TSTP Solution File: SYN076+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN076+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Thu Sep 29 23:53:36 EDT 2022
% Result : Theorem 1.94s 1.47s
% Output : Proof 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN076+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Mon Sep 5 01:46:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.94/1.47 % SZS status Theorem
% 1.94/1.47 % SZS output start Proof
% 1.94/1.47 tff(tptp_fun_Y_0_type, type, (
% 1.94/1.47 tptp_fun_Y_0: $i)).
% 1.94/1.47 tff(tptp_fun_X_1_type, type, (
% 1.94/1.47 tptp_fun_X_1: $i)).
% 1.94/1.47 tff(tptp_fun_W_6_type, type, (
% 1.94/1.47 tptp_fun_W_6: $i > $i)).
% 1.94/1.47 tff(tptp_fun_Z_5_type, type, (
% 1.94/1.47 tptp_fun_Z_5: $i)).
% 1.94/1.47 tff(big_f_type, type, (
% 1.94/1.47 big_f: ( $i * $i ) > $o)).
% 1.94/1.47 tff(tptp_fun_Y_7_type, type, (
% 1.94/1.47 tptp_fun_Y_7: ( $i * $i ) > $i)).
% 1.94/1.47 tff(tptp_fun_Z1_9_type, type, (
% 1.94/1.47 tptp_fun_Z1_9: $i > $i)).
% 1.94/1.47 tff(tptp_fun_W1_8_type, type, (
% 1.94/1.47 tptp_fun_W1_8: $i)).
% 1.94/1.47 tff(tptp_fun_X1_10_type, type, (
% 1.94/1.47 tptp_fun_X1_10: ( $i * $i ) > $i)).
% 1.94/1.47 tff(tptp_fun_Y1_11_type, type, (
% 1.94/1.47 tptp_fun_Y1_11: $i > $i)).
% 1.94/1.47 tff(tptp_fun_X_2_type, type, (
% 1.94/1.47 tptp_fun_X_2: $i > $i)).
% 1.94/1.47 tff(tptp_fun_X1_13_type, type, (
% 1.94/1.47 tptp_fun_X1_13: ( $i * $i ) > $i)).
% 1.94/1.47 tff(tptp_fun_Z1_12_type, type, (
% 1.94/1.47 tptp_fun_Z1_12: $i > $i)).
% 1.94/1.47 tff(tptp_fun_Y_4_type, type, (
% 1.94/1.47 tptp_fun_Y_4: ( $i * $i ) > $i)).
% 1.94/1.47 tff(tptp_fun_W_3_type, type, (
% 1.94/1.47 tptp_fun_W_3: $i > $i)).
% 1.94/1.47 tff(1,plain,
% 1.94/1.47 ((Y!0 = W1!8) <=> (W1!8 = Y!0)),
% 1.94/1.47 inference(commutativity,[status(thm)],[])).
% 1.94/1.47 tff(2,plain,
% 1.94/1.47 ((W1!8 = Y!0) <=> (Y!0 = W1!8)),
% 1.94/1.47 inference(symmetry,[status(thm)],[1])).
% 1.94/1.47 tff(3,assumption,(~(W1!8 = X!1)), introduced(assumption)).
% 1.94/1.47 tff(4,plain,
% 1.94/1.47 (((~(X!1 = Y!0)) & ![Z: $i] : ((Z = Y!0) | (Z = X!1))) <=> ((~(X!1 = Y!0)) & ![Z: $i] : ((Z = Y!0) | (Z = X!1)))),
% 1.94/1.47 inference(rewrite,[status(thm)],[])).
% 1.94/1.47 tff(5,plain,
% 1.94/1.47 (?[X: $i, Y: $i] : ((~(X = Y)) & ![Z: $i] : ((Z = Y) | (Z = X))) <=> ?[X: $i, Y: $i] : ((~(X = Y)) & ![Z: $i] : ((Z = Y) | (Z = X)))),
% 1.94/1.47 inference(rewrite,[status(thm)],[])).
% 1.94/1.47 tff(6,plain,
% 1.94/1.47 (^[X: $i, Y: $i] : rewrite(((~(X = Y)) & ![Z: $i] : ((Z = X) | (Z = Y))) <=> ((~(X = Y)) & ![Z: $i] : ((Z = Y) | (Z = X))))),
% 1.94/1.47 inference(bind,[status(th)],[])).
% 1.94/1.47 tff(7,plain,
% 1.94/1.47 (?[X: $i, Y: $i] : ((~(X = Y)) & ![Z: $i] : ((Z = X) | (Z = Y))) <=> ?[X: $i, Y: $i] : ((~(X = Y)) & ![Z: $i] : ((Z = Y) | (Z = X)))),
% 1.94/1.47 inference(quant_intro,[status(thm)],[6])).
% 1.94/1.47 tff(8,axiom,(?[X: $i, Y: $i] : ((~(X = Y)) & ![Z: $i] : ((Z = X) | (Z = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel53_1')).
% 1.94/1.47 tff(9,plain,
% 1.94/1.47 (?[X: $i, Y: $i] : ((~(X = Y)) & ![Z: $i] : ((Z = Y) | (Z = X)))),
% 1.94/1.47 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.94/1.47 tff(10,plain,
% 1.94/1.47 (?[X: $i, Y: $i] : ((~(X = Y)) & ![Z: $i] : ((Z = Y) | (Z = X)))),
% 1.94/1.47 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.94/1.47 tff(11,plain,
% 1.94/1.47 ((~(X!1 = Y!0)) & ![Z: $i] : ((Z = Y!0) | (Z = X!1))),
% 1.94/1.47 inference(modus_ponens,[status(thm)],[10, 4])).
% 1.94/1.47 tff(12,plain,
% 1.94/1.47 (![Z: $i] : ((Z = Y!0) | (Z = X!1))),
% 1.94/1.47 inference(and_elim,[status(thm)],[11])).
% 1.94/1.47 tff(13,plain,
% 1.94/1.47 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((W1!8 = X!1) | (W1!8 = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (W1!8 = X!1) | (W1!8 = Y!0))),
% 1.94/1.47 inference(rewrite,[status(thm)],[])).
% 1.94/1.47 tff(14,plain,
% 1.94/1.47 (((W1!8 = Y!0) | (W1!8 = X!1)) <=> ((W1!8 = X!1) | (W1!8 = Y!0))),
% 1.94/1.47 inference(rewrite,[status(thm)],[])).
% 1.94/1.47 tff(15,plain,
% 1.94/1.47 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((W1!8 = Y!0) | (W1!8 = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((W1!8 = X!1) | (W1!8 = Y!0)))),
% 1.94/1.47 inference(monotonicity,[status(thm)],[14])).
% 1.94/1.47 tff(16,plain,
% 1.94/1.47 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((W1!8 = Y!0) | (W1!8 = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (W1!8 = X!1) | (W1!8 = Y!0))),
% 1.94/1.47 inference(transitivity,[status(thm)],[15, 13])).
% 1.94/1.47 tff(17,plain,
% 1.94/1.47 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((W1!8 = Y!0) | (W1!8 = X!1))),
% 1.94/1.47 inference(quant_inst,[status(thm)],[])).
% 1.94/1.47 tff(18,plain,
% 1.94/1.47 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (W1!8 = X!1) | (W1!8 = Y!0)),
% 1.94/1.47 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.94/1.47 tff(19,plain,
% 1.94/1.47 ((W1!8 = X!1) | (W1!8 = Y!0)),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[18, 12])).
% 1.94/1.47 tff(20,plain,
% 1.94/1.47 (W1!8 = Y!0),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[19, 3])).
% 1.94/1.47 tff(21,plain,
% 1.94/1.47 (Y!0 = W1!8),
% 1.94/1.47 inference(modus_ponens,[status(thm)],[20, 2])).
% 1.94/1.47 tff(22,plain,
% 1.94/1.47 ((tptp_fun_X1_13(X!1, X!1) = W1!8) <=> (tptp_fun_X1_13(X!1, X!1) = Y!0)),
% 1.94/1.47 inference(monotonicity,[status(thm)],[20])).
% 1.94/1.47 tff(23,plain,
% 1.94/1.47 ((tptp_fun_X1_13(X!1, X!1) = Y!0) <=> (tptp_fun_X1_13(X!1, X!1) = W1!8)),
% 1.94/1.47 inference(symmetry,[status(thm)],[22])).
% 1.94/1.47 tff(24,plain,
% 1.94/1.47 ((X!1 = W1!8) <=> (W1!8 = X!1)),
% 1.94/1.47 inference(commutativity,[status(thm)],[])).
% 1.94/1.47 tff(25,assumption,(X!1 = W1!8), introduced(assumption)).
% 1.94/1.47 tff(26,plain,
% 1.94/1.47 (W1!8 = X!1),
% 1.94/1.47 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.94/1.47 tff(27,plain,
% 1.94/1.47 ($false),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[3, 26])).
% 1.94/1.47 tff(28,plain,((~(X!1 = W1!8)) | (W1!8 = X!1)), inference(lemma,lemma(discharge,[]))).
% 1.94/1.47 tff(29,plain,
% 1.94/1.47 (~(X!1 = W1!8)),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[28, 3])).
% 1.94/1.47 tff(30,assumption,(tptp_fun_X_2(Y!0) = Y!0), introduced(assumption)).
% 1.94/1.47 tff(31,plain,
% 1.94/1.47 (Y!0 = tptp_fun_X_2(Y!0)),
% 1.94/1.47 inference(symmetry,[status(thm)],[30])).
% 1.94/1.47 tff(32,plain,
% 1.94/1.47 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 1.94/1.47 inference(monotonicity,[status(thm)],[31, 30])).
% 1.94/1.47 tff(33,plain,
% 1.94/1.47 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 1.94/1.47 inference(symmetry,[status(thm)],[32])).
% 1.94/1.47 tff(34,assumption,(~(tptp_fun_Y1_11(Y!0) = Y!0)), introduced(assumption)).
% 1.94/1.47 tff(35,assumption,(~big_f(tptp_fun_X_2(Y!0), Y!0)), introduced(assumption)).
% 1.94/1.47 tff(36,plain,
% 1.94/1.47 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y1_11(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y1_11(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = X!1))),
% 1.94/1.47 inference(rewrite,[status(thm)],[])).
% 1.94/1.47 tff(37,plain,
% 1.94/1.47 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y1_11(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = X!1))),
% 1.94/1.47 inference(quant_inst,[status(thm)],[])).
% 1.94/1.47 tff(38,plain,
% 1.94/1.47 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y1_11(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = X!1)),
% 1.94/1.47 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.94/1.47 tff(39,plain,
% 1.94/1.47 ((tptp_fun_Y1_11(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = X!1)),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[38, 12])).
