Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SET732+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n009.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 : Sat Jun 21 05:26:14 AM UTC 2025

% Result   : Theorem 0.20s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET732+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Jun 20 05:39:03 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 0.20/0.40  % SZS status Theorem
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  tff(apply_type, type, (
% 0.20/0.40     apply: ( $i * $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_Y_20_type, type, (
% 0.20/0.40     tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_G_41_type, type, (
% 0.20/0.40     tptp_fun_G_41: $i)).
% 0.20/0.40  tff(tptp_fun_A_40_type, type, (
% 0.20/0.40     tptp_fun_A_40: $i)).
% 0.20/0.40  tff(image2_type, type, (
% 0.20/0.40     image2: ( $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_F_42_type, type, (
% 0.20/0.40     tptp_fun_F_42: $i)).
% 0.20/0.40  tff(tptp_fun_X_23_type, type, (
% 0.20/0.40     tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 0.20/0.40  tff(member_type, type, (
% 0.20/0.40     member: ( $i * $i ) > $o)).
% 0.20/0.40  tff(surjective_type, type, (
% 0.20/0.40     surjective: ( $i * $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_E_19_type, type, (
% 0.20/0.40     tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.20/0.40  tff(injective_type, type, (
% 0.20/0.40     injective: ( $i * $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_X2_17_type, type, (
% 0.20/0.40     tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_X1_18_type, type, (
% 0.20/0.40     tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_Y_16_type, type, (
% 0.20/0.40     tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_B_39_type, type, (
% 0.20/0.40     tptp_fun_B_39: $i)).
% 0.20/0.40  tff(subset_type, type, (
% 0.20/0.40     subset: ( $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_X_0_type, type, (
% 0.20/0.40     tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.40  tff(one_to_one_type, type, (
% 0.20/0.40     one_to_one: ( $i * $i * $i ) > $o)).
% 0.20/0.40  tff(maps_type, type, (
% 0.20/0.40     maps: ( $i * $i * $i ) > $o)).
% 0.20/0.40  tff(1,plain,
% 0.20/0.40      (^[F: $i, A: $i, Y: $i] : refl((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(2,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40  tff(3,plain,
% 0.20/0.40      (^[F: $i, A: $i, Y: $i] : rewrite((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(4,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40  tff(5,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.20/0.40      inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40  tff(6,plain,
% 0.20/0.40      (^[F: $i, A: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) <=> ((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))), rewrite((member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(7,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40  tff(8,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y))) <=> ![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.20/0.40      inference(rewrite,[status(thm)],[])).
% 0.20/0.40  tff(9,axiom,(![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','image2')).
% 0.20/0.40  tff(10,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.40  tff(11,plain,(
% 0.20/0.40      ![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.20/0.40      inference(skolemize,[status(sab)],[10])).
% 0.20/0.40  tff(12,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.40  tff(13,plain,
% 0.20/0.40      (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.40  tff(14,plain,
% 0.20/0.40      (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))))),
% 0.20/0.40      inference(rewrite,[status(thm)],[])).
% 0.20/0.40  tff(15,plain,
% 0.20/0.40      ((~((~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))) | (~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))) <=> (~((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.20/0.40      inference(rewrite,[status(thm)],[])).
% 0.20/0.40  tff(16,plain,
% 0.20/0.40      (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))) | (~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))))),
% 0.20/0.40      inference(monotonicity,[status(thm)],[15])).
% 0.20/0.40  tff(17,plain,
% 0.20/0.40      (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))) | (~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))))),
% 0.20/0.41      inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.41  tff(18,plain,
% 0.20/0.41      ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))) | (~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))),
% 0.20/0.41      inference(quant_inst,[status(thm)],[])).
% 0.20/0.41  tff(19,plain,
% 0.20/0.41      ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.41  tff(20,plain,
% 0.20/0.41      (~((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[19, 13])).
% 0.20/0.41  tff(21,plain,
% 0.20/0.41      (((~(member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))) | ((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))),
% 0.20/0.41      inference(tautology,[status(thm)],[])).
