TSTP Solution File: SET763+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET763+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 05:07:55 EDT 2022
% Result : Theorem 25.28s 16.46s
% Output : Proof 25.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET763+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 07:50:29 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.
% 25.28/16.46 % SZS status Theorem
% 25.28/16.46 % SZS output start Proof
% 25.28/16.46 tff(member_type, type, (
% 25.28/16.46 member: ( $i * $i ) > $o)).
% 25.28/16.46 tff(empty_set_type, type, (
% 25.28/16.46 empty_set: $i)).
% 25.28/16.46 tff(tptp_fun_Y_3_type, type, (
% 25.28/16.46 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 25.28/16.46 tff(tptp_fun_F_42_type, type, (
% 25.28/16.46 tptp_fun_F_42: $i)).
% 25.28/16.46 tff(tptp_fun_B_40_type, type, (
% 25.28/16.46 tptp_fun_B_40: $i)).
% 25.28/16.46 tff(tptp_fun_X_0_type, type, (
% 25.28/16.46 tptp_fun_X_0: ( $i * $i ) > $i)).
% 25.28/16.46 tff(tptp_fun_X_39_type, type, (
% 25.28/16.46 tptp_fun_X_39: $i)).
% 25.28/16.46 tff(image2_type, type, (
% 25.28/16.46 image2: ( $i * $i ) > $i)).
% 25.28/16.46 tff(apply_type, type, (
% 25.28/16.46 apply: ( $i * $i * $i ) > $o)).
% 25.28/16.46 tff(tptp_fun_X_23_type, type, (
% 25.28/16.46 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 25.28/16.46 tff(tptp_fun_A_41_type, type, (
% 25.28/16.46 tptp_fun_A_41: $i)).
% 25.28/16.46 tff(subset_type, type, (
% 25.28/16.46 subset: ( $i * $i ) > $o)).
% 25.28/16.46 tff(equal_set_type, type, (
% 25.28/16.46 equal_set: ( $i * $i ) > $o)).
% 25.28/16.46 tff(maps_type, type, (
% 25.28/16.46 maps: ( $i * $i * $i ) > $o)).
% 25.28/16.46 tff(tptp_fun_X_4_type, type, (
% 25.28/16.46 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 25.28/16.46 tff(tptp_fun_Y2_5_type, type, (
% 25.28/16.46 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 25.28/16.46 tff(tptp_fun_Y1_6_type, type, (
% 25.28/16.46 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 25.28/16.46 tff(tptp_fun_X_7_type, type, (
% 25.28/16.46 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 25.28/16.46 tff(1,assumption,(~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set)), introduced(assumption)).
% 25.28/16.46 tff(2,assumption,((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))), introduced(assumption)).
% 25.28/16.46 tff(3,plain,
% 25.28/16.46 (^[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))))))))),
% 25.28/16.46 inference(bind,[status(th)],[])).
% 25.28/16.46 tff(4,plain,
% 25.28/16.46 (![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)))))))),
% 25.28/16.46 inference(quant_intro,[status(thm)],[3])).
% 25.28/16.46 tff(5,plain,
% 25.28/16.46 (^[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))))))))),
% 25.28/16.46 inference(bind,[status(th)],[])).
% 25.28/16.46 tff(6,plain,
% 25.28/16.46 (![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)))))))),
% 25.28/16.46 inference(quant_intro,[status(thm)],[5])).
% 25.28/16.46 tff(7,plain,
% 25.28/16.46 (![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)))))))),
% 25.28/16.46 inference(transitivity,[status(thm)],[6, 4])).
% 25.28/16.46 tff(8,plain,
% 25.28/16.46 (^[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)))))))))),
% 25.28/16.46 inference(bind,[status(th)],[])).
% 25.28/16.46 tff(9,plain,
% 25.28/16.46 (![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)))))))),
% 25.28/16.46 inference(quant_intro,[status(thm)],[8])).
% 25.28/16.46 tff(10,plain,
% 25.28/16.46 (![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)))),
% 25.28/16.46 inference(rewrite,[status(thm)],[])).