% 1.94/1.47 tff(40,plain,
% 1.94/1.47 (tptp_fun_Y1_11(Y!0) = X!1),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[39, 34])).
% 1.94/1.47 tff(41,assumption,(~big_f(Y!0, tptp_fun_Y1_11(Y!0))), introduced(assumption)).
% 1.94/1.47 tff(42,assumption,(~big_f(X!1, tptp_fun_Y1_11(Y!0))), introduced(assumption)).
% 1.94/1.47 tff(43,plain,
% 1.94/1.47 ((Y!0 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_Z1_9(W1!8) = Y!0)),
% 1.94/1.47 inference(commutativity,[status(thm)],[])).
% 1.94/1.47 tff(44,plain,
% 1.94/1.47 ((~(Y!0 = tptp_fun_Z1_9(W1!8))) <=> (~(tptp_fun_Z1_9(W1!8) = Y!0))),
% 1.94/1.47 inference(monotonicity,[status(thm)],[43])).
% 1.94/1.47 tff(45,assumption,(~big_f(X!1, Y!0)), introduced(assumption)).
% 1.94/1.47 tff(46,plain,
% 1.94/1.47 ((Y!0 = X!1) <=> (X!1 = Y!0)),
% 1.94/1.47 inference(commutativity,[status(thm)],[])).
% 1.94/1.47 tff(47,assumption,(~(tptp_fun_X_2(X!1) = X!1)), introduced(assumption)).
% 1.94/1.47 tff(48,assumption,(~(tptp_fun_Y_4(Y!0, Y!0) = Y!0)), introduced(assumption)).
% 1.94/1.47 tff(49,assumption,(~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))), introduced(assumption)).
% 1.94/1.47 tff(50,plain,
% 1.94/1.47 ((~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))) | ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 1.94/1.47 inference(quant_inst,[status(thm)],[])).
% 1.94/1.47 tff(51,plain,
% 1.94/1.47 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[50, 49])).
% 1.94/1.47 tff(52,plain,
% 1.94/1.47 ((~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 1.94/1.47 inference(tautology,[status(thm)],[])).
% 1.94/1.47 tff(53,plain,
% 1.94/1.47 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[52, 51, 30])).
% 1.94/1.47 tff(54,plain,
% 1.94/1.47 (((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))) | ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 1.94/1.47 inference(tautology,[status(thm)],[])).
% 1.94/1.47 tff(55,plain,
% 1.94/1.47 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[54, 53])).
% 1.94/1.47 tff(56,plain,
% 1.94/1.47 ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))))),
% 1.94/1.47 inference(quant_inst,[status(thm)],[])).
% 1.94/1.47 tff(57,plain,
% 1.94/1.47 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 1.94/1.47 inference(unit_resolution,[status(thm)],[56, 55])).
% 1.94/1.47 tff(58,plain,
% 1.94/1.47 ((![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))))) | ![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) <=> (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))))) | ![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))))))),
% 1.94/1.47 inference(rewrite,[status(thm)],[])).
% 1.94/1.47 tff(59,plain,
% 1.94/1.47 (^[W1: $i] : trans(monotonicity(rewrite(((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) <=> ((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))), rewrite(((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))) <=> ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))), ((((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))) <=> (((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))))), rewrite((((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))) <=> (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))), ((((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))) <=> (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))))),
% 1.94/1.47 inference(bind,[status(th)],[])).
% 1.94/1.47 tff(60,plain,
% 1.94/1.47 (![W1: $i] : (((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))) <=> ![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 1.94/1.47 inference(quant_intro,[status(thm)],[59])).
% 1.94/1.47 tff(61,plain,
% 1.94/1.47 (^[Z: $i] : trans(monotonicity(rewrite(((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) <=> ((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))), rewrite(((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))) <=> ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))), ((((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) <=> (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))))), rewrite((((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) <=> (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))), ((((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) <=> (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))))),
% 1.94/1.48 inference(bind,[status(th)],[])).
% 1.94/1.48 tff(62,plain,
% 1.94/1.48 (![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) <=> ![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 1.94/1.48 inference(quant_intro,[status(thm)],[61])).
% 1.94/1.48 tff(63,plain,
% 1.94/1.48 ((![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) | ![W1: $i] : (((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))) <=> (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))))) | ![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))))))),
% 1.94/1.48 inference(monotonicity,[status(thm)],[62, 60])).
% 1.94/1.48 tff(64,plain,
% 1.94/1.48 ((![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) | ![W1: $i] : (((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))) <=> (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))))) | ![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))))))),
% 1.94/1.48 inference(transitivity,[status(thm)],[63, 58])).
% 1.94/1.48 tff(65,plain,
% 1.94/1.48 (((![X: $i] : ((![W: $i] : (~(big_f(X, tptp_fun_Y_7(W, X)) <=> (tptp_fun_Y_7(W, X) = W))) | (X = Z!5)) & (![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))) | ![Y1: $i] : ((![Z1: $i] : (~(big_f(tptp_fun_X1_10(Z1, Y1), Y1) <=> (tptp_fun_X1_10(Z1, Y1) = Z1))) | (Y1 = W1!8)) & (![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))) & (![Z: $i] : ((![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))) | (tptp_fun_X_2(Z) = Z)) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) | ![W1: $i] : ((![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))) | (tptp_fun_Y1_11(W1) = W1)) & (![Z1: $i] : (~(big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1)) <=> (tptp_fun_X1_13(Z1, W1) = Z1))) | (~(tptp_fun_Y1_11(W1) = W1)))))) <=> ((![X: $i] : (((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W))) & (![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))) | ![Y1: $i] : (((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1))) & (![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))) & (![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) | ![W1: $i] : (((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 1.94/1.48 inference(rewrite,[status(thm)],[])).
% 1.94/1.48 tff(66,plain,
% 1.94/1.48 (((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))) <=> ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))),
% 1.94/1.48 inference(rewrite,[status(thm)],[])).
% 1.94/1.48 tff(67,plain,
% 1.94/1.48 ((~(?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))) <=> ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))),
% 1.94/1.48 inference(rewrite,[status(thm)],[])).
% 1.94/1.48 tff(68,plain,
% 1.94/1.48 ((?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))) <=> (?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))),
% 1.94/1.48 inference(rewrite,[status(thm)],[])).
% 1.94/1.48 tff(69,plain,
% 1.94/1.48 ((~(?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))) <=> (~(?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))))),
% 1.94/1.48 inference(monotonicity,[status(thm)],[68])).
% 1.94/1.48 tff(70,plain,
% 1.94/1.48 ((~(?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))) <=> ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))),
% 1.94/1.48 inference(transitivity,[status(thm)],[69, 67])).
% 1.94/1.48 tff(71,axiom,(~(?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel53')).
% 1.94/1.48 tff(72,plain,
% 1.94/1.48 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.94/1.48 tff(73,plain,
% 1.94/1.48 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[72, 66])).
% 1.94/1.48 tff(74,plain,
% 1.94/1.48 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.94/1.48 tff(75,plain,
% 1.94/1.48 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[74, 66])).
% 1.94/1.48 tff(76,plain,
% 1.94/1.48 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[75, 66])).
% 1.94/1.48 tff(77,plain,
% 1.94/1.48 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[76, 66])).
% 1.94/1.48 tff(78,plain,
% 1.94/1.48 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> ?[W1: $i] : ![Y1: $i] : (?[Z1: $i] : ![X1: $i] : (big_f(X1, Y1) <=> (X1 = Z1)) <=> (Y1 = W1))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[77, 66])).
% 1.94/1.48 tff(79,plain,(
% 1.94/1.48 (![X: $i] : ((![W: $i] : (~(big_f(X, tptp_fun_Y_7(W, X)) <=> (tptp_fun_Y_7(W, X) = W))) | (X = Z!5)) & (![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))) | ![Y1: $i] : ((![Z1: $i] : (~(big_f(tptp_fun_X1_10(Z1, Y1), Y1) <=> (tptp_fun_X1_10(Z1, Y1) = Z1))) | (Y1 = W1!8)) & (![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))) & (![Z: $i] : ((![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))) | (tptp_fun_X_2(Z) = Z)) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) | ![W1: $i] : ((![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))) | (tptp_fun_Y1_11(W1) = W1)) & (![Z1: $i] : (~(big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1)) <=> (tptp_fun_X1_13(Z1, W1) = Z1))) | (~(tptp_fun_Y1_11(W1) = W1)))))),
% 1.94/1.48 inference(skolemize,[status(sab)],[78])).
% 1.94/1.48 tff(80,plain,
% 1.94/1.48 ((![X: $i] : (((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W))) & (![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))) | ![Y1: $i] : (((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1))) & (![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))) & (![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) | ![W1: $i] : (((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1)))))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[79, 65])).
% 1.94/1.48 tff(81,plain,
% 1.94/1.48 (![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & ((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))) | ![W1: $i] : (((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1)))) & ((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))),
% 1.94/1.48 inference(and_elim,[status(thm)],[80])).
% 1.94/1.48 tff(82,plain,
% 1.94/1.48 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W)))))) | ![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 1.94/1.48 inference(modus_ponens,[status(thm)],[81, 64])).
% 1.94/1.48 tff(83,plain,
% 1.94/1.48 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 1.94/1.48 inference(unit_resolution,[status(thm)],[82, 57])).
% 1.94/1.48 tff(84,plain,
% 1.94/1.48 ((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))))),
% 1.94/1.48 inference(quant_inst,[status(thm)],[])).
% 1.94/1.48 tff(85,plain,
% 1.94/1.48 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 1.94/1.48 inference(unit_resolution,[status(thm)],[84, 83])).
% 1.94/1.48 tff(86,plain,
% 1.94/1.48 (((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))) | ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 1.94/1.48 inference(tautology,[status(thm)],[])).
% 1.94/1.48 tff(87,plain,
% 1.94/1.48 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[86, 85])).
% 1.94/1.49 tff(88,plain,
% 1.94/1.49 ((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))))),
% 1.94/1.49 inference(quant_inst,[status(thm)],[])).
% 1.94/1.49 tff(89,plain,
% 1.94/1.49 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[88, 83])).
% 1.94/1.49 tff(90,plain,
% 1.94/1.49 (((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))) | ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 1.94/1.49 inference(tautology,[status(thm)],[])).
% 1.94/1.49 tff(91,plain,
% 1.94/1.49 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[90, 89])).
% 1.94/1.49 tff(92,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(Y!0, Y!0) = Y!0) | (tptp_fun_Y_4(Y!0, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(Y!0, Y!0) = Y!0) | (tptp_fun_Y_4(Y!0, Y!0) = X!1))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(93,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(Y!0, Y!0) = Y!0) | (tptp_fun_Y_4(Y!0, Y!0) = X!1))),
% 1.94/1.49 inference(quant_inst,[status(thm)],[])).