% 0.20/0.41  tff(22,plain,
% 0.20/0.41      ((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.41  tff(23,plain,
% 0.20/0.41      (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(24,plain,
% 0.20/0.41      (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[23])).
% 0.20/0.41  tff(25,plain,
% 0.20/0.41      (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(26,plain,
% 0.20/0.41      (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[25])).
% 0.20/0.41  tff(27,plain,
% 0.20/0.41      (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.41      inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.41  tff(28,plain,
% 0.20/0.41      (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(29,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[28])).
% 0.20/0.42  tff(30,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(31,plain,
% 0.20/0.42      (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(32,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[31])).
% 0.20/0.42  tff(33,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.20/0.42  tff(34,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.42  tff(35,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.42  tff(36,plain,(
% 0.20/0.42      ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.20/0.42      inference(skolemize,[status(sab)],[35])).
% 0.20/0.42  tff(37,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.42  tff(38,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[37, 27])).
% 0.20/0.42  tff(39,plain,
% 0.20/0.42      ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(G!41, A!40, image2(F!42, A!40))) | ![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~((~member(tptp_fun_E_19(Y, A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_E_19(Y, A!40, G!41), Y))))))) | (~(surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(40,plain,
% 0.20/0.42      (~((~((~surjective(G!41, A!40, image2(F!42, A!40))) | ![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~((~member(tptp_fun_E_19(Y, A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_E_19(Y, A!40, G!41), Y))))))) | (~(surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.42  tff(41,plain,
% 0.20/0.42      (((~((~surjective(G!41, A!40, image2(F!42, A!40))) | ![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~((~member(tptp_fun_E_19(Y, A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_E_19(Y, A!40, G!41), Y))))))) | (~(surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))))) | (surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(42,plain,
% 0.20/0.42      (surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.42  tff(43,assumption,((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))))))), introduced(assumption)).
% 0.20/0.42  tff(44,plain,
% 0.20/0.42      (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(45,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[44])).
% 0.20/0.42  tff(46,plain,
% 0.20/0.42      (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(47,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[46])).
% 0.20/0.42  tff(48,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.42      inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.42  tff(49,plain,
% 0.20/0.42      (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(50,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[49])).
% 0.20/0.42  tff(51,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(52,plain,
% 0.20/0.42      (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(53,plain,
% 0.20/0.42      (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[52])).
% 0.20/0.43  tff(54,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.20/0.43  tff(55,plain,
% 0.20/0.43      (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.43  tff(56,plain,
% 0.20/0.43      (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.43  tff(57,plain,(
% 0.20/0.43      ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.20/0.43      inference(skolemize,[status(sab)],[56])).
% 0.20/0.43  tff(58,plain,
% 0.20/0.43      (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.43  tff(59,plain,
% 0.20/0.43      (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[58, 48])).
% 0.20/0.43  tff(60,plain,
% 0.20/0.43      (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(61,plain,
% 0.21/0.43      ((~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, image2(F!42, A!40))) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))))))) <=> (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(62,plain,
% 0.21/0.43      (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, image2(F!42, A!40))) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.21/0.43      inference(monotonicity,[status(thm)],[61])).
% 0.21/0.43  tff(63,plain,
% 0.21/0.43      (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, image2(F!42, A!40))) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.21/0.44      inference(transitivity,[status(thm)],[62, 60])).
% 0.21/0.44  tff(64,plain,
% 0.21/0.44      ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, image2(F!42, A!40))) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))))))))),
% 0.21/0.44      inference(quant_inst,[status(thm)],[])).
% 0.21/0.44  tff(65,plain,
% 0.21/0.44      ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))))))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.44  tff(66,plain,
% 0.21/0.44      ($false),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[65, 59, 43])).
% 0.21/0.44  tff(67,plain,(~((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44  tff(68,plain,
% 0.21/0.44      (((~((~injective(G!41, A!40, image2(F!42, A!40))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, image2(F!42, A!40))) | (~member(X1, A!40)) | (~apply(G!41, X1, Y)) | (~apply(G!41, X2, Y))))) | (~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))))))) | (injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(69,plain,
% 0.21/0.44      (injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.44  tff(70,assumption,(~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))), introduced(assumption)).