% 25.28/16.46 tff(11,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')).
% 25.28/16.46 tff(12,plain,
% 25.28/16.46 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 25.28/16.46 inference(modus_ponens,[status(thm)],[11, 10])).
% 25.28/16.46 tff(13,plain,(
% 25.28/16.46 ![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)))))),
% 25.28/16.46 inference(skolemize,[status(sab)],[12])).
% 25.28/16.46 tff(14,plain,
% 25.28/16.46 (![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)))))))),
% 25.28/16.46 inference(modus_ponens,[status(thm)],[13, 9])).
% 25.28/16.46 tff(15,plain,
% 25.28/16.46 (![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)))))))),
% 25.28/16.46 inference(modus_ponens,[status(thm)],[14, 7])).
% 25.28/16.46 tff(16,plain,
% 25.28/16.46 (((~![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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))))),
% 25.28/16.46 inference(rewrite,[status(thm)],[])).
% 25.28/16.46 tff(17,plain,
% 25.28/16.46 ((~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))) <=> (~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))))),
% 25.28/16.46 inference(rewrite,[status(thm)],[])).
% 25.28/16.46 tff(18,plain,
% 25.28/16.46 (((~![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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))))),
% 25.28/16.47 inference(monotonicity,[status(thm)],[17])).
% 25.28/16.47 tff(19,plain,
% 25.28/16.47 (((~![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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))))),
% 25.28/16.47 inference(transitivity,[status(thm)],[18, 16])).
% 25.28/16.47 tff(20,plain,
% 25.28/16.47 ((~![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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))),
% 25.28/16.47 inference(quant_inst,[status(thm)],[])).
% 25.28/16.47 tff(21,plain,
% 25.28/16.47 ((~![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_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 25.28/16.47 tff(22,plain,
% 25.28/16.47 ($false),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[21, 15, 2])).
% 25.28/16.47 tff(23,plain,(~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))), inference(lemma,lemma(discharge,[]))).
% 25.28/16.47 tff(24,plain,
% 25.28/16.47 (((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))) | (member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(25,plain,
% 25.28/16.47 (member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[24, 23])).
% 25.28/16.47 tff(26,assumption,(![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))), introduced(assumption)).
% 25.28/16.47 tff(27,plain,
% 25.28/16.47 (^[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))))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(28,plain,
% 25.28/16.47 (![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)))))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[27])).
% 25.28/16.47 tff(29,plain,
% 25.28/16.47 (^[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))))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(30,plain,
% 25.28/16.47 (![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)))))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[29])).
% 25.28/16.47 tff(31,plain,
% 25.28/16.47 (![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)))))))),
% 25.28/16.47 inference(transitivity,[status(thm)],[30, 28])).
% 25.28/16.47 tff(32,plain,
% 25.28/16.47 (^[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)))))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(33,plain,
% 25.28/16.47 (![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)))))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[32])).
% 25.28/16.47 tff(34,plain,
% 25.28/16.47 (![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)))),
% 25.28/16.47 inference(rewrite,[status(thm)],[])).
% 25.28/16.47 tff(35,plain,
% 25.28/16.47 (^[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))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(36,plain,
% 25.28/16.47 (![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)))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[35])).
% 25.28/16.47 tff(37,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')).
% 25.28/16.47 tff(38,plain,
% 25.28/16.47 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[37, 36])).
% 25.28/16.47 tff(39,plain,
% 25.28/16.47 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[38, 34])).
% 25.28/16.47 tff(40,plain,(
% 25.28/16.47 ![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)))))),
% 25.28/16.47 inference(skolemize,[status(sab)],[39])).
% 25.28/16.47 tff(41,plain,
% 25.28/16.47 (![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)))))))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[40, 33])).
% 25.28/16.47 tff(42,plain,
% 25.28/16.47 (![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)))))))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[41, 31])).
% 25.28/16.47 tff(43,plain,
% 25.28/16.47 ((~![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(X!39, empty_set)) | ![X: $i] : ((~member(X, X!39)) | member(X, empty_set)))) | (~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))))))),
% 25.28/16.47 inference(quant_inst,[status(thm)],[])).