% 1.94/1.49 tff(94,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(Y!0, Y!0) = Y!0) | (tptp_fun_Y_4(Y!0, Y!0) = X!1)),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.94/1.49 tff(95,plain,
% 1.94/1.49 ((tptp_fun_Y_4(Y!0, Y!0) = Y!0) | (tptp_fun_Y_4(Y!0, Y!0) = X!1)),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[94, 12])).
% 1.94/1.49 tff(96,plain,
% 1.94/1.49 (tptp_fun_Y_4(Y!0, Y!0) = X!1),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[95, 48])).
% 1.94/1.49 tff(97,plain,
% 1.94/1.49 (((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) | (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 1.94/1.49 inference(tautology,[status(thm)],[])).
% 1.94/1.49 tff(98,plain,
% 1.94/1.49 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[97, 49, 48])).
% 1.94/1.49 tff(99,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(X!1) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(X!1) = Y!0))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(100,plain,
% 1.94/1.49 (((tptp_fun_X_2(X!1) = Y!0) | (tptp_fun_X_2(X!1) = X!1)) <=> ((tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(X!1) = Y!0))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(101,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X_2(X!1) = Y!0) | (tptp_fun_X_2(X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(X!1) = Y!0)))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[100])).
% 1.94/1.49 tff(102,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X_2(X!1) = Y!0) | (tptp_fun_X_2(X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(X!1) = Y!0))),
% 1.94/1.49 inference(transitivity,[status(thm)],[101, 99])).
% 1.94/1.49 tff(103,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X_2(X!1) = Y!0) | (tptp_fun_X_2(X!1) = X!1))),
% 1.94/1.49 inference(quant_inst,[status(thm)],[])).
% 1.94/1.49 tff(104,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(X!1) = Y!0)),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.94/1.49 tff(105,plain,
% 1.94/1.49 ((tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(X!1) = Y!0)),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[104, 12])).
% 1.94/1.49 tff(106,plain,
% 1.94/1.49 (tptp_fun_X_2(X!1) = Y!0),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[105, 47])).
% 1.94/1.49 tff(107,assumption,(~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))), introduced(assumption)).
% 1.94/1.49 tff(108,assumption,(tptp_fun_Y_4(Y!0, Y!0) = X!1), introduced(assumption)).
% 1.94/1.49 tff(109,assumption,(tptp_fun_Y1_11(Y!0) = Y!0), introduced(assumption)).
% 1.94/1.49 tff(110,plain,
% 1.94/1.49 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 1.94/1.49 inference(monotonicity,[status(thm)],[31, 109])).
% 1.94/1.49 tff(111,plain,
% 1.94/1.49 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(Y!0), Y!0))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[110])).
% 1.94/1.49 tff(112,assumption,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))), introduced(assumption)).
% 1.94/1.49 tff(113,plain,
% 1.94/1.49 ((~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 1.94/1.49 inference(tautology,[status(thm)],[])).
% 1.94/1.49 tff(114,plain,
% 1.94/1.49 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[113, 109, 112])).
% 1.94/1.49 tff(115,plain,
% 1.94/1.49 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))) | ((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0))),
% 1.94/1.49 inference(quant_inst,[status(thm)],[])).
% 1.94/1.49 tff(116,plain,
% 1.94/1.49 ((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0)),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[115, 114])).
% 1.94/1.49 tff(117,assumption,((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0)), introduced(assumption)).
% 1.94/1.49 tff(118,assumption,(~(tptp_fun_X1_13(Y!0, Y!0) = Y!0)), introduced(assumption)).
% 1.94/1.49 tff(119,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(Y!0, Y!0) = Y!0) | (tptp_fun_X1_13(Y!0, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(Y!0, Y!0) = Y!0) | (tptp_fun_X1_13(Y!0, Y!0) = X!1))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(120,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(Y!0, Y!0) = Y!0) | (tptp_fun_X1_13(Y!0, Y!0) = X!1))),
% 1.94/1.49 inference(quant_inst,[status(thm)],[])).
% 1.94/1.49 tff(121,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(Y!0, Y!0) = Y!0) | (tptp_fun_X1_13(Y!0, Y!0) = X!1)),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.94/1.49 tff(122,plain,
% 1.94/1.49 ((tptp_fun_X1_13(Y!0, Y!0) = Y!0) | (tptp_fun_X1_13(Y!0, Y!0) = X!1)),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[121, 12])).
% 1.94/1.49 tff(123,plain,
% 1.94/1.49 (tptp_fun_X1_13(Y!0, Y!0) = X!1),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[122, 118])).
% 1.94/1.49 tff(124,plain,
% 1.94/1.49 (big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, Y!0)),
% 1.94/1.49 inference(monotonicity,[status(thm)],[123, 109])).
% 1.94/1.49 tff(125,plain,
% 1.94/1.49 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(symmetry,[status(thm)],[124])).
% 1.94/1.49 tff(126,plain,
% 1.94/1.49 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0)))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[125])).
% 1.94/1.49 tff(127,plain,
% 1.94/1.49 (~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[45, 126])).
% 1.94/1.49 tff(128,plain,
% 1.94/1.49 ((~((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0))) | big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0)) | (tptp_fun_X1_13(Y!0, Y!0) = Y!0)),
% 1.94/1.49 inference(tautology,[status(thm)],[])).
% 1.94/1.49 tff(129,plain,
% 1.94/1.49 (big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[128, 118, 117])).
% 1.94/1.49 tff(130,plain,
% 1.94/1.49 ($false),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[129, 127])).
% 1.94/1.49 tff(131,plain,((tptp_fun_X1_13(Y!0, Y!0) = Y!0) | big_f(X!1, Y!0) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.49 tff(132,plain,
% 1.94/1.49 (tptp_fun_X1_13(Y!0, Y!0) = Y!0),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[131, 117, 109, 45])).
% 1.94/1.49 tff(133,plain,
% 1.94/1.49 (big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[132])).
% 1.94/1.49 tff(134,plain,
% 1.94/1.49 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(symmetry,[status(thm)],[133])).
% 1.94/1.49 tff(135,assumption,(big_f(Y!0, tptp_fun_Y1_11(Y!0))), introduced(assumption)).
% 1.94/1.49 tff(136,plain,
% 1.94/1.49 (big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.94/1.49 tff(137,plain,
% 1.94/1.49 ((~((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0))) | (~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_X1_13(Y!0, Y!0) = Y!0))),
% 1.94/1.49 inference(tautology,[status(thm)],[])).
% 1.94/1.49 tff(138,plain,
% 1.94/1.49 (~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[137, 132, 117])).
% 1.94/1.49 tff(139,plain,
% 1.94/1.49 ($false),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[138, 136])).
% 1.94/1.49 tff(140,plain,((~((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 1.94/1.49 tff(141,plain,
% 1.94/1.49 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[140, 116, 45, 109])).
% 1.94/1.49 tff(142,plain,
% 1.94/1.49 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[141, 111])).
% 1.94/1.49 tff(143,assumption,((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))), introduced(assumption)).
% 1.94/1.49 tff(144,assumption,(~(tptp_fun_Y1_11(X!1) = X!1)), introduced(assumption)).
% 1.94/1.49 tff(145,assumption,((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))), introduced(assumption)).
% 1.94/1.49 tff(146,plain,
% 1.94/1.49 (Y!0 = tptp_fun_Y1_11(Y!0)),
% 1.94/1.49 inference(symmetry,[status(thm)],[109])).
% 1.94/1.49 tff(147,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = Y!0))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(148,plain,
% 1.94/1.49 (((tptp_fun_Y1_11(X!1) = Y!0) | (tptp_fun_Y1_11(X!1) = X!1)) <=> ((tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = Y!0))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(149,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y1_11(X!1) = Y!0) | (tptp_fun_Y1_11(X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = Y!0)))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[148])).
% 1.94/1.49 tff(150,plain,
% 1.94/1.49 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y1_11(X!1) = Y!0) | (tptp_fun_Y1_11(X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = Y!0))),
% 1.94/1.49 inference(transitivity,[status(thm)],[149, 147])).
% 1.94/1.49 tff(151,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y1_11(X!1) = Y!0) | (tptp_fun_Y1_11(X!1) = X!1))),
% 1.94/1.49 inference(quant_inst,[status(thm)],[])).
% 1.94/1.49 tff(152,plain,
% 1.94/1.49 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = Y!0)),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.94/1.49 tff(153,plain,
% 1.94/1.49 ((tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = Y!0)),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[152, 12])).
% 1.94/1.49 tff(154,plain,
% 1.94/1.49 (tptp_fun_Y1_11(X!1) = Y!0),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[153, 144])).
% 1.94/1.49 tff(155,plain,
% 1.94/1.49 (tptp_fun_Y1_11(X!1) = tptp_fun_Y1_11(Y!0)),
% 1.94/1.49 inference(transitivity,[status(thm)],[154, 146])).
% 1.94/1.49 tff(156,assumption,(tptp_fun_Z1_12(X!1) = Y!0), introduced(assumption)).
% 1.94/1.49 tff(157,plain,
% 1.94/1.49 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[156, 155])).
% 1.94/1.49 tff(158,plain,
% 1.94/1.49 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.49 inference(symmetry,[status(thm)],[157])).
% 1.94/1.49 tff(159,plain,
% 1.94/1.49 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[158])).
% 1.94/1.49 tff(160,plain,
% 1.94/1.49 (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[41, 159])).
% 1.94/1.49 tff(161,plain,
% 1.94/1.49 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 1.94/1.49 inference(tautology,[status(thm)],[])).
% 1.94/1.49 tff(162,plain,
% 1.94/1.49 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[161, 144, 145])).
% 1.94/1.49 tff(163,plain,
% 1.94/1.49 (((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))) <=> ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(164,plain,
% 1.94/1.49 ((big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> $true) <=> big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(165,plain,
% 1.94/1.49 ((tptp_fun_Z1_12(X!1) = tptp_fun_Z1_12(X!1)) <=> $true),
% 1.94/1.49 inference(rewrite,[status(thm)],[])).
% 1.94/1.49 tff(166,plain,
% 1.94/1.49 ((big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_Z1_12(X!1) = tptp_fun_Z1_12(X!1))) <=> (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> $true)),
% 1.94/1.49 inference(monotonicity,[status(thm)],[165])).
% 1.94/1.49 tff(167,plain,
% 1.94/1.49 ((big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_Z1_12(X!1) = tptp_fun_Z1_12(X!1))) <=> big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.49 inference(transitivity,[status(thm)],[166, 164])).
% 1.94/1.49 tff(168,plain,
% 1.94/1.49 (((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_Z1_12(X!1) = tptp_fun_Z1_12(X!1)))) <=> ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))),
% 1.94/1.49 inference(monotonicity,[status(thm)],[167])).