% 0.21/0.44  tff(71,plain,
% 0.21/0.44      (((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))) | member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(72,plain,
% 0.21/0.44      (member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.44  tff(73,plain,
% 0.21/0.44      (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(74,plain,
% 0.21/0.44      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[73])).
% 0.21/0.44  tff(75,plain,
% 0.21/0.44      (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(76,plain,
% 0.21/0.44      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[75])).
% 0.21/0.44  tff(77,plain,
% 0.21/0.44      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.44      inference(transitivity,[status(thm)],[76, 74])).
% 0.21/0.44  tff(78,plain,
% 0.21/0.44      (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(79,plain,
% 0.21/0.44      (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[78])).
% 0.21/0.44  tff(80,plain,
% 0.21/0.44      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(81,plain,
% 0.21/0.44      (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(82,plain,
% 0.21/0.44      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[81])).
% 0.21/0.45  tff(83,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.21/0.45  tff(84,plain,
% 0.21/0.45      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.45  tff(85,plain,
% 0.21/0.45      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.45  tff(86,plain,(
% 0.21/0.45      ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.21/0.45      inference(skolemize,[status(sab)],[85])).
% 0.21/0.45  tff(87,plain,
% 0.21/0.45      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[86, 79])).
% 0.21/0.45  tff(88,plain,
% 0.21/0.45      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[87, 77])).
% 0.21/0.45  tff(89,plain,
% 0.21/0.45      ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~(subset(image2(F!42, A!40), B!39) | (~((~member(tptp_fun_X_0(B!39, image2(F!42, A!40)), image2(F!42, A!40))) | member(tptp_fun_X_0(B!39, image2(F!42, A!40)), B!39)))))))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(90,plain,
% 0.21/0.45      (~((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~(subset(image2(F!42, A!40), B!39) | (~((~member(tptp_fun_X_0(B!39, image2(F!42, A!40)), image2(F!42, A!40))) | member(tptp_fun_X_0(B!39, image2(F!42, A!40)), B!39))))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.21/0.45  tff(91,plain,
% 0.21/0.45      (((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~(subset(image2(F!42, A!40), B!39) | (~((~member(tptp_fun_X_0(B!39, image2(F!42, A!40)), image2(F!42, A!40))) | member(tptp_fun_X_0(B!39, image2(F!42, A!40)), B!39)))))) | ((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(92,plain,
% 0.21/0.45      ((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.45  tff(93,plain,
% 0.21/0.45      ((![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) & subset(image2(F!42, A!40), B!39) & maps(F!42, A!40, B!39) & injective(F!42, A!40, B!39) & (~one_to_one(G!41, A!40, image2(F!42, A!40)))) <=> (![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) & subset(image2(F!42, A!40), B!39) & maps(F!42, A!40, B!39) & injective(F!42, A!40, B!39) & (~one_to_one(G!41, A!40, image2(F!42, A!40))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(94,plain,
% 0.21/0.45      ((~![F: $i, G: $i, A: $i, B: $i] : ((~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | (~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~injective(F, A, B)) | one_to_one(G, A, image2(F, A)))) <=> (~![F: $i, G: $i, A: $i, B: $i] : ((~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | (~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~injective(F, A, B)) | one_to_one(G, A, image2(F, A))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(95,plain,
% 0.21/0.45      ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : (((((maps(F, A, B) & subset(C, B)) & (image2(F, A) = C)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, C)) => (apply(G, X, Y) <=> apply(F, X, Y)))) & injective(F, A, B)) => one_to_one(G, A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i] : ((~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | (~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~injective(F, A, B)) | one_to_one(G, A, image2(F, A))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(96,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : (((((maps(F, A, B) & subset(C, B)) & (image2(F, A) = C)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, C)) => (apply(G, X, Y) <=> apply(F, X, Y)))) & injective(F, A, B)) => one_to_one(G, A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII23')).