% 25.28/16.47 tff(44,plain,
% 25.28/16.47 (~((~((~subset(X!39, empty_set)) | ![X: $i] : ((~member(X, X!39)) | member(X, empty_set)))) | (~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))))))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[43, 42])).
% 25.28/16.47 tff(45,plain,
% 25.28/16.47 (((~((~subset(X!39, empty_set)) | ![X: $i] : ((~member(X, X!39)) | member(X, empty_set)))) | (~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))))) | (subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(46,plain,
% 25.28/16.47 (subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[45, 44])).
% 25.28/16.47 tff(47,assumption,((~((~subset(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))))), introduced(assumption)).
% 25.28/16.47 tff(48,plain,
% 25.28/16.47 ((~![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(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))))))),
% 25.28/16.47 inference(quant_inst,[status(thm)],[])).
% 25.28/16.47 tff(49,plain,
% 25.28/16.47 ($false),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[48, 42, 47])).
% 25.28/16.47 tff(50,plain,(~((~((~subset(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))))), inference(lemma,lemma(discharge,[]))).
% 25.28/16.47 tff(51,plain,
% 25.28/16.47 (((~((~subset(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))))) | (subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(52,plain,
% 25.28/16.47 (subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[51, 50])).
% 25.28/16.47 tff(53,assumption,(member(tptp_fun_X_0(X!39, empty_set), empty_set)), introduced(assumption)).
% 25.28/16.47 tff(54,plain,
% 25.28/16.47 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(55,plain,
% 25.28/16.47 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[54])).
% 25.28/16.47 tff(56,plain,
% 25.28/16.47 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 25.28/16.47 inference(rewrite,[status(thm)],[])).
% 25.28/16.47 tff(57,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','empty_set')).
% 25.28/16.47 tff(58,plain,
% 25.28/16.47 (![X: $i] : (~member(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 25.28/16.47 tff(59,plain,(
% 25.28/16.47 ![X: $i] : (~member(X, empty_set))),
% 25.28/16.47 inference(skolemize,[status(sab)],[58])).
% 25.28/16.47 tff(60,plain,
% 25.28/16.47 (![X: $i] : (~member(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[59, 55])).
% 25.28/16.47 tff(61,plain,
% 25.28/16.47 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(X!39, empty_set), empty_set))),
% 25.28/16.47 inference(quant_inst,[status(thm)],[])).
% 25.28/16.47 tff(62,plain,
% 25.28/16.47 ($false),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[61, 60, 53])).
% 25.28/16.47 tff(63,plain,(~member(tptp_fun_X_0(X!39, empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 25.28/16.47 tff(64,plain,
% 25.28/16.47 (((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)) | member(tptp_fun_X_0(X!39, empty_set), empty_set)),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(65,plain,
% 25.28/16.47 ((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[64, 63])).
% 25.28/16.47 tff(66,plain,
% 25.28/16.47 ((~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))) | subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(67,plain,
% 25.28/16.47 ((~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))) | subset(empty_set, X!39)),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[66, 65])).
% 25.28/16.47 tff(68,plain,
% 25.28/16.47 (subset(empty_set, X!39)),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[67, 52])).
% 25.28/16.47 tff(69,plain,
% 25.28/16.47 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(70,plain,
% 25.28/16.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[69])).
% 25.28/16.47 tff(71,plain,
% 25.28/16.47 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(72,plain,
% 25.28/16.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[71])).
% 25.28/16.47 tff(73,plain,
% 25.28/16.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 25.28/16.47 inference(rewrite,[status(thm)],[])).
% 25.28/16.47 tff(74,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 25.28/16.47 tff(75,plain,
% 25.28/16.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 25.28/16.47 tff(76,plain,(
% 25.28/16.47 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 25.28/16.47 inference(skolemize,[status(sab)],[75])).
% 25.28/16.47 tff(77,plain,
% 25.28/16.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[76, 72])).
% 25.28/16.47 tff(78,plain,
% 25.28/16.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[77, 70])).