% 1.94/1.49 tff(169,plain,
% 1.94/1.49 (((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_Z1_12(X!1) = tptp_fun_Z1_12(X!1)))) <=> ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))),
% 1.94/1.49 inference(transitivity,[status(thm)],[168, 163])).
% 1.94/1.49 tff(170,plain,
% 1.94/1.49 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_Z1_12(X!1) = tptp_fun_Z1_12(X!1)))),
% 1.94/1.49 inference(quant_inst,[status(thm)],[])).
% 1.94/1.49 tff(171,plain,
% 1.94/1.49 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.49 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.94/1.49 tff(172,plain,
% 1.94/1.49 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[171, 162])).
% 1.94/1.49 tff(173,plain,
% 1.94/1.49 ($false),
% 1.94/1.49 inference(unit_resolution,[status(thm)],[172, 160])).
% 1.94/1.49 tff(174,plain,((tptp_fun_Y1_11(X!1) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_Z1_12(X!1) = Y!0)) | (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.50 tff(175,plain,
% 1.94/1.50 (~(tptp_fun_Z1_12(X!1) = Y!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[174, 145, 109, 144, 41])).
% 1.94/1.50 tff(176,assumption,(tptp_fun_Z1_12(X!1) = X!1), introduced(assumption)).
% 1.94/1.50 tff(177,plain,
% 1.94/1.50 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 1.94/1.50 inference(monotonicity,[status(thm)],[176, 154])).
% 1.94/1.50 tff(178,plain,
% 1.94/1.50 (big_f(X!1, Y!0) <=> big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.50 inference(symmetry,[status(thm)],[177])).
% 1.94/1.50 tff(179,plain,
% 1.94/1.50 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[178])).
% 1.94/1.50 tff(180,plain,
% 1.94/1.50 (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[45, 179])).
% 1.94/1.50 tff(181,plain,
% 1.94/1.50 ($false),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[172, 180])).
% 1.94/1.50 tff(182,plain,((tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | (~(tptp_fun_Z1_12(X!1) = X!1)) | (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.50 tff(183,plain,
% 1.94/1.50 (~(tptp_fun_Z1_12(X!1) = X!1)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[182, 145, 144, 45])).
% 1.94/1.50 tff(184,plain,
% 1.94/1.50 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_12(X!1) = Y!0) | (tptp_fun_Z1_12(X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Z1_12(X!1) = Y!0) | (tptp_fun_Z1_12(X!1) = X!1))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(185,plain,
% 1.94/1.50 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_12(X!1) = Y!0) | (tptp_fun_Z1_12(X!1) = X!1))),
% 1.94/1.50 inference(quant_inst,[status(thm)],[])).
% 1.94/1.50 tff(186,plain,
% 1.94/1.50 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Z1_12(X!1) = Y!0) | (tptp_fun_Z1_12(X!1) = X!1)),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.94/1.50 tff(187,plain,
% 1.94/1.50 ((tptp_fun_Z1_12(X!1) = Y!0) | (tptp_fun_Z1_12(X!1) = X!1)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[186, 12])).
% 1.94/1.50 tff(188,plain,
% 1.94/1.50 ($false),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[187, 183, 175])).
% 1.94/1.50 tff(189,plain,((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.50 tff(190,plain,
% 1.94/1.50 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[189, 109, 144, 45, 41])).
% 1.94/1.50 tff(191,plain,
% 1.94/1.50 (((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))) | ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 1.94/1.50 inference(tautology,[status(thm)],[])).
% 1.94/1.50 tff(192,plain,
% 1.94/1.50 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[191, 190])).
% 1.94/1.50 tff(193,plain,
% 1.94/1.50 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[88, 192])).
% 1.94/1.50 tff(194,plain,
% 1.94/1.50 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[82, 193])).
% 1.94/1.50 tff(195,plain,
% 1.94/1.50 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[56, 194])).
% 1.94/1.50 tff(196,plain,
% 1.94/1.50 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[54, 195])).
% 1.94/1.50 tff(197,plain,
% 1.94/1.50 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[52, 196, 30])).
% 1.94/1.50 tff(198,plain,
% 1.94/1.50 ((~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))) | ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 1.94/1.50 inference(quant_inst,[status(thm)],[])).
% 1.94/1.50 tff(199,plain,
% 1.94/1.50 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[198, 197])).
% 1.94/1.50 tff(200,assumption,(~(tptp_fun_Y_4(X!1, Y!0) = X!1)), introduced(assumption)).
% 1.94/1.50 tff(201,plain,
% 1.94/1.50 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, Y!0) = X!1) | (tptp_fun_Y_4(X!1, Y!0) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(X!1, Y!0) = X!1) | (tptp_fun_Y_4(X!1, Y!0) = Y!0))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(202,plain,
% 1.94/1.50 (((tptp_fun_Y_4(X!1, Y!0) = Y!0) | (tptp_fun_Y_4(X!1, Y!0) = X!1)) <=> ((tptp_fun_Y_4(X!1, Y!0) = X!1) | (tptp_fun_Y_4(X!1, Y!0) = Y!0))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(203,plain,
% 1.94/1.50 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, Y!0) = Y!0) | (tptp_fun_Y_4(X!1, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, Y!0) = X!1) | (tptp_fun_Y_4(X!1, Y!0) = Y!0)))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[202])).
% 1.94/1.50 tff(204,plain,
% 1.94/1.50 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, Y!0) = Y!0) | (tptp_fun_Y_4(X!1, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(X!1, Y!0) = X!1) | (tptp_fun_Y_4(X!1, Y!0) = Y!0))),
% 1.94/1.50 inference(transitivity,[status(thm)],[203, 201])).
% 1.94/1.50 tff(205,plain,
% 1.94/1.50 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, Y!0) = Y!0) | (tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 1.94/1.50 inference(quant_inst,[status(thm)],[])).
% 1.94/1.50 tff(206,plain,
% 1.94/1.50 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(X!1, Y!0) = X!1) | (tptp_fun_Y_4(X!1, Y!0) = Y!0)),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.94/1.50 tff(207,plain,
% 1.94/1.50 ((tptp_fun_Y_4(X!1, Y!0) = X!1) | (tptp_fun_Y_4(X!1, Y!0) = Y!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[206, 12])).
% 1.94/1.50 tff(208,plain,
% 1.94/1.50 (tptp_fun_Y_4(X!1, Y!0) = Y!0),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[207, 200])).
% 1.94/1.50 tff(209,plain,
% 1.94/1.50 (tptp_fun_Y_4(X!1, Y!0) = tptp_fun_Y1_11(Y!0)),
% 1.94/1.50 inference(transitivity,[status(thm)],[208, 146])).
% 1.94/1.50 tff(210,plain,
% 1.94/1.50 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[30, 209])).
% 1.94/1.50 tff(211,plain,
% 1.94/1.50 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 1.94/1.50 inference(symmetry,[status(thm)],[210])).
% 1.94/1.50 tff(212,plain,
% 1.94/1.50 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[211])).
% 1.94/1.50 tff(213,plain,
% 1.94/1.50 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[41, 212])).
% 1.94/1.50 tff(214,assumption,((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)), introduced(assumption)).
% 1.94/1.50 tff(215,plain,
% 1.94/1.50 ((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) | (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 1.94/1.50 inference(tautology,[status(thm)],[])).
% 1.94/1.50 tff(216,plain,
% 1.94/1.50 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[215, 200, 214])).
% 1.94/1.50 tff(217,plain,
% 1.94/1.50 ($false),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[216, 213])).
% 1.94/1.50 tff(218,plain,((tptp_fun_Y_4(X!1, Y!0) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.50 tff(219,plain,
% 1.94/1.50 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[218, 199, 30, 41, 109])).
% 1.94/1.50 tff(220,plain,
% 1.94/1.50 ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))))),
% 1.94/1.50 inference(quant_inst,[status(thm)],[])).
% 1.94/1.50 tff(221,plain,
% 1.94/1.50 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[220, 194])).
% 1.94/1.50 tff(222,plain,
% 1.94/1.50 (((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))) | ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))),
% 1.94/1.50 inference(tautology,[status(thm)],[])).
% 1.94/1.50 tff(223,plain,
% 1.94/1.50 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[222, 221])).
% 1.94/1.50 tff(224,plain,
% 1.94/1.50 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 1.94/1.50 inference(tautology,[status(thm)],[])).
% 1.94/1.50 tff(225,plain,
% 1.94/1.50 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[224, 223, 47])).
% 1.94/1.50 tff(226,plain,
% 1.94/1.50 (((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(227,plain,
% 1.94/1.50 ((big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> $true) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(228,plain,
% 1.94/1.50 ((tptp_fun_W_3(X!1) = tptp_fun_W_3(X!1)) <=> $true),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(229,plain,
% 1.94/1.50 ((big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> (tptp_fun_W_3(X!1) = tptp_fun_W_3(X!1))) <=> (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> $true)),
% 1.94/1.50 inference(monotonicity,[status(thm)],[228])).
% 1.94/1.50 tff(230,plain,
% 1.94/1.50 ((big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> (tptp_fun_W_3(X!1) = tptp_fun_W_3(X!1))) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.50 inference(transitivity,[status(thm)],[229, 227])).
% 1.94/1.50 tff(231,plain,
% 1.94/1.50 (((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> (tptp_fun_W_3(X!1) = tptp_fun_W_3(X!1)))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[230])).
% 1.94/1.50 tff(232,plain,
% 1.94/1.50 (((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> (tptp_fun_W_3(X!1) = tptp_fun_W_3(X!1)))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 1.94/1.50 inference(transitivity,[status(thm)],[231, 226])).
% 1.94/1.50 tff(233,plain,
% 1.94/1.50 ((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> (tptp_fun_W_3(X!1) = tptp_fun_W_3(X!1)))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(234,plain,
% 1.94/1.51 ((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.94/1.51 tff(235,plain,
% 1.94/1.51 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[234, 225])).
% 1.94/1.51 tff(236,plain,
% 1.94/1.51 ((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))) | (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) | (~(tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 1.94/1.51 inference(tautology,[status(thm)],[])).
% 1.94/1.51 tff(237,plain,
% 1.94/1.51 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[236, 219, 199])).
% 1.94/1.51 tff(238,assumption,(tptp_fun_W_3(X!1) = Y!0), introduced(assumption)).
% 1.94/1.51 tff(239,plain,
% 1.94/1.51 (tptp_fun_W_3(X!1) = tptp_fun_Y1_11(Y!0)),
% 1.94/1.51 inference(transitivity,[status(thm)],[238, 146])).
% 1.94/1.51 tff(240,assumption,(tptp_fun_X_2(X!1) = Y!0), introduced(assumption)).
