TSTP Solution File: SET759+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET759+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 05:07:54 EDT 2022
% Result : Theorem 0.15s 0.37s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET759+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Sep 3 07:45:39 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.15/0.37 % SZS status Theorem
% 0.15/0.37 % SZS output start Proof
% 0.15/0.37 tff(apply_type, type, (
% 0.15/0.37 apply: ( $i * $i * $i ) > $o)).
% 0.15/0.37 tff(tptp_fun_Y_3_type, type, (
% 0.15/0.37 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_F_42_type, type, (
% 0.15/0.37 tptp_fun_F_42: $i)).
% 0.15/0.37 tff(tptp_fun_B_40_type, type, (
% 0.15/0.37 tptp_fun_B_40: $i)).
% 0.15/0.37 tff(tptp_fun_X_0_type, type, (
% 0.15/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_X_39_type, type, (
% 0.15/0.37 tptp_fun_X_39: $i)).
% 0.15/0.37 tff(inverse_image3_type, type, (
% 0.15/0.37 inverse_image3: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_A_41_type, type, (
% 0.15/0.37 tptp_fun_A_41: $i)).
% 0.15/0.37 tff(image3_type, type, (
% 0.15/0.37 image3: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(member_type, type, (
% 0.15/0.37 member: ( $i * $i ) > $o)).
% 0.15/0.37 tff(tptp_fun_X_24_type, type, (
% 0.15/0.37 tptp_fun_X_24: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(subset_type, type, (
% 0.15/0.37 subset: ( $i * $i ) > $o)).
% 0.15/0.37 tff(tptp_fun_Y_26_type, type, (
% 0.15/0.37 tptp_fun_Y_26: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(injective_type, type, (
% 0.15/0.37 injective: ( $i * $i * $i ) > $o)).
% 0.15/0.37 tff(maps_type, type, (
% 0.15/0.37 maps: ( $i * $i * $i ) > $o)).
% 0.15/0.37 tff(equal_set_type, type, (
% 0.15/0.37 equal_set: ( $i * $i ) > $o)).
% 0.15/0.37 tff(tptp_fun_Y_16_type, type, (
% 0.15/0.37 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_X2_17_type, type, (
% 0.15/0.37 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_X1_18_type, type, (
% 0.15/0.37 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_X_4_type, type, (
% 0.15/0.37 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_Y2_5_type, type, (
% 0.15/0.37 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_Y1_6_type, type, (
% 0.15/0.37 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_X_7_type, type, (
% 0.15/0.37 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(1,plain,
% 0.15/0.37 (^[F: $i, A: $i, B: $i, Y: $i] : refl((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(2,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.37 tff(3,plain,
% 0.15/0.37 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(4,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.15/0.37 tff(5,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.15/0.37 tff(6,plain,
% 0.15/0.37 (^[F: $i, A: $i, B: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) <=> ((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & apply(F, X, Y)) <=> (~((~member(X, A)) | (~apply(F, X, Y))))), ((~(member(X, A) & apply(F, X, Y))) <=> (~(~((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(X, A)) | (~apply(F, X, Y))))) <=> ((~member(X, A)) | (~apply(F, X, Y)))), ((~(member(X, A) & apply(F, X, Y))) <=> ((~member(X, A)) | (~apply(F, X, Y)))))), (![X: $i] : (~(member(X, A) & apply(F, X, Y))) <=> ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), rewrite((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(7,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.15/0.37 tff(8,plain,
% 0.15/0.37 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(9,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.15/0.37 tff(10,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y)))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(11,axiom,(![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','image3')).
% 0.15/0.37 tff(12,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.15/0.37 tff(13,plain,(
% 0.15/0.37 ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.15/0.37 inference(skolemize,[status(sab)],[12])).
% 0.15/0.37 tff(14,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.15/0.37 tff(15,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.15/0.37 tff(16,plain,
% 0.15/0.37 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.15/0.37 tff(17,plain,
% 0.15/0.37 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(18,plain,
% 0.15/0.38 ((~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))) <=> (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(19,plain,
% 0.15/0.38 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.15/0.38 tff(20,plain,
% 0.15/0.38 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[19, 17])).