% 25.28/16.47 tff(79,plain,
% 25.28/16.47 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(X!39, empty_set) <=> (~((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))))),
% 25.28/16.47 inference(quant_inst,[status(thm)],[])).
% 25.28/16.47 tff(80,plain,
% 25.28/16.47 (equal_set(X!39, empty_set) <=> (~((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[79, 78])).
% 25.28/16.47 tff(81,plain,
% 25.28/16.47 ((~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set)))),
% 25.28/16.47 inference(rewrite,[status(thm)],[])).
% 25.28/16.47 tff(82,plain,
% 25.28/16.47 ((~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & subset(X, A)) & equal_set(image2(F, X), empty_set)) => equal_set(X, empty_set))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set)))),
% 25.28/16.47 inference(rewrite,[status(thm)],[])).
% 25.28/16.47 tff(83,axiom,(~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & subset(X, A)) & equal_set(image2(F, X), empty_set)) => equal_set(X, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIIa13')).
% 25.28/16.47 tff(84,plain,
% 25.28/16.47 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[83, 82])).
% 25.28/16.47 tff(85,plain,
% 25.28/16.47 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[84, 81])).
% 25.28/16.47 tff(86,plain,
% 25.28/16.47 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[85, 81])).
% 25.28/16.47 tff(87,plain,
% 25.28/16.47 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[86, 81])).
% 25.28/16.47 tff(88,plain,
% 25.28/16.47 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[87, 81])).
% 25.28/16.47 tff(89,plain,
% 25.28/16.47 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[88, 81])).
% 25.28/16.47 tff(90,plain,
% 25.28/16.47 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[89, 81])).
% 25.28/16.47 tff(91,plain,(
% 25.28/16.47 ~((~(maps(F!42, A!41, B!40) & subset(X!39, A!41) & equal_set(image2(F!42, X!39), empty_set))) | equal_set(X!39, empty_set))),
% 25.28/16.47 inference(skolemize,[status(sab)],[90])).
% 25.28/16.47 tff(92,plain,
% 25.28/16.47 (~equal_set(X!39, empty_set)),
% 25.28/16.47 inference(or_elim,[status(thm)],[91])).
% 25.28/16.47 tff(93,plain,
% 25.28/16.47 ((~(equal_set(X!39, empty_set) <=> (~((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))))) | equal_set(X!39, empty_set) | ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(94,plain,
% 25.28/16.47 ((~(equal_set(X!39, empty_set) <=> (~((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))))) | ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[93, 92])).
% 25.28/16.47 tff(95,plain,
% 25.28/16.47 ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[94, 80])).
% 25.28/16.47 tff(96,plain,
% 25.28/16.47 ((~((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))) | (~subset(X!39, empty_set)) | (~subset(empty_set, X!39))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(97,plain,
% 25.28/16.47 ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[96, 95])).
% 25.28/16.47 tff(98,plain,
% 25.28/16.47 (~subset(X!39, empty_set)),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[97, 68])).
% 25.28/16.47 tff(99,plain,
% 25.28/16.47 ((~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))))) | subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(100,plain,
% 25.28/16.47 ((~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))))) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[99, 98])).
% 25.28/16.47 tff(101,plain,
% 25.28/16.47 (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[100, 46])).
% 25.28/16.47 tff(102,plain,
% 25.28/16.47 (((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)) | member(tptp_fun_X_0(empty_set, X!39), X!39)),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(103,plain,
% 25.28/16.47 (member(tptp_fun_X_0(empty_set, X!39), X!39)),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[102, 101])).
% 25.28/16.47 tff(104,plain,
% 25.28/16.47 ((~![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(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41)))))))),
% 25.28/16.47 inference(quant_inst,[status(thm)],[])).
% 25.28/16.47 tff(105,plain,
% 25.28/16.47 (~((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41))))))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[104, 42])).
% 25.28/16.47 tff(106,plain,
% 25.28/16.47 (((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41)))))) | ((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(107,plain,
% 25.28/16.47 ((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[106, 105])).