% 1.94/1.51 tff(241,plain,
% 1.94/1.51 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[240, 239])).
% 1.94/1.51 tff(242,plain,
% 1.94/1.51 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.51 inference(symmetry,[status(thm)],[241])).
% 1.94/1.51 tff(243,plain,
% 1.94/1.51 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[242])).
% 1.94/1.51 tff(244,plain,
% 1.94/1.51 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[41, 243])).
% 1.94/1.51 tff(245,assumption,(big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))), introduced(assumption)).
% 1.94/1.51 tff(246,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[245, 244])).
% 1.94/1.51 tff(247,plain,((~(tptp_fun_W_3(X!1) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(248,plain,
% 1.94/1.51 (~(tptp_fun_W_3(X!1) = Y!0)),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[247, 235, 41, 109, 106])).
% 1.94/1.51 tff(249,plain,
% 1.94/1.51 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_3(X!1) = Y!0) | (tptp_fun_W_3(X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_3(X!1) = Y!0) | (tptp_fun_W_3(X!1) = X!1))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(250,plain,
% 1.94/1.51 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_3(X!1) = Y!0) | (tptp_fun_W_3(X!1) = X!1))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(251,plain,
% 1.94/1.51 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_3(X!1) = Y!0) | (tptp_fun_W_3(X!1) = X!1)),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.94/1.51 tff(252,plain,
% 1.94/1.51 ((tptp_fun_W_3(X!1) = Y!0) | (tptp_fun_W_3(X!1) = X!1)),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[251, 12])).
% 1.94/1.51 tff(253,plain,
% 1.94/1.51 (tptp_fun_W_3(X!1) = X!1),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[252, 248])).
% 1.94/1.51 tff(254,assumption,(tptp_fun_Y_4(X!1, Y!0) = X!1), introduced(assumption)).
% 1.94/1.51 tff(255,plain,
% 1.94/1.51 (X!1 = tptp_fun_Y_4(X!1, Y!0)),
% 1.94/1.51 inference(symmetry,[status(thm)],[254])).
% 1.94/1.51 tff(256,assumption,(tptp_fun_W_3(X!1) = X!1), introduced(assumption)).
% 1.94/1.51 tff(257,plain,
% 1.94/1.51 (tptp_fun_W_3(X!1) = tptp_fun_Y_4(X!1, Y!0)),
% 1.94/1.51 inference(transitivity,[status(thm)],[256, 255])).
% 1.94/1.51 tff(258,plain,
% 1.94/1.51 (tptp_fun_X_2(X!1) = tptp_fun_X_2(Y!0)),
% 1.94/1.51 inference(transitivity,[status(thm)],[240, 31])).
% 1.94/1.51 tff(259,plain,
% 1.94/1.51 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[258, 257])).
% 1.94/1.51 tff(260,plain,
% 1.94/1.51 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.51 inference(symmetry,[status(thm)],[259])).
% 1.94/1.51 tff(261,plain,
% 1.94/1.51 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[260])).
% 1.94/1.51 tff(262,assumption,(~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))), introduced(assumption)).
% 1.94/1.51 tff(263,plain,
% 1.94/1.51 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.94/1.51 tff(264,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[245, 263])).
% 1.94/1.51 tff(265,plain,((~(tptp_fun_W_3(X!1) = X!1)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) | (~(tptp_fun_Y_4(X!1, Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(266,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[265, 253, 237, 235, 219, 30, 106])).
% 1.94/1.51 tff(267,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(268,plain,
% 1.94/1.51 (tptp_fun_Y1_11(X!1) = X!1),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[267, 141, 30, 47, 109, 45])).
% 1.94/1.51 tff(269,plain,
% 1.94/1.51 ((~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 1.94/1.51 inference(tautology,[status(thm)],[])).
% 1.94/1.51 tff(270,plain,
% 1.94/1.51 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[269, 268, 143])).
% 1.94/1.51 tff(271,plain,
% 1.94/1.51 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))) | ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(272,plain,
% 1.94/1.51 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[271, 270])).
% 1.94/1.51 tff(273,plain,
% 1.94/1.51 (Y!0 = tptp_fun_X_2(X!1)),
% 1.94/1.51 inference(symmetry,[status(thm)],[240])).
% 1.94/1.51 tff(274,plain,
% 1.94/1.51 (tptp_fun_X_2(Y!0) = tptp_fun_X_2(X!1)),
% 1.94/1.51 inference(transitivity,[status(thm)],[30, 273])).
% 1.94/1.51 tff(275,plain,
% 1.94/1.51 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 1.94/1.51 inference(monotonicity,[status(thm)],[274, 108])).
% 1.94/1.51 tff(276,plain,
% 1.94/1.51 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 1.94/1.51 inference(symmetry,[status(thm)],[275])).
% 1.94/1.51 tff(277,assumption,(tptp_fun_Y1_11(X!1) = X!1), introduced(assumption)).
% 1.94/1.51 tff(278,assumption,(~(tptp_fun_X1_13(X!1, X!1) = X!1)), introduced(assumption)).
% 1.94/1.51 tff(279,plain,
% 1.94/1.51 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, X!1) = X!1) | (tptp_fun_X1_13(X!1, X!1) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(X!1, X!1) = X!1) | (tptp_fun_X1_13(X!1, X!1) = Y!0))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(280,plain,
% 1.94/1.51 (((tptp_fun_X1_13(X!1, X!1) = Y!0) | (tptp_fun_X1_13(X!1, X!1) = X!1)) <=> ((tptp_fun_X1_13(X!1, X!1) = X!1) | (tptp_fun_X1_13(X!1, X!1) = Y!0))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(281,plain,
% 1.94/1.51 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, X!1) = Y!0) | (tptp_fun_X1_13(X!1, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, X!1) = X!1) | (tptp_fun_X1_13(X!1, X!1) = Y!0)))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[280])).
% 1.94/1.51 tff(282,plain,
% 1.94/1.51 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, X!1) = Y!0) | (tptp_fun_X1_13(X!1, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(X!1, X!1) = X!1) | (tptp_fun_X1_13(X!1, X!1) = Y!0))),
% 1.94/1.51 inference(transitivity,[status(thm)],[281, 279])).
% 1.94/1.51 tff(283,plain,
% 1.94/1.51 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, X!1) = Y!0) | (tptp_fun_X1_13(X!1, X!1) = X!1))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(284,plain,
% 1.94/1.51 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(X!1, X!1) = X!1) | (tptp_fun_X1_13(X!1, X!1) = Y!0)),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.94/1.51 tff(285,plain,
% 1.94/1.51 ((tptp_fun_X1_13(X!1, X!1) = X!1) | (tptp_fun_X1_13(X!1, X!1) = Y!0)),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[284, 12])).
% 1.94/1.51 tff(286,plain,
% 1.94/1.51 (tptp_fun_X1_13(X!1, X!1) = Y!0),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[285, 278])).
% 1.94/1.51 tff(287,plain,
% 1.94/1.51 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_X_2(X!1)),
% 1.94/1.51 inference(transitivity,[status(thm)],[286, 273])).
% 1.94/1.51 tff(288,plain,
% 1.94/1.51 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 1.94/1.51 inference(monotonicity,[status(thm)],[287, 277])).
% 1.94/1.51 tff(289,plain,
% 1.94/1.51 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 1.94/1.51 inference(transitivity,[status(thm)],[288, 276])).
% 1.94/1.51 tff(290,assumption,((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)), introduced(assumption)).
% 1.94/1.51 tff(291,plain,
% 1.94/1.51 ((~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) | (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 1.94/1.51 inference(tautology,[status(thm)],[])).
% 1.94/1.51 tff(292,plain,
% 1.94/1.51 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[291, 278, 290])).
% 1.94/1.51 tff(293,plain,
% 1.94/1.51 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[292, 289])).
% 1.94/1.51 tff(294,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[107, 293])).
% 1.94/1.51 tff(295,plain,((tptp_fun_X1_13(X!1, X!1) = X!1) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_Y_4(Y!0, Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(296,plain,
% 1.94/1.51 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[295, 268, 107, 106, 108, 30, 272])).
% 1.94/1.51 tff(297,assumption,(tptp_fun_X1_13(X!1, X!1) = X!1), introduced(assumption)).
% 1.94/1.51 tff(298,assumption,(![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), introduced(assumption)).
% 1.94/1.51 tff(299,plain,
% 1.94/1.51 (((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | big_f(X!1, tptp_fun_W_6(X!1))) <=> ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | big_f(X!1, tptp_fun_W_6(X!1)))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(300,plain,
% 1.94/1.51 ((big_f(X!1, tptp_fun_W_6(X!1)) <=> $true) <=> big_f(X!1, tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(301,plain,
% 1.94/1.51 ((tptp_fun_W_6(X!1) = tptp_fun_W_6(X!1)) <=> $true),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(302,plain,
% 1.94/1.51 ((big_f(X!1, tptp_fun_W_6(X!1)) <=> (tptp_fun_W_6(X!1) = tptp_fun_W_6(X!1))) <=> (big_f(X!1, tptp_fun_W_6(X!1)) <=> $true)),
% 1.94/1.51 inference(monotonicity,[status(thm)],[301])).
% 1.94/1.51 tff(303,plain,
% 1.94/1.51 ((big_f(X!1, tptp_fun_W_6(X!1)) <=> (tptp_fun_W_6(X!1) = tptp_fun_W_6(X!1))) <=> big_f(X!1, tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(transitivity,[status(thm)],[302, 300])).
% 1.94/1.51 tff(304,plain,
% 1.94/1.51 (((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (big_f(X!1, tptp_fun_W_6(X!1)) <=> (tptp_fun_W_6(X!1) = tptp_fun_W_6(X!1)))) <=> ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | big_f(X!1, tptp_fun_W_6(X!1)))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[303])).
% 1.94/1.51 tff(305,plain,
% 1.94/1.51 (((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (big_f(X!1, tptp_fun_W_6(X!1)) <=> (tptp_fun_W_6(X!1) = tptp_fun_W_6(X!1)))) <=> ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | big_f(X!1, tptp_fun_W_6(X!1)))),
% 1.94/1.51 inference(transitivity,[status(thm)],[304, 299])).
% 1.94/1.51 tff(306,plain,
% 1.94/1.51 ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (big_f(X!1, tptp_fun_W_6(X!1)) <=> (tptp_fun_W_6(X!1) = tptp_fun_W_6(X!1)))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(307,plain,
% 1.94/1.51 ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | big_f(X!1, tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.94/1.51 tff(308,plain,
% 1.94/1.51 (big_f(X!1, tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[307, 298])).
% 1.94/1.51 tff(309,assumption,(tptp_fun_W_6(X!1) = X!1), introduced(assumption)).