% 0.15/0.39 tff(21,plain,
% 0.15/0.39 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(22,plain,
% 0.15/0.39 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.15/0.39 tff(23,plain,
% 0.15/0.39 (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.15/0.39 tff(24,plain,
% 0.15/0.39 (((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(25,plain,
% 0.15/0.39 ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.15/0.39 tff(26,plain,
% 0.15/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(27,plain,
% 0.15/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.15/0.39 tff(28,plain,
% 0.15/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(29,plain,
% 0.15/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.15/0.39 tff(30,plain,
% 0.15/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[29, 27])).
% 0.15/0.39 tff(31,plain,
% 0.15/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(32,plain,
% 0.15/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.15/0.39 tff(33,plain,
% 0.15/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(34,plain,
% 0.15/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(35,plain,
% 0.15/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.15/0.39 tff(36,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.15/0.40 tff(37,plain,
% 0.15/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.15/0.40 tff(38,plain,
% 0.15/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.15/0.40 tff(39,plain,(
% 0.15/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.15/0.40 inference(skolemize,[status(sab)],[38])).
% 0.15/0.40 tff(40,plain,
% 0.15/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.15/0.40 tff(41,plain,
% 0.15/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.15/0.40 tff(42,plain,
% 0.15/0.40 ((~![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, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | ![X: $i] : ((~member(X, X!39)) | member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))) | (~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(43,plain,
% 0.15/0.40 (~((~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | ![X: $i] : ((~member(X, X!39)) | member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))) | (~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))))),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.15/0.40 tff(44,plain,
% 0.15/0.40 (((~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | ![X: $i] : ((~member(X, X!39)) | member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))) | (~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))))) | (subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))),
% 0.15/0.40 inference(tautology,[status(thm)],[])).
% 0.15/0.40 tff(45,plain,
% 0.15/0.40 (subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.15/0.40 tff(46,assumption,((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))))), introduced(assumption)).
% 0.15/0.40 tff(47,plain,
% 0.15/0.40 ((~![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(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(48,plain,
% 0.15/0.40 ($false),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[47, 41, 46])).
% 0.15/0.40 tff(49,plain,(~((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.40 tff(50,plain,
% 0.15/0.40 (((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))))) | (subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))),
% 0.15/0.40 inference(tautology,[status(thm)],[])).
% 0.15/0.40 tff(51,plain,
% 0.15/0.40 (subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.15/0.40 tff(52,plain,
% 0.15/0.40 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(53,plain,
% 0.15/0.41 (~((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[52, 16])).
% 0.15/0.41 tff(54,plain,
% 0.15/0.41 (((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(55,plain,
% 0.15/0.41 ((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.15/0.41 tff(56,plain,
% 0.15/0.41 (^[F: $i, B: $i, A: $i, X: $i] : refl((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(57,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.15/0.41 tff(58,plain,
% 0.15/0.41 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(59,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.15/0.41 tff(60,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[59, 57])).
% 0.15/0.41 tff(61,plain,
% 0.15/0.41 (^[F: $i, B: $i, A: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) <=> ((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, X, Y)) <=> (~((~member(Y, B)) | (~apply(F, X, Y))))), ((~(member(Y, B) & apply(F, X, Y))) <=> (~(~((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, X, Y))))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))), ((~(member(Y, B) & apply(F, X, Y))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, X, Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), rewrite((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(62,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.15/0.41 tff(63,plain,
% 0.15/0.41 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(64,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.15/0.41 tff(65,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))) <=> ![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(66,axiom,(![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','inverse_image3')).
% 0.15/0.41 tff(67,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.15/0.41 tff(68,plain,(
% 0.15/0.41 ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.15/0.41 inference(skolemize,[status(sab)],[67])).
% 0.15/0.41 tff(69,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.15/0.41 tff(70,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.15/0.41 tff(71,plain,
% 0.15/0.41 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.15/0.41 tff(72,plain,
% 0.15/0.41 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y)))))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(73,plain,
% 0.15/0.41 (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.15/0.42 tff(74,plain,
% 0.15/0.42 (((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y)))))) | ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(75,plain,
% 0.15/0.42 ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.15/0.42 tff(76,assumption,(~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))), introduced(assumption)).
% 0.15/0.42 tff(77,plain,
% 0.15/0.42 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(78,plain,
% 0.15/0.42 (member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.15/0.42 tff(79,plain,
% 0.15/0.42 ((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(80,plain,
% 0.15/0.42 ((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.15/0.42 tff(81,plain,
% 0.15/0.42 (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.15/0.42 tff(82,plain,
% 0.15/0.42 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(83,plain,
% 0.15/0.42 (member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.15/0.42 tff(84,plain,
% 0.15/0.42 ((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(85,plain,
% 0.15/0.43 ((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.15/0.43 tff(86,plain,
% 0.15/0.43 (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[85, 55])).