% 0.21/0.45  tff(97,plain,
% 0.21/0.45      (~![F: $i, G: $i, A: $i, B: $i] : ((~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | (~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~injective(F, A, B)) | one_to_one(G, A, image2(F, A)))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.45  tff(98,plain,
% 0.21/0.45      (~![F: $i, G: $i, A: $i, B: $i] : ((~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | (~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~injective(F, A, B)) | one_to_one(G, A, image2(F, A)))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[97, 94])).
% 0.21/0.45  tff(99,plain,
% 0.21/0.45      (~![F: $i, G: $i, A: $i, B: $i] : ((~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | (~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~injective(F, A, B)) | one_to_one(G, A, image2(F, A)))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[98, 94])).
% 0.21/0.45  tff(100,plain,
% 0.21/0.45      (~![F: $i, G: $i, A: $i, B: $i] : ((~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | (~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~injective(F, A, B)) | one_to_one(G, A, image2(F, A)))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[99, 94])).
% 0.21/0.45  tff(101,plain,
% 0.21/0.45      (![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) & subset(image2(F!42, A!40), B!39) & maps(F!42, A!40, B!39) & injective(F!42, A!40, B!39) & (~one_to_one(G!41, A!40, image2(F!42, A!40)))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[100, 93])).
% 0.21/0.45  tff(102,plain,
% 0.21/0.45      (subset(image2(F!42, A!40), B!39)),
% 0.21/0.45      inference(and_elim,[status(thm)],[101])).
% 0.21/0.45  tff(103,plain,
% 0.21/0.45      ((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(104,plain,
% 0.21/0.45      ((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.45  tff(105,plain,
% 0.21/0.45      (![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[104, 92])).
% 0.21/0.45  tff(106,plain,
% 0.21/0.45      (((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39))) <=> ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(107,plain,
% 0.21/0.45      ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(108,plain,
% 0.21/0.45      ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.45  tff(109,plain,
% 0.21/0.45      (member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[108, 105, 72])).
% 0.21/0.45  tff(110,plain,
% 0.21/0.45      (((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))) | member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(111,plain,
% 0.21/0.45      (member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[110, 70])).
% 0.21/0.45  tff(112,plain,
% 0.21/0.45      (^[X: $i, Y: $i] : refl(((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) <=> ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(113,plain,
% 0.21/0.45      (![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) <=> ![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[112])).
% 0.21/0.45  tff(114,plain,
% 0.21/0.45      (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A!40) & member(Y, image2(F!42, A!40))) <=> (~((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))), ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) <=> (~(~((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))))), rewrite((~(~((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))) <=> ((~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))), ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) <=> ((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))), (((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> (((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))))), rewrite((((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))), (((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(115,plain,
% 0.21/0.45      (![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> ![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[114])).
% 0.21/0.45  tff(116,plain,
% 0.21/0.45      (![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y)))),
% 0.21/0.45      inference(and_elim,[status(thm)],[101])).
% 0.21/0.45  tff(117,plain,
% 0.21/0.45      (![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.45  tff(118,plain,
% 0.21/0.45      (![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[117, 113])).
% 0.21/0.45  tff(119,plain,
% 0.21/0.45      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(120,plain,
% 0.21/0.46      (((apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))) <=> ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(121,plain,
% 0.21/0.46      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))))),
% 0.21/0.46      inference(monotonicity,[status(thm)],[120])).
% 0.21/0.46  tff(122,plain,
% 0.21/0.46      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.46      inference(transitivity,[status(thm)],[121, 119])).
% 0.21/0.46  tff(123,plain,
% 0.21/0.46      ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))),
% 0.21/0.46      inference(quant_inst,[status(thm)],[])).
% 0.21/0.46  tff(124,plain,
% 0.21/0.46      ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))),
% 0.21/0.46      inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.46  tff(125,plain,
% 0.21/0.46      (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[124, 118, 72, 111])).
% 0.21/0.46  tff(126,plain,
% 0.21/0.46      (((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))) | apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.46      inference(tautology,[status(thm)],[])).
% 0.21/0.46  tff(127,plain,
% 0.21/0.46      (apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[126, 70])).
