TSTP Solution File: SET731+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET731+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET731+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 : n001.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 07:56:40 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(apply_type, type, (
% 0.21/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_Y_20_type, type, (
% 0.21/0.42 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_G_42_type, type, (
% 0.21/0.42 tptp_fun_G_42: $i)).
% 0.21/0.42 tff(tptp_fun_A_41_type, type, (
% 0.21/0.42 tptp_fun_A_41: $i)).
% 0.21/0.42 tff(tptp_fun_C_39_type, type, (
% 0.21/0.42 tptp_fun_C_39: $i)).
% 0.21/0.42 tff(tptp_fun_X_23_type, type, (
% 0.21/0.42 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_F_43_type, type, (
% 0.21/0.42 tptp_fun_F_43: $i)).
% 0.21/0.42 tff(member_type, type, (
% 0.21/0.42 member: ( $i * $i ) > $o)).
% 0.21/0.42 tff(image2_type, type, (
% 0.21/0.42 image2: ( $i * $i ) > $i)).
% 0.21/0.42 tff(surjective_type, type, (
% 0.21/0.42 surjective: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(subset_type, type, (
% 0.21/0.42 subset: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_B_40_type, type, (
% 0.21/0.42 tptp_fun_B_40: $i)).
% 0.21/0.42 tff(maps_type, type, (
% 0.21/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_E_19_type, type, (
% 0.21/0.42 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[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))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (^[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))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (^[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)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 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/sandbox2/benchmark/Axioms/SET006+1.ax','image2')).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.42 tff(11,plain,(
% 0.21/0.42 ![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)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 ((~![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))))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (~((~((~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)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (((~((~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))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 ((~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)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (((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)))) & (~surjective(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))) & (~surjective(G!42, A!41, C!39)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 ((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)))) <=> (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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (((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)))) & (~surjective(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)))) & (~surjective(G!42, A!41, C!39)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[19])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (((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)))) & (~surjective(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))) & (~surjective(G!42, A!41, C!39)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[20, 18])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 ((~![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))))) | surjective(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))))) | surjective(G, A, C)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 ((~![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)))) => surjective(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))))) | surjective(G, A, C)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 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)))) => surjective(G, A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII22')).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (~![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))))) | surjective(G, A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (~![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))))) | surjective(G, A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (~![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))))) | surjective(G, A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (~![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))))) | surjective(G, A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (~![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))))) | surjective(G, A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (~![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))))) | surjective(G, A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (~![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))))) | surjective(G, A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (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))) & (~surjective(G!42, A!41, C!39))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (image2(F!43, A!41) = C!39),
% 0.21/0.43 inference(and_elim,[status(thm)],[32])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (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)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (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))),
% 0.21/0.43 inference(symmetry,[status(thm)],[34])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (^[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))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (![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)))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (^[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))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (![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)))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (![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)))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[39, 37])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (^[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)))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (![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)))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (^[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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (![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)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.43 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/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.43 tff(51,plain,(
% 0.21/0.43 ![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)))))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[50])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (![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)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (![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)))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (![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)))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[53, 40])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 ((~![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)))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (~((~((~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))))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (((~((~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))))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (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)))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (~surjective(G!42, A!41, C!39)),
% 0.21/0.44 inference(and_elim,[status(thm)],[32])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((~(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)))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 ((~(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)))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (~((~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))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (((~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)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (member(tptp_fun_Y_20(C!39, A!41, G!42), C!39)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (member(tptp_fun_Y_20(C!39, A!41, G!42), image2(F!43, A!41))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[64, 35])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 ((~((~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)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (~((~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))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[66, 65, 17])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (((~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)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (member(tptp_fun_X_23(tptp_fun_Y_20(C!39, A!41, G!42), A!41, F!43), A!41)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~(member(X, A!41) & member(Y, C!39))) | (apply(G!42, X, Y) <=> apply(F!43, X, Y)))),
% 0.21/0.44 inference(and_elim,[status(thm)],[32])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((apply(G!42, X, Y) <=> apply(F!43, X, Y)) | (~member(X, A!41)) | (~member(Y, C!39)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (((~![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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (((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))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (((~![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)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (((~![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))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[79, 77])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 ((~![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)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 ((~![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)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (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))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[82, 76, 64, 69])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (((~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))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (![E: $i] : ((~member(E, A!41)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, A!41, G!42))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[84, 62])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (((~![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 ((~![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))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 (~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))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[88, 85, 69])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (((~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))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (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))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[90, 67])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 ((~(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)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 ((~(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))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[93, 89, 83])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------