% 0.15/0.43 tff(87,plain,
% 0.15/0.43 (((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(88,plain,
% 0.15/0.43 (member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.15/0.43 tff(89,plain,
% 0.15/0.43 ((~![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)))))))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(90,plain,
% 0.15/0.43 (~((~((~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))))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[89, 41])).
% 0.15/0.43 tff(91,plain,
% 0.15/0.43 (((~((~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)))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(92,plain,
% 0.15/0.43 ((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.15/0.43 tff(93,plain,
% 0.15/0.43 ((~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X)))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(94,plain,
% 0.15/0.43 ((~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & injective(F, A, B)) & subset(X, A)) => equal_set(inverse_image3(F, image3(F, X, B), A), X))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X)))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(95,axiom,(~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & injective(F, A, B)) & subset(X, A)) => equal_set(inverse_image3(F, image3(F, X, B), A), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIIa09')).
% 0.15/0.43 tff(96,plain,
% 0.15/0.43 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.15/0.43 tff(97,plain,
% 0.15/0.43 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[96, 93])).
% 0.15/0.43 tff(98,plain,
% 0.15/0.43 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.15/0.43 tff(99,plain,
% 0.15/0.43 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[98, 93])).
% 0.15/0.43 tff(100,plain,
% 0.15/0.43 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[99, 93])).
% 0.15/0.43 tff(101,plain,
% 0.15/0.43 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.15/0.43 tff(102,plain,
% 0.15/0.43 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[101, 93])).
% 0.15/0.44 tff(103,plain,(
% 0.15/0.44 ~((~(maps(F!42, A!41, B!40) & injective(F!42, A!41, B!40) & subset(X!39, A!41))) | equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))),
% 0.15/0.44 inference(skolemize,[status(sab)],[102])).
% 0.15/0.44 tff(104,plain,
% 0.15/0.44 (maps(F!42, A!41, B!40) & injective(F!42, A!41, B!40) & subset(X!39, A!41)),
% 0.15/0.44 inference(or_elim,[status(thm)],[103])).
% 0.15/0.44 tff(105,plain,
% 0.15/0.44 (subset(X!39, A!41)),
% 0.15/0.44 inference(and_elim,[status(thm)],[104])).
% 0.15/0.44 tff(106,plain,
% 0.15/0.44 ((~((~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))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(107,plain,
% 0.15/0.44 ((~((~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))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.15/0.44 tff(108,plain,
% 0.15/0.44 (![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[107, 92])).
% 0.15/0.44 tff(109,plain,
% 0.15/0.44 (((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))) <=> ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(110,plain,
% 0.15/0.44 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(111,plain,
% 0.15/0.44 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.15/0.44 tff(112,plain,
% 0.15/0.44 (member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[111, 108, 88])).
% 0.15/0.44 tff(113,plain,
% 0.15/0.44 (((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(114,plain,
% 0.15/0.44 (apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[113, 86])).
% 0.15/0.44 tff(115,plain,
% 0.15/0.44 (((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(116,plain,
% 0.15/0.44 (member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[115, 86])).
% 0.15/0.44 tff(117,plain,
% 0.15/0.44 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(118,plain,
% 0.15/0.44 (apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[117, 81])).
% 0.15/0.44 tff(119,plain,
% 0.15/0.44 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(120,plain,
% 0.15/0.44 (member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[119, 81])).
% 0.15/0.44 tff(121,plain,
% 0.15/0.44 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(122,plain,
% 0.15/0.44 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[121])).
% 0.15/0.44 tff(123,plain,
% 0.15/0.44 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(124,plain,
% 0.15/0.44 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[123])).
% 0.15/0.44 tff(125,plain,
% 0.15/0.44 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[124, 122])).
% 0.15/0.44 tff(126,plain,
% 0.15/0.44 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(127,plain,
% 0.15/0.45 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[126])).
% 0.15/0.45 tff(128,plain,
% 0.15/0.45 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(129,plain,
% 0.15/0.45 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(130,plain,
% 0.15/0.45 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[129])).