% 0.21/0.46  tff(128,plain,
% 0.21/0.46      ((~(apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.46      inference(tautology,[status(thm)],[])).
% 0.21/0.46  tff(129,plain,
% 0.21/0.46      ((~(apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))) | apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[128, 127])).
% 0.21/0.46  tff(130,plain,
% 0.21/0.46      (apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[129, 125])).
% 0.21/0.46  tff(131,plain,
% 0.21/0.46      (((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))) | member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.21/0.46      inference(tautology,[status(thm)],[])).
% 0.21/0.46  tff(132,plain,
% 0.21/0.46      (member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[131, 70])).
% 0.21/0.46  tff(133,plain,
% 0.21/0.46      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(134,plain,
% 0.21/0.47      (((apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))) <=> ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(135,plain,
% 0.21/0.47      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))))),
% 0.21/0.47      inference(monotonicity,[status(thm)],[134])).
% 0.21/0.47  tff(136,plain,
% 0.21/0.47      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.47      inference(transitivity,[status(thm)],[135, 133])).
% 0.21/0.47  tff(137,plain,
% 0.21/0.47      ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))),
% 0.21/0.47      inference(quant_inst,[status(thm)],[])).
% 0.21/0.47  tff(138,plain,
% 0.21/0.47      ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.47  tff(139,plain,
% 0.21/0.47      (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[138, 118, 72, 132])).
% 0.21/0.47  tff(140,plain,
% 0.21/0.47      (((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))) | apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(141,plain,
% 0.21/0.47      (apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[140, 70])).
% 0.21/0.47  tff(142,plain,
% 0.21/0.47      ((~(apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(143,plain,
% 0.21/0.47      ((~(apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))) | apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[142, 141])).
% 0.21/0.47  tff(144,plain,
% 0.21/0.47      (apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[143, 139])).
% 0.21/0.47  tff(145,plain,
% 0.21/0.47      (((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))) | (~(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(146,plain,
% 0.21/0.47      (~(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[145, 70])).
% 0.21/0.47  tff(147,plain,
% 0.21/0.47      (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(148,plain,
% 0.21/0.47      ((~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)))))))) <=> (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(149,plain,
% 0.21/0.47      (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.21/0.47      inference(monotonicity,[status(thm)],[148])).
% 0.21/0.47  tff(150,plain,
% 0.21/0.47      (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.21/0.48      inference(transitivity,[status(thm)],[149, 147])).
% 0.21/0.48  tff(151,plain,
% 0.21/0.48      ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39))))))))),
% 0.21/0.48      inference(quant_inst,[status(thm)],[])).
% 0.21/0.48  tff(152,plain,
% 0.21/0.48      ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.48  tff(153,plain,
% 0.21/0.48      (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[152, 59])).
% 0.21/0.48  tff(154,plain,
% 0.21/0.48      (((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))) | ((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(155,plain,
% 0.21/0.48      ((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[154, 153])).
% 0.21/0.48  tff(156,plain,
% 0.21/0.48      (injective(F!42, A!40, B!39)),
% 0.21/0.48      inference(and_elim,[status(thm)],[101])).
% 0.21/0.48  tff(157,plain,
% 0.21/0.48      ((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | (~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(158,plain,
% 0.21/0.48      ((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[157, 156])).
% 0.21/0.48  tff(159,plain,
% 0.21/0.48      (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[158, 155])).
% 0.21/0.48  tff(160,plain,
% 0.21/0.48      (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | ((~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)))),
% 0.21/0.48      inference(rewrite,[status(thm)],[])).
% 0.21/0.48  tff(161,plain,
% 0.21/0.48      (((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41)))) <=> ((~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)))),
% 0.21/0.48      inference(rewrite,[status(thm)],[])).
% 0.21/0.48  tff(162,plain,
% 0.21/0.48      (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | ((~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39))))),
% 0.21/0.48      inference(monotonicity,[status(thm)],[161])).
% 0.21/0.48  tff(163,plain,
% 0.21/0.48      (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)))),
% 0.21/0.48      inference(transitivity,[status(thm)],[162, 160])).