% 25.28/16.47 tff(108,plain,
% 25.28/16.47 (maps(F!42, A!41, B!40) & subset(X!39, A!41) & equal_set(image2(F!42, X!39), empty_set)),
% 25.28/16.47 inference(or_elim,[status(thm)],[91])).
% 25.28/16.47 tff(109,plain,
% 25.28/16.47 (subset(X!39, A!41)),
% 25.28/16.47 inference(and_elim,[status(thm)],[108])).
% 25.28/16.47 tff(110,plain,
% 25.28/16.47 ((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 25.28/16.47 inference(tautology,[status(thm)],[])).
% 25.28/16.47 tff(111,plain,
% 25.28/16.47 ((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[110, 109])).
% 25.28/16.47 tff(112,plain,
% 25.28/16.47 (![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[111, 107])).
% 25.28/16.47 tff(113,plain,
% 25.28/16.47 (((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41))) <=> ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41))),
% 25.28/16.47 inference(rewrite,[status(thm)],[])).
% 25.28/16.47 tff(114,plain,
% 25.28/16.47 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41))),
% 25.28/16.47 inference(quant_inst,[status(thm)],[])).
% 25.28/16.47 tff(115,plain,
% 25.28/16.47 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41)),
% 25.28/16.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 25.28/16.47 tff(116,plain,
% 25.28/16.47 (member(tptp_fun_X_0(empty_set, X!39), A!41)),
% 25.28/16.47 inference(unit_resolution,[status(thm)],[115, 112, 103])).
% 25.28/16.47 tff(117,plain,
% 25.28/16.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(118,plain,
% 25.28/16.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[117])).
% 25.28/16.47 tff(119,plain,
% 25.28/16.47 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(120,plain,
% 25.28/16.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[119])).
% 25.28/16.47 tff(121,plain,
% 25.28/16.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 25.28/16.47 inference(bind,[status(th)],[])).
% 25.28/16.47 tff(122,plain,
% 25.28/16.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 25.28/16.47 inference(quant_intro,[status(thm)],[121])).
% 25.28/16.47 tff(123,plain,
% 25.28/16.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 25.40/16.47 inference(transitivity,[status(thm)],[122, 120])).
% 25.40/16.47 tff(124,plain,
% 25.40/16.47 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))), rewrite((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 25.40/16.48 inference(bind,[status(th)],[])).
% 25.40/16.48 tff(125,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 25.40/16.48 inference(quant_intro,[status(thm)],[124])).
% 25.40/16.48 tff(126,plain,
% 25.40/16.48 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))))),
% 25.40/16.48 inference(bind,[status(th)],[])).
% 25.40/16.48 tff(127,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 25.40/16.48 inference(quant_intro,[status(thm)],[126])).
% 25.40/16.48 tff(128,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 25.40/16.48 inference(rewrite,[status(thm)],[])).
% 25.40/16.48 tff(129,plain,
% 25.40/16.48 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 25.40/16.48 inference(bind,[status(th)],[])).
% 25.40/16.48 tff(130,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 25.40/16.48 inference(quant_intro,[status(thm)],[129])).
% 25.40/16.48 tff(131,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 25.40/16.48 tff(132,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 25.40/16.48 inference(modus_ponens,[status(thm)],[131, 130])).
% 25.40/16.48 tff(133,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 25.40/16.48 inference(modus_ponens,[status(thm)],[132, 128])).
% 25.40/16.48 tff(134,plain,(
% 25.40/16.48 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 25.40/16.48 inference(skolemize,[status(sab)],[133])).
% 25.40/16.48 tff(135,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 25.40/16.48 inference(modus_ponens,[status(thm)],[134, 127])).
% 25.40/16.48 tff(136,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 25.40/16.48 inference(modus_ponens,[status(thm)],[135, 125])).
% 25.40/16.48 tff(137,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 25.40/16.48 inference(modus_ponens,[status(thm)],[136, 123])).
% 25.40/16.48 tff(138,plain,
% 25.40/16.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 25.40/16.48 inference(modus_ponens,[status(thm)],[137, 118])).
% 25.40/16.48 tff(139,plain,
% 25.40/16.48 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))),
% 25.40/16.48 inference(quant_inst,[status(thm)],[])).