% 0.15/0.45 tff(131,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','injective')).
% 0.15/0.45 tff(132,plain,
% 0.15/0.45 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.15/0.45 tff(133,plain,
% 0.15/0.45 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.15/0.45 tff(134,plain,(
% 0.15/0.45 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.15/0.45 inference(skolemize,[status(sab)],[133])).
% 0.15/0.45 tff(135,plain,
% 0.15/0.45 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.15/0.45 tff(136,plain,
% 0.15/0.45 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.15/0.45 tff(137,plain,
% 0.15/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)))))))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(138,plain,
% 0.15/0.45 ((~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)))))))) <=> (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(139,plain,
% 0.15/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)))))))))),
% 0.15/0.45 inference(monotonicity,[status(thm)],[138])).
% 0.15/0.45 tff(140,plain,
% 0.15/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)))))))))),
% 0.15/0.45 inference(transitivity,[status(thm)],[139, 137])).
% 0.15/0.45 tff(141,plain,
% 0.15/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(142,plain,
% 0.15/0.46 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.15/0.46 tff(143,plain,
% 0.15/0.46 (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)))))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[142, 136])).
% 0.15/0.46 tff(144,plain,
% 0.15/0.46 (((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))) | ((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(145,plain,
% 0.15/0.46 ((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.15/0.46 tff(146,plain,
% 0.15/0.46 (injective(F!42, A!41, B!40)),
% 0.15/0.46 inference(and_elim,[status(thm)],[104])).
% 0.15/0.46 tff(147,plain,
% 0.15/0.46 ((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(148,plain,
% 0.15/0.46 ((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.15/0.46 tff(149,plain,
% 0.15/0.46 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.15/0.46 tff(150,plain,
% 0.15/0.46 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(151,plain,
% 0.15/0.46 (((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) <=> ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(152,plain,
% 0.15/0.47 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))))),
% 0.15/0.47 inference(monotonicity,[status(thm)],[151])).
% 0.15/0.47 tff(153,plain,
% 0.15/0.47 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))),
% 0.15/0.47 inference(transitivity,[status(thm)],[152, 150])).
% 0.15/0.47 tff(154,plain,
% 0.15/0.47 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(155,plain,
% 0.15/0.48 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.15/0.48 tff(156,plain,
% 0.15/0.48 ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[155, 149, 120, 118, 116, 114])).
% 0.15/0.48 tff(157,plain,
% 0.15/0.48 (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[156, 112])).
% 0.15/0.48 tff(158,plain,
% 0.15/0.48 (member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39) <=> member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)),
% 0.15/0.48 inference(monotonicity,[status(thm)],[157])).
% 0.15/0.48 tff(159,plain,
% 0.15/0.48 (member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39) <=> member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.15/0.48 inference(symmetry,[status(thm)],[158])).
% 0.15/0.48 tff(160,plain,
% 0.15/0.48 ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)) <=> (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[159])).
% 0.15/0.48 tff(161,plain,
% 0.15/0.48 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(162,plain,
% 0.15/0.48 (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[161, 76])).
% 0.15/0.48 tff(163,plain,
% 0.15/0.48 (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[162, 160])).
% 0.15/0.48 tff(164,plain,
% 0.15/0.48 ($false),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[88, 163])).
% 0.15/0.48 tff(165,plain,((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.48 tff(166,plain,
% 0.15/0.48 ((~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))) | subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(167,plain,
% 0.15/0.48 ((~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))) | subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.15/0.48 tff(168,plain,
% 0.15/0.48 (subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[167, 51])).
% 0.15/0.48 tff(169,plain,
% 0.15/0.48 (^[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))))))),
% 0.15/0.48 inference(bind,[status(th)],[])).
% 0.15/0.48 tff(170,plain,
% 0.15/0.48 (![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)))))),
% 0.15/0.48 inference(quant_intro,[status(thm)],[169])).
% 0.15/0.48 tff(171,plain,
% 0.15/0.48 (^[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))))))),
% 0.15/0.48 inference(bind,[status(th)],[])).
% 0.15/0.48 tff(172,plain,
% 0.15/0.48 (![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)))))),
% 0.15/0.48 inference(quant_intro,[status(thm)],[171])).
% 0.15/0.48 tff(173,plain,
% 0.15/0.48 (![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)))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(174,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')).