% 0.21/0.48  tff(164,plain,
% 0.21/0.48      ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.48      inference(quant_inst,[status(thm)],[])).
% 0.21/0.48  tff(165,plain,
% 0.21/0.48      ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.48  tff(166,plain,
% 0.21/0.48      ($false),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[165, 159, 111, 132, 146, 144, 130, 109])).
% 0.21/0.48  tff(167,plain,((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48  tff(168,plain,
% 0.21/0.48      ((~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))))) | injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(169,plain,
% 0.21/0.48      ((~(injective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_16(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_X1_18(image2(F!42, A!40), A!40, G!41) = tptp_fun_X2_17(image2(F!42, A!40), A!40, G!41)))))) | injective(G!41, A!40, image2(F!42, A!40))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[168, 167])).
% 0.21/0.48  tff(170,plain,
% 0.21/0.48      (injective(G!41, A!40, image2(F!42, A!40))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[169, 69])).
% 0.21/0.48  tff(171,plain,
% 0.21/0.48      (^[F: $i, A: $i, B: $i] : refl((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))),
% 0.21/0.48      inference(bind,[status(th)],[])).
% 0.21/0.48  tff(172,plain,
% 0.21/0.48      (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.48      inference(quant_intro,[status(thm)],[171])).
% 0.21/0.48  tff(173,plain,
% 0.21/0.48      (^[F: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((injective(F, A, B) & surjective(F, A, B)) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))), rewrite((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))), rewrite((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))))),
% 0.21/0.48      inference(bind,[status(th)],[])).
% 0.21/0.48  tff(174,plain,
% 0.21/0.48      (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.48      inference(quant_intro,[status(thm)],[173])).
% 0.21/0.48  tff(175,plain,
% 0.21/0.48      (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.48      inference(rewrite,[status(thm)],[])).
% 0.21/0.48  tff(176,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.21/0.48  tff(177,plain,
% 0.21/0.48      (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.48  tff(178,plain,(
% 0.21/0.48      ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.48      inference(skolemize,[status(sab)],[177])).
% 0.21/0.48  tff(179,plain,
% 0.21/0.48      (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[178, 174])).
% 0.21/0.48  tff(180,plain,
% 0.21/0.48      (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[179, 172])).
% 0.21/0.48  tff(181,plain,
% 0.21/0.48      ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))) <=> one_to_one(G!41, A!40, image2(F!42, A!40))))),
% 0.21/0.48      inference(quant_inst,[status(thm)],[])).
% 0.21/0.48  tff(182,plain,
% 0.21/0.48      (~(((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))) <=> one_to_one(G!41, A!40, image2(F!42, A!40)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[181, 180])).
% 0.21/0.48  tff(183,plain,
% 0.21/0.48      (~one_to_one(G!41, A!40, image2(F!42, A!40))),
% 0.21/0.48      inference(and_elim,[status(thm)],[101])).
% 0.21/0.48  tff(184,plain,
% 0.21/0.48      ((((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))) <=> one_to_one(G!41, A!40, image2(F!42, A!40))) | ((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))) | one_to_one(G!41, A!40, image2(F!42, A!40))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(185,plain,
% 0.21/0.48      ((((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))) <=> one_to_one(G!41, A!40, image2(F!42, A!40))) | ((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40))))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[184, 183])).
% 0.21/0.48  tff(186,plain,
% 0.21/0.48      ((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[185, 182])).
% 0.21/0.48  tff(187,plain,
% 0.21/0.48      ((~((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40))))) | (~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))),
% 0.21/0.48      inference(tautology,[status(thm)],[])).
% 0.21/0.48  tff(188,plain,
% 0.21/0.48      ((~injective(G!41, A!40, image2(F!42, A!40))) | (~surjective(G!41, A!40, image2(F!42, A!40)))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[187, 186])).
% 0.21/0.48  tff(189,plain,
% 0.21/0.48      (~surjective(G!41, A!40, image2(F!42, A!40))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[188, 170])).
% 0.21/0.48  tff(190,plain,
% 0.21/0.48      ((~(surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))) | surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))),
% 0.21/0.49      inference(tautology,[status(thm)],[])).