% 1.94/1.51 tff(310,plain,
% 1.94/1.51 (X!1 = tptp_fun_W_6(X!1)),
% 1.94/1.51 inference(symmetry,[status(thm)],[309])).
% 1.94/1.51 tff(311,plain,
% 1.94/1.51 (tptp_fun_Y1_11(X!1) = tptp_fun_W_6(X!1)),
% 1.94/1.51 inference(transitivity,[status(thm)],[277, 310])).
% 1.94/1.51 tff(312,plain,
% 1.94/1.51 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[297, 311])).
% 1.94/1.51 tff(313,plain,
% 1.94/1.51 (big_f(X!1, tptp_fun_W_6(X!1)) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.51 inference(symmetry,[status(thm)],[312])).
% 1.94/1.51 tff(314,assumption,(big_f(X!1, tptp_fun_W_6(X!1))), introduced(assumption)).
% 1.94/1.51 tff(315,plain,
% 1.94/1.51 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.94/1.51 tff(316,plain,
% 1.94/1.51 ((~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) | (~(tptp_fun_X1_13(X!1, X!1) = X!1))),
% 1.94/1.51 inference(tautology,[status(thm)],[])).
% 1.94/1.51 tff(317,plain,
% 1.94/1.51 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[316, 297, 290])).
% 1.94/1.51 tff(318,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[317, 315])).
% 1.94/1.51 tff(319,plain,((~(tptp_fun_X1_13(X!1, X!1) = X!1)) | (~big_f(X!1, tptp_fun_W_6(X!1))) | (~(tptp_fun_W_6(X!1) = X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(320,plain,
% 1.94/1.51 (~(tptp_fun_W_6(X!1) = X!1)),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[319, 308, 297, 277, 290])).
% 1.94/1.51 tff(321,plain,
% 1.94/1.51 ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1)))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(322,plain,
% 1.94/1.51 (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[321, 298])).
% 1.94/1.51 tff(323,plain,
% 1.94/1.51 ((~(big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1)))) | big_f(X!1, Y!0) | (~(Y!0 = tptp_fun_W_6(X!1)))),
% 1.94/1.51 inference(tautology,[status(thm)],[])).
% 1.94/1.51 tff(324,plain,
% 1.94/1.51 (~(Y!0 = tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[323, 322, 45])).
% 1.94/1.51 tff(325,plain,
% 1.94/1.51 ((tptp_fun_W_6(X!1) = Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 1.94/1.51 inference(commutativity,[status(thm)],[])).
% 1.94/1.51 tff(326,assumption,(tptp_fun_W_6(X!1) = Y!0), introduced(assumption)).
% 1.94/1.51 tff(327,plain,
% 1.94/1.51 (Y!0 = tptp_fun_W_6(X!1)),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[326, 325])).
% 1.94/1.51 tff(328,assumption,(~(Y!0 = tptp_fun_W_6(X!1))), introduced(assumption)).
% 1.94/1.51 tff(329,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[328, 327])).
% 1.94/1.51 tff(330,plain,((~(tptp_fun_W_6(X!1) = Y!0)) | (Y!0 = tptp_fun_W_6(X!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(331,plain,
% 1.94/1.51 (~(tptp_fun_W_6(X!1) = Y!0)),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[330, 324])).
% 1.94/1.51 tff(332,plain,
% 1.94/1.51 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_6(X!1) = Y!0) | (tptp_fun_W_6(X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_6(X!1) = Y!0) | (tptp_fun_W_6(X!1) = X!1))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(333,plain,
% 1.94/1.51 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_6(X!1) = Y!0) | (tptp_fun_W_6(X!1) = X!1))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(334,plain,
% 1.94/1.51 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_6(X!1) = Y!0) | (tptp_fun_W_6(X!1) = X!1)),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.94/1.51 tff(335,plain,
% 1.94/1.51 ((tptp_fun_W_6(X!1) = Y!0) | (tptp_fun_W_6(X!1) = X!1)),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[334, 12])).
% 1.94/1.51 tff(336,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[335, 331, 320])).
% 1.94/1.51 tff(337,plain,((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (~(tptp_fun_X1_13(X!1, X!1) = X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 1.94/1.52 tff(338,plain,
% 1.94/1.52 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[337, 296, 268, 272, 45])).
% 1.94/1.52 tff(339,plain,
% 1.94/1.52 ((Y!0 = tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 1.94/1.52 inference(commutativity,[status(thm)],[])).
% 1.94/1.52 tff(340,assumption,(~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), introduced(assumption)).
% 1.94/1.52 tff(341,assumption,(![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))), introduced(assumption)).
% 1.94/1.52 tff(342,plain,
% 1.94/1.52 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(343,plain,
% 1.94/1.52 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[342, 341])).
% 1.94/1.52 tff(344,plain,
% 1.94/1.52 (((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))))) | ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))),
% 1.94/1.52 inference(tautology,[status(thm)],[])).
% 1.94/1.52 tff(345,plain,
% 1.94/1.52 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[344, 343])).
% 1.94/1.52 tff(346,plain,
% 1.94/1.52 ((~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))) | (~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 1.94/1.52 inference(tautology,[status(thm)],[])).
% 1.94/1.52 tff(347,plain,
% 1.94/1.52 (~(X!1 = Z!5)),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[346, 345, 340])).
% 1.94/1.52 tff(348,plain,
% 1.94/1.52 ((Z!5 = X!1) <=> (X!1 = Z!5)),
% 1.94/1.52 inference(commutativity,[status(thm)],[])).
% 1.94/1.52 tff(349,assumption,(Z!5 = X!1), introduced(assumption)).
% 1.94/1.52 tff(350,plain,
% 1.94/1.52 (X!1 = Z!5),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[349, 348])).
% 1.94/1.52 tff(351,assumption,(~(X!1 = Z!5)), introduced(assumption)).
% 1.94/1.52 tff(352,plain,
% 1.94/1.52 ($false),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[351, 350])).
% 1.94/1.52 tff(353,plain,((~(Z!5 = X!1)) | (X!1 = Z!5)), inference(lemma,lemma(discharge,[]))).
% 1.94/1.52 tff(354,plain,
% 1.94/1.52 (~(Z!5 = X!1)),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[353, 347])).
% 1.94/1.52 tff(355,plain,
% 1.94/1.52 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((Z!5 = X!1) | (Z!5 = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (Z!5 = X!1) | (Z!5 = Y!0))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(356,plain,
% 1.94/1.52 (((Z!5 = Y!0) | (Z!5 = X!1)) <=> ((Z!5 = X!1) | (Z!5 = Y!0))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(357,plain,
% 1.94/1.52 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((Z!5 = Y!0) | (Z!5 = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((Z!5 = X!1) | (Z!5 = Y!0)))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[356])).
% 1.94/1.52 tff(358,plain,
% 1.94/1.52 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((Z!5 = Y!0) | (Z!5 = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (Z!5 = X!1) | (Z!5 = Y!0))),
% 1.94/1.52 inference(transitivity,[status(thm)],[357, 355])).
% 1.94/1.52 tff(359,plain,
% 1.94/1.52 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((Z!5 = Y!0) | (Z!5 = X!1))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(360,plain,
% 1.94/1.52 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (Z!5 = X!1) | (Z!5 = Y!0)),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.94/1.52 tff(361,plain,
% 1.94/1.52 ((Z!5 = X!1) | (Z!5 = Y!0)),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[360, 12])).
% 1.94/1.52 tff(362,plain,
% 1.94/1.52 (Z!5 = Y!0),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[361, 354])).
% 1.94/1.52 tff(363,plain,
% 1.94/1.52 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 1.94/1.52 inference(monotonicity,[status(thm)],[362])).
% 1.94/1.52 tff(364,plain,
% 1.94/1.52 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[363])).
% 1.94/1.52 tff(365,plain,
% 1.94/1.52 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 1.94/1.52 inference(transitivity,[status(thm)],[364, 339])).
% 1.94/1.52 tff(366,plain,
% 1.94/1.52 ((~(Y!0 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[365])).
% 1.94/1.52 tff(367,plain,
% 1.94/1.52 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(368,plain,
% 1.94/1.52 ((~(~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))) <=> ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(369,plain,
% 1.94/1.52 (($false | (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))) <=> (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(370,plain,
% 1.94/1.52 ((~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))) <=> (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(371,plain,
% 1.94/1.52 ((~$true) <=> $false),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(372,plain,
% 1.94/1.52 (($true | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W))) <=> $true),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(373,plain,
% 1.94/1.52 ((Z!5 = Z!5) <=> $true),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(374,plain,
% 1.94/1.52 (((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W))) <=> ($true | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[373])).
% 1.94/1.52 tff(375,plain,
% 1.94/1.52 (((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W))) <=> $true),
% 1.94/1.52 inference(transitivity,[status(thm)],[374, 372])).
% 1.94/1.52 tff(376,plain,
% 1.94/1.52 ((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) <=> (~$true)),
% 1.94/1.52 inference(monotonicity,[status(thm)],[375])).
% 1.94/1.52 tff(377,plain,
% 1.94/1.52 ((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) <=> $false),
% 1.94/1.52 inference(transitivity,[status(thm)],[376, 371])).
% 1.94/1.52 tff(378,plain,
% 1.94/1.52 (((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) | (~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))))) <=> ($false | (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[377, 370])).
% 1.94/1.52 tff(379,plain,
% 1.94/1.52 (((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) | (~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))))) <=> (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))),
% 1.94/1.52 inference(transitivity,[status(thm)],[378, 369])).
% 1.94/1.52 tff(380,plain,
% 1.94/1.52 ((~((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) | (~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))))) <=> (~(~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[379])).
% 1.94/1.52 tff(381,plain,
% 1.94/1.52 ((~((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) | (~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))))) <=> ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 1.94/1.52 inference(transitivity,[status(thm)],[380, 368])).
% 1.94/1.52 tff(382,plain,
% 1.94/1.52 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) | (~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[381])).
% 1.94/1.52 tff(383,plain,
% 1.94/1.52 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) | (~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))),
% 1.94/1.52 inference(transitivity,[status(thm)],[382, 367])).
% 1.94/1.52 tff(384,plain,
% 1.94/1.52 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((Z!5 = Z!5) | ![W: $i] : ((~big_f(Z!5, tptp_fun_Y_7(W, Z!5))) <=> (tptp_fun_Y_7(W, Z!5) = W)))) | (~((~(Z!5 = Z!5)) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(385,plain,
% 1.94/1.52 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | ![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.94/1.52 tff(386,plain,
% 1.94/1.52 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[385, 341])).
% 1.94/1.52 tff(387,plain,
% 1.94/1.52 ((~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))) | (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5)))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(388,plain,
% 1.94/1.52 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[387, 386])).