% 25.40/16.48 tff(140,plain,
% 25.40/16.48 (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))))))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[139, 138])).
% 25.41/16.48 tff(141,plain,
% 25.41/16.48 (((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))) | ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))),
% 25.41/16.48 inference(tautology,[status(thm)],[])).
% 25.41/16.48 tff(142,plain,
% 25.41/16.48 ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[141, 140])).
% 25.41/16.48 tff(143,plain,
% 25.41/16.48 (maps(F!42, A!41, B!40)),
% 25.41/16.48 inference(and_elim,[status(thm)],[108])).
% 25.41/16.48 tff(144,plain,
% 25.41/16.48 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 25.41/16.48 inference(tautology,[status(thm)],[])).
% 25.41/16.48 tff(145,plain,
% 25.41/16.48 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[144, 143])).
% 25.41/16.48 tff(146,plain,
% 25.41/16.48 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[145, 142])).
% 25.41/16.48 tff(147,plain,
% 25.41/16.48 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))) | ![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 25.41/16.48 inference(tautology,[status(thm)],[])).
% 25.41/16.48 tff(148,plain,
% 25.41/16.48 (![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[147, 146])).
% 25.41/16.48 tff(149,plain,
% 25.41/16.48 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))),
% 25.41/16.48 inference(rewrite,[status(thm)],[])).
% 25.41/16.48 tff(150,plain,
% 25.41/16.48 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))),
% 25.41/16.48 inference(quant_inst,[status(thm)],[])).
% 25.41/16.48 tff(151,plain,
% 25.41/16.48 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))),
% 25.41/16.48 inference(modus_ponens,[status(thm)],[150, 149])).
% 25.41/16.48 tff(152,plain,
% 25.41/16.48 (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[151, 148, 116])).
% 25.41/16.48 tff(153,plain,
% 25.41/16.48 (((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))) | apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))),
% 25.41/16.48 inference(tautology,[status(thm)],[])).
% 25.41/16.48 tff(154,plain,
% 25.41/16.48 (apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[153, 152])).
% 25.41/16.48 tff(155,plain,
% 25.41/16.48 (((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) <=> ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 25.41/16.48 inference(rewrite,[status(thm)],[])).
% 25.41/16.48 tff(156,plain,
% 25.41/16.48 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 25.41/16.48 inference(quant_inst,[status(thm)],[])).
% 25.41/16.48 tff(157,plain,
% 25.41/16.48 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))),
% 25.41/16.48 inference(modus_ponens,[status(thm)],[156, 155])).
% 25.41/16.48 tff(158,plain,
% 25.41/16.48 ($false),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[157, 103, 154, 26])).
% 25.41/16.48 tff(159,plain,(~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))), inference(lemma,lemma(discharge,[]))).
% 25.41/16.48 tff(160,plain,
% 25.41/16.48 ((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 25.41/16.48 inference(tautology,[status(thm)],[])).
% 25.41/16.48 tff(161,plain,
% 25.41/16.48 ((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[160, 159])).
% 25.41/16.48 tff(162,plain,
% 25.41/16.48 (member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[161, 25])).
% 25.41/16.48 tff(163,plain,
% 25.41/16.48 ((~![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(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~(subset(image2(F!42, X!39), empty_set) | (~((~member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), image2(F!42, X!39))) | member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), empty_set)))))))),
% 25.41/16.48 inference(quant_inst,[status(thm)],[])).
% 25.41/16.48 tff(164,plain,
% 25.41/16.48 (~((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~(subset(image2(F!42, X!39), empty_set) | (~((~member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), image2(F!42, X!39))) | member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), empty_set))))))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[163, 42])).
% 25.41/16.48 tff(165,plain,
% 25.41/16.48 (((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~(subset(image2(F!42, X!39), empty_set) | (~((~member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), image2(F!42, X!39))) | member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), empty_set)))))) | ((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))),
% 25.41/16.48 inference(tautology,[status(thm)],[])).
