0.19/0.48 (^[F: $i, A: $i, B: $i] : refl((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(179,plain,
% 0.19/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.48 tff(180,plain,
% 0.19/0.48 (^[F: $i, A: $i, B: $i] : rewrite((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(181,plain,
% 0.19/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.49 tff(182,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(183,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.19/0.49 tff(184,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.49 tff(185,plain,(
% 0.19/0.49 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[184])).
% 0.19/0.49 tff(186,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.19/0.49 tff(187,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.19/0.49 tff(188,plain,
% 0.19/0.49 ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(G!42, A!41, C!39) <=> (~((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(189,plain,
% 0.19/0.49 (one_to_one(G!42, A!41, C!39) <=> (~((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.19/0.49 tff(190,plain,
% 0.19/0.49 (~one_to_one(G!42, A!41, C!39)),
% 0.19/0.49 inference(and_elim,[status(thm)],[32])).
% 0.19/0.49 tff(191,plain,
% 0.19/0.49 ((~(one_to_one(G!42, A!41, C!39) <=> (~((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39)))))) | one_to_one(G!42, A!41, C!39) | ((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(192,plain,
% 0.19/0.49 ((~(one_to_one(G!42, A!41, C!39) <=> (~((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39)))))) | ((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.19/0.49 tff(193,plain,
% 0.19/0.49 ((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.19/0.49 tff(194,plain,
% 0.19/0.49 ((~((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39)))) | (~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(195,plain,
% 0.19/0.49 ((~injective(G!42, A!41, C!39)) | (~surjective(G!42, A!41, C!39))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.19/0.49 tff(196,plain,
% 0.19/0.49 (~surjective(G!42, A!41, C!39)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[195, 177])).
% 0.19/0.49 tff(197,plain,
% 0.19/0.49 ((~(surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))))))) | surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42)))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(198,plain,
% 0.19/0.49 ((~(surjective(G!42, A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))))))) | (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42)))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (~((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[198, 58])).
% 0.19/0.49 tff(200,plain,
% 0.19/0.49 (((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42)))))) | member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(201,plain,
% 0.19/0.49 (member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 (member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[201, 35])).
% 0.19/0.49 tff(203,plain,
% 0.19/0.49 ((~((~member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))))) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 (~((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[203, 202, 17])).
% 0.19/0.49 tff(205,plain,
% 0.19/0.49 (((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))) | member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(206,plain,
% 0.19/0.49 (member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.19/0.49 tff(207,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(208,plain,
% 0.19/0.49 (((apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39))) <=> ((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(209,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)))) <=> ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[209, 207])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | ((apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(212,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))) | (~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.49 tff(213,plain,
% 0.19/0.49 (apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[212, 97, 201, 206])).
% 0.19/0.49 tff(214,plain,
% 0.19/0.49 (((~member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42)))))) | ![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(215,plain,
% 0.19/0.49 (![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[214, 199])).
% 0.19/0.49 tff(216,plain,
% 0.19/0.49 (((~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))) | ((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))) <=> ((~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 ((~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))) | ((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(218,plain,
% 0.19/0.50 ((~![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.50 tff(219,plain,
% 0.19/0.50 (~apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[218, 215, 206])).
% 0.19/0.50 tff(220,plain,
% 0.19/0.50 (((~member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))) | apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(221,plain,
% 0.19/0.50 (apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[220, 204])).
% 0.19/0.50 tff(222,plain,
% 0.19/0.50 ((~(apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))) | apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(223,plain,
% 0.19/0.50 ((~(apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)) <=> apply(F!43, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42)))) | apply(G!42, tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, G!42))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.19/0.50 tff(224,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[223, 219, 213])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------