TSTP Solution File: SET714+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET714+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:07:43 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET714+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 07:42:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(apply_type, type, (
% 0.12/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_X_15_type, type, (
% 0.12/0.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.12/0.40 tff(compose_function_type, type, (
% 0.12/0.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_A_40_type, type, (
% 0.12/0.40 tptp_fun_A_40: $i)).
% 0.12/0.40 tff(tptp_fun_B_39_type, type, (
% 0.12/0.40 tptp_fun_B_39: $i)).
% 0.12/0.40 tff(tptp_fun_F_41_type, type, (
% 0.12/0.40 tptp_fun_F_41: $i)).
% 0.12/0.40 tff(inverse_function_type, type, (
% 0.12/0.40 inverse_function: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(member_type, type, (
% 0.12/0.40 member: ( $i * $i ) > $o)).
% 0.12/0.40 tff(identity_type, type, (
% 0.12/0.40 identity: ( $i * $i ) > $o)).
% 0.12/0.40 tff(one_to_one_type, type, (
% 0.12/0.40 one_to_one: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(maps_type, type, (
% 0.12/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_X_4_type, type, (
% 0.12/0.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y2_5_type, type, (
% 0.12/0.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y1_6_type, type, (
% 0.12/0.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X_7_type, type, (
% 0.12/0.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.12/0.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(7,plain,
% 0.12/0.41 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(10,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.41 tff(11,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','identity')).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.41 tff(13,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.41 tff(14,plain,(
% 0.12/0.41 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[13])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~((~((~identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (((~((~identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 ((~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 ((~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(23,axiom,(~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII05')).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(inverse_function(F, A, B), F, A, B, A), A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.41 tff(31,plain,(
% 0.20/0.41 ~((~(maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39))) | identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40))),
% 0.20/0.41 inference(skolemize,[status(sab)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40)),
% 0.20/0.41 inference(or_elim,[status(thm)],[31])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~(identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))) | identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~(identity(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))) | (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (^[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)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![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))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (^[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)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (^[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)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (^[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))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (^[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)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (![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))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![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))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (^[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)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (![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))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.43 tff(52,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/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.43 tff(55,plain,(
% 0.20/0.43 ![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))))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[54])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 44])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![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))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 39])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 ((~![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!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y))))))))) | ((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39)),
% 0.20/0.44 inference(or_elim,[status(thm)],[31])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (maps(F!41, A!40, B!39)),
% 0.20/0.44 inference(and_elim,[status(thm)],[64])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 ((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[67, 63])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[73, 70, 37])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)))) | apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)))) | member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.45 tff(89,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.45 tff(92,plain,(
% 0.20/0.45 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[91])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))))) <=> ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ((~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))) <=> (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))))) <=> ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))))) <=> ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[98, 96])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | 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compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, 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compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.48 tff(101,plain,
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% 0.20/0.48 inference(transitivity,[status(thm)],[100, 95])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (~((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[103, 94, 37])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (((~((~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_8(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41, inverse_function(F!41, A!40, B!39)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))))) | (apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (~apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[107, 35])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))) | apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 ((~(apply(compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[110, 106])).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 (((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))) <=> ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(114,plain,
% 0.20/0.50 ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), Y)) | (~apply(inverse_function(F!41, A!40, B!39), Y, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[114, 111, 78, 76])).
% 0.20/0.50 tff(116,plain,
% 0.20/0.50 ((~(apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))) | (~apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 (~(apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[116, 76, 115])).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : refl(((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.50 tff(120,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Y, B)) <=> (~((~member(Y, B)) | (~member(X, A))))), ((~(member(X, A) & member(Y, B))) <=> (~(~((~member(Y, B)) | (~member(X, A))))))), rewrite((~(~((~member(Y, B)) | (~member(X, A))))) <=> ((~member(Y, B)) | (~member(X, A)))), ((~(member(X, A) & member(Y, B))) <=> ((~member(Y, B)) | (~member(X, A))))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> (((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))), rewrite((((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : rewrite(((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.50 tff(125,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.20/0.50 tff(128,plain,(
% 0.20/0.50 ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[127])).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 (((apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40))) <=> ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(133,plain,
% 0.20/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40)), B!39, F!41), tptp_fun_X_15(A!40, compose_function(inverse_function(F!41, A!40, B!39), F!41, A!40, B!39, A!40))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[136, 130, 37, 78, 117])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------