% 1.94/1.52 tff(389,plain,
% 1.94/1.52 (Z!5 = tptp_fun_X_2(Y!0)),
% 1.94/1.52 inference(transitivity,[status(thm)],[362, 31])).
% 1.94/1.52 tff(390,plain,
% 1.94/1.52 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 1.94/1.52 inference(monotonicity,[status(thm)],[389])).
% 1.94/1.52 tff(391,plain,
% 1.94/1.52 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 1.94/1.52 inference(symmetry,[status(thm)],[390])).
% 1.94/1.52 tff(392,plain,
% 1.94/1.52 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Z!5, Y!0))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[391])).
% 1.94/1.52 tff(393,plain,
% 1.94/1.52 (~big_f(Z!5, Y!0)),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[35, 392])).
% 1.94/1.52 tff(394,plain,
% 1.94/1.52 ((~(big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5)))) | big_f(Z!5, Y!0) | (~(Y!0 = tptp_fun_W_6(Z!5)))),
% 1.94/1.52 inference(tautology,[status(thm)],[])).
% 1.94/1.52 tff(395,plain,
% 1.94/1.52 (~(Y!0 = tptp_fun_W_6(Z!5))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[394, 393, 388])).
% 1.94/1.52 tff(396,plain,
% 1.94/1.52 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[395, 366])).
% 1.94/1.52 tff(397,plain,
% 1.94/1.52 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_6(Y!0) = X!1) | (tptp_fun_W_6(Y!0) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_6(Y!0) = X!1) | (tptp_fun_W_6(Y!0) = Y!0))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(398,plain,
% 1.94/1.52 (((tptp_fun_W_6(Y!0) = Y!0) | (tptp_fun_W_6(Y!0) = X!1)) <=> ((tptp_fun_W_6(Y!0) = X!1) | (tptp_fun_W_6(Y!0) = Y!0))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(399,plain,
% 1.94/1.52 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_6(Y!0) = Y!0) | (tptp_fun_W_6(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_6(Y!0) = X!1) | (tptp_fun_W_6(Y!0) = Y!0)))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[398])).
% 1.94/1.52 tff(400,plain,
% 1.94/1.52 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_6(Y!0) = Y!0) | (tptp_fun_W_6(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_6(Y!0) = X!1) | (tptp_fun_W_6(Y!0) = Y!0))),
% 2.02/1.53 inference(transitivity,[status(thm)],[399, 397])).
% 2.02/1.53 tff(401,plain,
% 2.02/1.53 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_6(Y!0) = Y!0) | (tptp_fun_W_6(Y!0) = X!1))),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(402,plain,
% 2.02/1.53 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_6(Y!0) = X!1) | (tptp_fun_W_6(Y!0) = Y!0)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[401, 400])).
% 2.02/1.53 tff(403,plain,
% 2.02/1.53 ((tptp_fun_W_6(Y!0) = X!1) | (tptp_fun_W_6(Y!0) = Y!0)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[402, 12])).
% 2.02/1.53 tff(404,plain,
% 2.02/1.53 (tptp_fun_W_6(Y!0) = X!1),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[403, 396])).
% 2.02/1.53 tff(405,plain,
% 2.02/1.53 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.53 inference(monotonicity,[status(thm)],[273, 404])).
% 2.02/1.53 tff(406,plain,
% 2.02/1.53 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.02/1.53 inference(symmetry,[status(thm)],[405])).
% 2.02/1.53 tff(407,plain,
% 2.02/1.53 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[406])).
% 2.02/1.53 tff(408,plain,
% 2.02/1.53 (tptp_fun_Y_4(Z!5, Y!0) = tptp_fun_Y_4(Y!0, Y!0)),
% 2.02/1.53 inference(monotonicity,[status(thm)],[362])).
% 2.02/1.53 tff(409,plain,
% 2.02/1.53 (tptp_fun_Y_4(Z!5, Y!0) = X!1),
% 2.02/1.53 inference(transitivity,[status(thm)],[408, 108])).
% 2.02/1.53 tff(410,plain,
% 2.02/1.53 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Z!5, Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.53 inference(monotonicity,[status(thm)],[274, 409])).
% 2.02/1.53 tff(411,plain,
% 2.02/1.53 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Z!5, Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), X!1))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[410])).
% 2.02/1.53 tff(412,assumption,(Z!5 = Y!0), introduced(assumption)).
% 2.02/1.53 tff(413,plain,
% 2.02/1.53 (tptp_fun_Y_4(Z!5, Y!0) = tptp_fun_Y_4(Y!0, Y!0)),
% 2.02/1.53 inference(monotonicity,[status(thm)],[412])).
% 2.02/1.53 tff(414,plain,
% 2.02/1.53 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Z!5, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[413])).
% 2.02/1.53 tff(415,assumption,(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Z!5, Y!0))), introduced(assumption)).
% 2.02/1.53 tff(416,plain,
% 2.02/1.53 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[415, 414])).
% 2.02/1.53 tff(417,plain,
% 2.02/1.53 ($false),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[107, 416])).
% 2.02/1.53 tff(418,plain,((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Z!5, Y!0))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) | (~(Z!5 = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.53 tff(419,plain,
% 2.02/1.53 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Z!5, Y!0))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[418, 362, 107])).
% 2.02/1.53 tff(420,plain,
% 2.02/1.53 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[419, 411])).
% 2.02/1.53 tff(421,plain,
% 2.02/1.53 (~big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[420, 407])).
% 2.02/1.53 tff(422,assumption,(~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))), introduced(assumption)).
% 2.02/1.53 tff(423,plain,
% 2.02/1.53 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(424,plain,
% 2.02/1.53 ((~((~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))) | (~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))))) <=> (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(425,plain,
% 2.02/1.53 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))) | (~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[424])).
% 2.02/1.53 tff(426,plain,
% 2.02/1.53 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))) | (~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))))),
% 2.02/1.53 inference(transitivity,[status(thm)],[425, 423])).
% 2.02/1.53 tff(427,plain,
% 2.02/1.53 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))) | (~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))))))),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(428,plain,
% 2.02/1.53 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[427, 426])).
% 2.02/1.53 tff(429,plain,
% 2.02/1.53 (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[428, 341])).
% 2.02/1.53 tff(430,plain,
% 2.02/1.53 (((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))) | ((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))),
% 2.02/1.53 inference(tautology,[status(thm)],[])).
% 2.02/1.53 tff(431,plain,
% 2.02/1.53 ((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[430, 429])).
% 2.02/1.53 tff(432,plain,
% 2.02/1.53 ((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(tautology,[status(thm)],[])).
% 2.02/1.53 tff(433,plain,
% 2.02/1.53 (~(Y!0 = Z!5)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[432, 431, 422])).
% 2.02/1.53 tff(434,plain,
% 2.02/1.53 ((Z!5 = Y!0) <=> (Y!0 = Z!5)),
% 2.02/1.53 inference(commutativity,[status(thm)],[])).
% 2.02/1.53 tff(435,plain,
% 2.02/1.53 (Y!0 = Z!5),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[412, 434])).
% 2.02/1.53 tff(436,assumption,(~(Y!0 = Z!5)), introduced(assumption)).
% 2.02/1.53 tff(437,plain,
% 2.02/1.53 ($false),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[436, 435])).
% 2.02/1.53 tff(438,plain,((~(Z!5 = Y!0)) | (Y!0 = Z!5)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.53 tff(439,plain,
% 2.02/1.53 (~(Z!5 = Y!0)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[438, 433])).
% 2.02/1.53 tff(440,plain,
% 2.02/1.53 ($false),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[361, 439, 354])).
% 2.02/1.53 tff(441,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.53 tff(442,plain,
% 2.02/1.53 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[441, 341, 340])).
% 2.02/1.53 tff(443,plain,
% 2.02/1.53 (((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | big_f(Y!0, tptp_fun_W_6(Y!0))) <=> ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(444,plain,
% 2.02/1.53 ((big_f(Y!0, tptp_fun_W_6(Y!0)) <=> $true) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(445,plain,
% 2.02/1.53 ((tptp_fun_W_6(Y!0) = tptp_fun_W_6(Y!0)) <=> $true),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(446,plain,
% 2.02/1.53 ((big_f(Y!0, tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Y!0))) <=> (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> $true)),
% 2.02/1.53 inference(monotonicity,[status(thm)],[445])).
% 2.02/1.53 tff(447,plain,
% 2.02/1.53 ((big_f(Y!0, tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Y!0))) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.02/1.53 inference(transitivity,[status(thm)],[446, 444])).
% 2.02/1.53 tff(448,plain,
% 2.02/1.53 (((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Y!0)))) <=> ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[447])).
% 2.02/1.53 tff(449,plain,
% 2.02/1.53 (((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Y!0)))) <=> ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(transitivity,[status(thm)],[448, 443])).
% 2.02/1.53 tff(450,plain,
% 2.02/1.53 ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Y!0)))),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(451,plain,
% 2.02/1.53 ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[450, 449])).
% 2.02/1.53 tff(452,plain,
% 2.02/1.53 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[451, 442])).
% 2.02/1.53 tff(453,plain,
% 2.02/1.53 ($false),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[452, 421])).
% 2.02/1.53 tff(454,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y_4(Y!0, Y!0) = X!1)) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.53 tff(455,plain,
% 2.02/1.53 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[454, 338, 142, 30, 108, 107, 106])).
% 2.02/1.53 tff(456,plain,
% 2.02/1.53 ((![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~(![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~(![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))))) <=> (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))))))))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(457,plain,
% 2.02/1.53 ((![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~(![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~(![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))))) <=> (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~(![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~(![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8)))))))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(458,plain,
% 2.02/1.53 ((![X: $i] : (((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W))) & (![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))) | ![Y1: $i] : (((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1))) & (![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))) <=> (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~(![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~(![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8)))))))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(459,plain,
% 2.02/1.53 (![X: $i] : (((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W))) & (![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))) | ![Y1: $i] : (((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1))) & (![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))),
% 2.02/1.53 inference(and_elim,[status(thm)],[80])).
% 2.02/1.53 tff(460,plain,
% 2.02/1.53 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~(![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~(![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[459, 458])).
% 2.02/1.53 tff(461,plain,
% 2.02/1.53 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~(![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))) | (~(X = Z!5)))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~(![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1))) | (~(Y1 = W1!8))))))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[460, 457])).
% 2.02/1.53 tff(462,plain,
% 2.02/1.53 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))) | ![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[461, 456])).
% 2.02/1.53 tff(463,plain,
% 2.02/1.53 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[462, 455])).