% 0.21/0.49  tff(191,plain,
% 0.21/0.49      ((~(surjective(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))))) | (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[190, 189])).
% 0.21/0.49  tff(192,plain,
% 0.21/0.49      (~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[191, 42])).
% 0.21/0.49  tff(193,plain,
% 0.21/0.49      (((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.21/0.49      inference(tautology,[status(thm)],[])).
% 0.21/0.49  tff(194,plain,
% 0.21/0.49      (member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[193, 192])).
% 0.21/0.49  tff(195,plain,
% 0.21/0.49      ((~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))),
% 0.21/0.49      inference(tautology,[status(thm)],[])).
% 0.21/0.49  tff(196,plain,
% 0.21/0.49      ((~((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[195, 194])).
% 0.21/0.49  tff(197,plain,
% 0.21/0.49      (~((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[196, 22])).
% 0.21/0.49  tff(198,plain,
% 0.21/0.49      (((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))) | member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)),
% 0.21/0.49      inference(tautology,[status(thm)],[])).
% 0.21/0.49  tff(199,plain,
% 0.21/0.49      (member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[198, 197])).
% 0.21/0.49  tff(200,plain,
% 0.21/0.49      (((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))) | ![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.49      inference(tautology,[status(thm)],[])).
% 0.21/0.49  tff(201,plain,
% 0.21/0.49      (![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[200, 192])).
% 0.21/0.49  tff(202,plain,
% 0.21/0.49      (((~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))) | ((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))) <=> ((~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.49      inference(rewrite,[status(thm)],[])).
% 0.21/0.49  tff(203,plain,
% 0.21/0.49      ((~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))) | ((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.49      inference(quant_inst,[status(thm)],[])).
% 0.21/0.49  tff(204,plain,
% 0.21/0.49      ((~![E: $i] : ((~member(E, A!40)) | (~apply(G!41, E, tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))),
% 0.21/0.49      inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.49  tff(205,plain,
% 0.21/0.49      (~apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[204, 201, 199])).
% 0.21/0.49  tff(206,plain,
% 0.21/0.49      (((~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))) | apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.49      inference(tautology,[status(thm)],[])).
% 0.21/0.49  tff(207,plain,
% 0.21/0.49      (apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[206, 197])).
% 0.21/0.49  tff(208,plain,
% 0.21/0.49      ((~(apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))) | apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))),
% 0.21/0.49      inference(tautology,[status(thm)],[])).
% 0.21/0.49  tff(209,plain,
% 0.21/0.49      (~(apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))),
% 0.21/0.49      inference(unit_resolution,[status(thm)],[208, 207, 205])).
% 0.21/0.49  tff(210,plain,
% 0.21/0.49      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.49      inference(rewrite,[status(thm)],[])).
% 0.21/0.49  tff(211,plain,
% 0.21/0.49      (((apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))) <=> ((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.49      inference(rewrite,[status(thm)],[])).
% 0.21/0.49  tff(212,plain,
% 0.21/0.49      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))))),
% 0.21/0.49      inference(monotonicity,[status(thm)],[211])).
% 0.21/0.49  tff(213,plain,
% 0.21/0.49      (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))))),
% 0.21/0.50      inference(transitivity,[status(thm)],[212, 210])).
% 0.21/0.50  tff(214,plain,
% 0.21/0.50      ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))),
% 0.21/0.50      inference(quant_inst,[status(thm)],[])).
% 0.21/0.50  tff(215,plain,
% 0.21/0.50      ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), A!40)) | (apply(G!41, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_23(tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41), A!40, F!42), tptp_fun_Y_20(image2(F!42, A!40), A!40, G!41)))),
% 0.21/0.50      inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.50  tff(216,plain,
% 0.21/0.50      ($false),
% 0.21/0.50      inference(unit_resolution,[status(thm)],[215, 118, 194, 199, 209])).
% 0.21/0.50  % SZS output end Proof
% 0.21/0.50  % E exiting
%------------------------------------------------------------------------------