% 25.41/16.48 tff(166,plain,
% 25.41/16.48 ((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 25.41/16.48 inference(unit_resolution,[status(thm)],[165, 164])).
% 25.41/16.48 tff(167,plain,
% 25.41/16.48 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set)))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set))))))),
% 25.41/16.48 inference(rewrite,[status(thm)],[])).
% 25.41/16.48 tff(168,plain,
% 25.41/16.48 ((equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39)))))) <=> (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set)))))),
% 25.41/16.48 inference(rewrite,[status(thm)],[])).
% 25.41/16.48 tff(169,plain,
% 25.41/16.48 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set))))))),
% 25.41/16.49 inference(monotonicity,[status(thm)],[168])).
% 25.41/16.49 tff(170,plain,
% 25.41/16.49 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set))))))),
% 25.41/16.49 inference(transitivity,[status(thm)],[169, 167])).
% 25.41/16.49 tff(171,plain,
% 25.41/16.49 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39))))))),
% 25.41/16.49 inference(quant_inst,[status(thm)],[])).
% 25.41/16.49 tff(172,plain,
% 25.41/16.49 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set)))))),
% 25.41/16.49 inference(modus_ponens,[status(thm)],[171, 170])).
% 25.41/16.49 tff(173,plain,
% 25.41/16.49 (equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set))))),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[172, 78])).
% 25.41/16.49 tff(174,plain,
% 25.41/16.49 (equal_set(image2(F!42, X!39), empty_set)),
% 25.41/16.49 inference(and_elim,[status(thm)],[108])).
% 25.41/16.49 tff(175,plain,
% 25.41/16.49 ((~(equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set)))))) | (~equal_set(image2(F!42, X!39), empty_set)) | (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set))))),
% 25.41/16.49 inference(tautology,[status(thm)],[])).
% 25.41/16.49 tff(176,plain,
% 25.41/16.49 ((~(equal_set(image2(F!42, X!39), empty_set) <=> (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set)))))) | (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set))))),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[175, 174])).
% 25.41/16.49 tff(177,plain,
% 25.41/16.49 (~((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set)))),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[176, 173])).
% 25.41/16.49 tff(178,plain,
% 25.41/16.49 (((~subset(empty_set, image2(F!42, X!39))) | (~subset(image2(F!42, X!39), empty_set))) | subset(image2(F!42, X!39), empty_set)),
% 25.41/16.49 inference(tautology,[status(thm)],[])).
% 25.41/16.49 tff(179,plain,
% 25.41/16.49 (subset(image2(F!42, X!39), empty_set)),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[178, 177])).
% 25.41/16.49 tff(180,plain,
% 25.41/16.49 ((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 25.41/16.49 inference(tautology,[status(thm)],[])).
% 25.41/16.49 tff(181,plain,
% 25.41/16.49 ((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[180, 179])).
% 25.41/16.49 tff(182,plain,
% 25.41/16.49 (![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[181, 166])).
% 25.41/16.49 tff(183,plain,
% 25.41/16.49 (((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))) <=> ((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))),
% 25.41/16.49 inference(rewrite,[status(thm)],[])).
% 25.41/16.49 tff(184,plain,
% 25.41/16.49 ((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))),
% 25.41/16.49 inference(quant_inst,[status(thm)],[])).
% 25.41/16.49 tff(185,plain,
% 25.41/16.49 ((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set)),
% 25.41/16.49 inference(modus_ponens,[status(thm)],[184, 183])).
% 25.41/16.49 tff(186,plain,
% 25.41/16.49 ($false),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[185, 182, 162, 1])).
% 25.41/16.49 tff(187,plain,(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set)), inference(lemma,lemma(discharge,[]))).
% 25.41/16.49 tff(188,plain,
% 25.41/16.49 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))),
% 25.41/16.49 inference(quant_inst,[status(thm)],[])).
% 25.41/16.49 tff(189,plain,
% 25.41/16.49 ($false),
% 25.41/16.49 inference(unit_resolution,[status(thm)],[188, 60, 187])).
% 25.41/16.49 % SZS output end Proof
%------------------------------------------------------------------------------