% 0.15/0.48 tff(175,plain,
% 0.15/0.48 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.15/0.48 tff(176,plain,(
% 0.15/0.48 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.15/0.48 inference(skolemize,[status(sab)],[175])).
% 0.15/0.48 tff(177,plain,
% 0.15/0.48 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.15/0.48 tff(178,plain,
% 0.15/0.48 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.15/0.48 tff(179,plain,
% 0.15/0.48 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))))))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(180,plain,
% 0.15/0.49 ((equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))) <=> (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(181,plain,
% 0.15/0.49 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))))))),
% 0.15/0.49 inference(monotonicity,[status(thm)],[180])).
% 0.15/0.49 tff(182,plain,
% 0.15/0.49 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))))))),
% 0.15/0.49 inference(transitivity,[status(thm)],[181, 179])).
% 0.15/0.49 tff(183,plain,
% 0.15/0.49 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(184,plain,
% 0.15/0.49 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.15/0.49 tff(185,plain,
% 0.15/0.49 (equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[184, 178])).
% 0.15/0.49 tff(186,plain,
% 0.15/0.49 (~equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)),
% 0.15/0.49 inference(or_elim,[status(thm)],[103])).
% 0.15/0.49 tff(187,plain,
% 0.15/0.49 ((~(equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))))) | equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | ((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(188,plain,
% 0.15/0.49 ((~(equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) <=> (~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))))) | ((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.15/0.49 tff(189,plain,
% 0.15/0.49 ((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[188, 185])).
% 0.15/0.49 tff(190,plain,
% 0.15/0.49 ((~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(191,plain,
% 0.15/0.49 ((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.15/0.49 tff(192,plain,
% 0.15/0.49 (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[191, 168])).
% 0.15/0.49 tff(193,plain,
% 0.15/0.49 ((~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))) | subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(194,plain,
% 0.15/0.49 ((~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.15/0.49 tff(195,plain,
% 0.15/0.49 (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[194, 45])).
% 0.15/0.49 tff(196,plain,
% 0.15/0.49 (((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(197,plain,
% 0.15/0.49 (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.15/0.49 tff(198,plain,
% 0.15/0.49 (((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41))) <=> ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(199,plain,
% 0.15/0.49 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(200,plain,
% 0.15/0.49 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.15/0.49 tff(201,plain,
% 0.15/0.49 (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[200, 108, 197])).
% 0.15/0.49 tff(202,plain,
% 0.15/0.49 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.15/0.49 inference(bind,[status(th)],[])).
% 0.15/0.49 tff(203,plain,
% 0.15/0.49 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.15/0.49 inference(quant_intro,[status(thm)],[202])).
% 0.15/0.49 tff(204,plain,
% 0.15/0.49 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.15/0.50 inference(bind,[status(th)],[])).
% 0.15/0.50 tff(205,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.15/0.50 inference(quant_intro,[status(thm)],[204])).
% 0.15/0.50 tff(206,plain,
% 0.15/0.50 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.15/0.50 inference(bind,[status(th)],[])).
% 0.15/0.50 tff(207,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.15/0.50 inference(quant_intro,[status(thm)],[206])).
% 0.15/0.50 tff(208,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.15/0.50 inference(transitivity,[status(thm)],[207, 205])).
% 0.15/0.50 tff(209,plain,
% 0.15/0.50 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))), rewrite((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.15/0.50 inference(bind,[status(th)],[])).
% 0.15/0.50 tff(210,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.15/0.50 inference(quant_intro,[status(thm)],[209])).
% 0.15/0.50 tff(211,plain,
% 0.15/0.50 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))))),
% 0.15/0.50 inference(bind,[status(th)],[])).
% 0.15/0.50 tff(212,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.15/0.50 inference(quant_intro,[status(thm)],[211])).
% 0.15/0.50 tff(213,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(214,plain,
% 0.15/0.50 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.15/0.50 inference(bind,[status(th)],[])).
% 0.15/0.50 tff(215,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.15/0.50 inference(quant_intro,[status(thm)],[214])).
% 0.15/0.50 tff(216,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.15/0.50 tff(217,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.15/0.50 tff(218,plain,
% 0.15/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.15/0.50 tff(219,plain,(
% 0.15/0.50 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.15/0.51 inference(skolemize,[status(sab)],[218])).
% 0.15/0.51 tff(220,plain,
% 0.15/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.15/0.51 tff(221,plain,
% 0.15/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[220, 210])).
% 0.15/0.51 tff(222,plain,
% 0.15/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[221, 208])).
% 0.15/0.51 tff(223,plain,
% 0.15/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[222, 203])).
% 0.15/0.51 tff(224,plain,
% 0.15/0.51 ((~![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))))))))))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(225,plain,
% 0.15/0.51 (~((~((~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)))))))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.15/0.51 tff(226,plain,
% 0.15/0.51 (((~((~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)))))))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(227,plain,
% 0.15/0.51 ((~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))))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.15/0.51 tff(228,plain,
% 0.15/0.51 (maps(F!42, A!41, B!40)),
% 0.15/0.51 inference(and_elim,[status(thm)],[104])).
% 0.15/0.51 tff(229,plain,
% 0.15/0.51 ((~((~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))))))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(230,plain,
% 0.15/0.51 ((~((~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))))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.15/0.51 tff(231,plain,
% 0.15/0.51 (~((~![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)))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.15/0.51 tff(232,plain,
% 0.15/0.51 (((~![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))))))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(233,plain,
% 0.15/0.51 (![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))))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.15/0.51 tff(234,plain,
% 0.15/0.51 (((~![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(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), 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(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))),
% 0.15/0.51 inference(rewrite,[status(thm)],[])).
% 0.15/0.51 tff(235,plain,
% 0.15/0.51 ((~![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(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(236,plain,
% 0.15/0.51 ((~![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(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.15/0.52 tff(237,plain,
% 0.15/0.52 (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[236, 233, 201])).
% 0.15/0.52 tff(238,plain,
% 0.15/0.52 (((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))) | apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))),
% 0.15/0.52 inference(tautology,[status(thm)],[])).
% 0.15/0.52 tff(239,plain,
% 0.15/0.52 (apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.15/0.52 tff(240,plain,
% 0.15/0.52 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))))))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(241,plain,
% 0.15/0.52 (~((~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[240, 71])).
% 0.15/0.52 tff(242,plain,
% 0.15/0.52 (((~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))))) | (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))),
% 0.15/0.52 inference(tautology,[status(thm)],[])).
% 0.15/0.52 tff(243,plain,
% 0.15/0.52 (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.15/0.52 tff(244,plain,
% 0.15/0.52 (((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))),
% 0.15/0.52 inference(tautology,[status(thm)],[])).
% 0.15/0.52 tff(245,plain,
% 0.15/0.52 (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[244, 195])).
% 0.15/0.52 tff(246,plain,
% 0.15/0.52 ((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.15/0.52 inference(tautology,[status(thm)],[])).
% 0.15/0.52 tff(247,plain,
% 0.15/0.52 ((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.15/0.53 tff(248,plain,
% 0.15/0.53 (![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[247, 201, 243])).
% 0.15/0.53 tff(249,plain,
% 0.15/0.53 (((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) <=> ((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.53 inference(rewrite,[status(thm)],[])).
% 0.15/0.53 tff(250,plain,
% 0.15/0.53 ((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.53 inference(quant_inst,[status(thm)],[])).
% 0.15/0.53 tff(251,plain,
% 0.15/0.53 ((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))),
% 0.15/0.53 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.15/0.53 tff(252,plain,
% 0.15/0.53 (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[251, 248, 239])).
% 0.15/0.53 tff(253,plain,
% 0.15/0.53 (((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(254,plain,
% 0.15/0.53 (member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[253, 237])).
% 0.15/0.53 tff(255,plain,
% 0.15/0.53 ((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(256,plain,
% 0.15/0.54 ((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[255, 254, 252])).
% 0.15/0.54 tff(257,plain,
% 0.15/0.54 (![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[256, 25])).
% 0.15/0.54 tff(258,plain,
% 0.15/0.54 (((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) <=> ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.54 inference(rewrite,[status(thm)],[])).
% 0.15/0.54 tff(259,plain,
% 0.15/0.54 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.15/0.54 inference(quant_inst,[status(thm)],[])).
% 0.15/0.54 tff(260,plain,
% 0.15/0.54 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))),
% 0.15/0.54 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.15/0.54 tff(261,plain,
% 0.15/0.54 ($false),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[260, 197, 239, 257])).
% 0.15/0.54 % SZS output end Proof
%------------------------------------------------------------------------------