% 2.02/1.54 tff(464,plain,
% 2.02/1.54 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(465,plain,
% 2.02/1.54 ((~(~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))) <=> ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(466,plain,
% 2.02/1.54 (($false | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))) <=> (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(467,plain,
% 2.02/1.54 ((~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))) <=> (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(468,plain,
% 2.02/1.54 (($true | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1))) <=> $true),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(469,plain,
% 2.02/1.54 ((W1!8 = W1!8) <=> $true),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(470,plain,
% 2.02/1.54 (((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1))) <=> ($true | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[469])).
% 2.02/1.54 tff(471,plain,
% 2.02/1.54 (((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1))) <=> $true),
% 2.02/1.54 inference(transitivity,[status(thm)],[470, 468])).
% 2.02/1.54 tff(472,plain,
% 2.02/1.54 ((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) <=> (~$true)),
% 2.02/1.54 inference(monotonicity,[status(thm)],[471])).
% 2.02/1.54 tff(473,plain,
% 2.02/1.54 ((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) <=> $false),
% 2.02/1.54 inference(transitivity,[status(thm)],[472, 371])).
% 2.02/1.54 tff(474,plain,
% 2.02/1.54 (((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) | (~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))))) <=> ($false | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[473, 467])).
% 2.02/1.54 tff(475,plain,
% 2.02/1.54 (((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) | (~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))))) <=> (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))),
% 2.02/1.54 inference(transitivity,[status(thm)],[474, 466])).
% 2.02/1.54 tff(476,plain,
% 2.02/1.54 ((~((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) | (~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))))) <=> (~(~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[475])).
% 2.02/1.54 tff(477,plain,
% 2.02/1.54 ((~((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) | (~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))))) <=> ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(transitivity,[status(thm)],[476, 465])).
% 2.02/1.54 tff(478,plain,
% 2.02/1.54 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) | (~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[477])).
% 2.02/1.54 tff(479,plain,
% 2.02/1.54 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) | (~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))),
% 2.02/1.54 inference(transitivity,[status(thm)],[478, 464])).
% 2.02/1.54 tff(480,plain,
% 2.02/1.54 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((W1!8 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, W1!8), W1!8)) <=> (tptp_fun_X1_10(Z1, W1!8) = Z1)))) | (~((~(W1!8 = W1!8)) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))))))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(481,plain,
% 2.02/1.54 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | ![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[480, 479])).
% 2.02/1.54 tff(482,plain,
% 2.02/1.54 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[481, 463])).
% 2.02/1.54 tff(483,plain,
% 2.02/1.54 ((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(484,plain,
% 2.02/1.54 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[483, 482])).
% 2.02/1.54 tff(485,plain,
% 2.02/1.54 ((tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = X!1) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.02/1.54 inference(commutativity,[status(thm)],[])).
% 2.02/1.54 tff(486,assumption,(W1!8 = Y!0), introduced(assumption)).
% 2.02/1.54 tff(487,plain,
% 2.02/1.54 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.02/1.54 inference(transitivity,[status(thm)],[486, 31])).
% 2.02/1.54 tff(488,plain,
% 2.02/1.54 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[487])).
% 2.02/1.54 tff(489,plain,
% 2.02/1.54 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = X!1)),
% 2.02/1.54 inference(monotonicity,[status(thm)],[488])).
% 2.02/1.54 tff(490,plain,
% 2.02/1.54 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.02/1.54 inference(transitivity,[status(thm)],[489, 485])).
% 2.02/1.54 tff(491,plain,
% 2.02/1.54 ((X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.54 inference(symmetry,[status(thm)],[490])).
% 2.02/1.54 tff(492,plain,
% 2.02/1.54 ((X!1 = tptp_fun_Z1_9(W1!8)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[488])).
% 2.02/1.54 tff(493,plain,
% 2.02/1.54 ((X!1 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.54 inference(transitivity,[status(thm)],[492, 491])).
% 2.02/1.54 tff(494,plain,
% 2.02/1.54 ((~(X!1 = tptp_fun_Z1_9(W1!8))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[493])).
% 2.02/1.54 tff(495,assumption,(![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))), introduced(assumption)).
% 2.02/1.54 tff(496,plain,
% 2.02/1.54 ((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | (big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(497,plain,
% 2.02/1.54 (big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[496, 495])).
% 2.02/1.54 tff(498,plain,
% 2.02/1.54 (big_f(X!1, W1!8) <=> big_f(X!1, Y!0)),
% 2.02/1.54 inference(monotonicity,[status(thm)],[486])).
% 2.02/1.54 tff(499,plain,
% 2.02/1.54 (big_f(X!1, Y!0) <=> big_f(X!1, W1!8)),
% 2.02/1.54 inference(symmetry,[status(thm)],[498])).
% 2.02/1.54 tff(500,plain,
% 2.02/1.54 ((~big_f(X!1, Y!0)) <=> (~big_f(X!1, W1!8))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[499])).
% 2.02/1.54 tff(501,plain,
% 2.02/1.54 (~big_f(X!1, W1!8)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[45, 500])).
% 2.02/1.54 tff(502,plain,
% 2.02/1.54 ((~(big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8)))) | big_f(X!1, W1!8) | (~(X!1 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(tautology,[status(thm)],[])).
% 2.02/1.54 tff(503,plain,
% 2.02/1.54 (~(X!1 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[502, 501, 497])).
% 2.02/1.54 tff(504,plain,
% 2.02/1.54 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[503, 494])).
% 2.02/1.54 tff(505,plain,
% 2.02/1.54 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = tptp_fun_Z1_9(W1!8)),
% 2.02/1.54 inference(symmetry,[status(thm)],[488])).
% 2.02/1.54 tff(506,plain,
% 2.02/1.54 ((Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[505])).
% 2.02/1.54 tff(507,plain,
% 2.02/1.54 ((Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.02/1.54 inference(transitivity,[status(thm)],[506, 43])).
% 2.02/1.54 tff(508,plain,
% 2.02/1.54 ((Y!0 = tptp_fun_Z1_9(W1!8)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[488])).
% 2.02/1.54 tff(509,plain,
% 2.02/1.54 ((Y!0 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.02/1.54 inference(transitivity,[status(thm)],[508, 507])).
% 2.02/1.54 tff(510,plain,
% 2.02/1.54 ((~(Y!0 = tptp_fun_Z1_9(W1!8))) <=> (~(tptp_fun_Z1_9(W1!8) = Y!0))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[509])).
% 2.02/1.54 tff(511,plain,
% 2.02/1.54 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[483, 495])).
% 2.02/1.54 tff(512,plain,
% 2.02/1.54 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.02/1.54 inference(monotonicity,[status(thm)],[31, 486])).
% 2.02/1.54 tff(513,plain,
% 2.02/1.54 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, W1!8)),
% 2.02/1.54 inference(symmetry,[status(thm)],[512])).
% 2.02/1.54 tff(514,plain,
% 2.02/1.54 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, W1!8))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[513])).
% 2.02/1.54 tff(515,plain,
% 2.02/1.54 (~big_f(Y!0, W1!8)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[35, 514])).
% 2.02/1.54 tff(516,plain,
% 2.02/1.54 ((~(big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8)))) | big_f(Y!0, W1!8) | (~(Y!0 = tptp_fun_Z1_9(W1!8)))),
% 2.02/1.54 inference(tautology,[status(thm)],[])).
% 2.02/1.54 tff(517,plain,
% 2.02/1.54 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[516, 515, 511])).
% 2.02/1.54 tff(518,plain,
% 2.02/1.54 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[517, 510])).
% 2.02/1.54 tff(519,plain,
% 2.02/1.54 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_9(W1!8) = Y!0) | (tptp_fun_Z1_9(W1!8) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Z1_9(W1!8) = Y!0) | (tptp_fun_Z1_9(W1!8) = X!1))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(520,plain,
% 2.02/1.54 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_9(W1!8) = Y!0) | (tptp_fun_Z1_9(W1!8) = X!1))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(521,plain,
% 2.02/1.54 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Z1_9(W1!8) = Y!0) | (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[520, 519])).
% 2.02/1.54 tff(522,plain,
% 2.02/1.54 ((tptp_fun_Z1_9(W1!8) = Y!0) | (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[521, 12])).
% 2.02/1.54 tff(523,plain,
% 2.02/1.54 ($false),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[522, 518, 504])).
% 2.02/1.54 tff(524,plain,((~(W1!8 = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | big_f(X!1, Y!0) | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.54 tff(525,plain,
% 2.02/1.54 (~(W1!8 = Y!0)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[524, 482, 30, 45, 142])).
% 2.02/1.54 tff(526,plain,
% 2.02/1.54 (W1!8 = X!1),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[19, 525])).
% 2.02/1.54 tff(527,plain,
% 2.02/1.54 (Y!0 = tptp_fun_X_2(X!1)),
% 2.02/1.54 inference(symmetry,[status(thm)],[106])).
% 2.02/1.55 tff(528,plain,
% 2.02/1.55 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.55 inference(monotonicity,[status(thm)],[527, 526])).
% 2.02/1.55 tff(529,plain,
% 2.02/1.55 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, W1!8)),
% 2.02/1.55 inference(symmetry,[status(thm)],[528])).
% 2.02/1.55 tff(530,plain,
% 2.02/1.55 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, W1!8))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[529])).
% 2.02/1.55 tff(531,plain,
% 2.02/1.55 (tptp_fun_X_2(Y!0) = tptp_fun_X_2(X!1)),
% 2.02/1.55 inference(transitivity,[status(thm)],[30, 527])).
% 2.02/1.55 tff(532,plain,
% 2.02/1.55 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.55 inference(monotonicity,[status(thm)],[531, 108])).
% 2.02/1.55 tff(533,plain,
% 2.02/1.55 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), X!1))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[532])).
% 2.02/1.55 tff(534,plain,
% 2.02/1.55 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[107, 533])).
% 2.02/1.55 tff(535,plain,
% 2.02/1.55 (~big_f(Y!0, W1!8)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[534, 530])).
% 2.02/1.55 tff(536,plain,
% 2.02/1.55 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[516, 535, 484])).
% 2.02/1.55 tff(537,plain,
% 2.02/1.55 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[536, 44])).
% 2.02/1.55 tff(538,plain,
% 2.02/1.55 ((tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = tptp_fun_X1_13(X!1, X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.02/1.55 inference(commutativity,[status(thm)],[])).
% 2.02/1.55 tff(539,plain,
% 2.02/1.55 (X!1 = tptp_fun_X1_13(X!1, X!1)),
% 2.02/1.55 inference(symmetry,[status(thm)],[296])).
% 2.02/1.55 tff(540,plain,
% 2.02/1.55 (X!1 = tptp_fun_Y1_11(X!1)),
% 2.02/1.55 inference(symmetry,[status(thm)],[268])).
% 2.02/1.55 tff(541,plain,
% 2.02/1.55 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.02/1.55 inference(transitivity,[status(thm)],[526, 540])).
% 2.02/1.55 tff(542,plain,
% 2.02/1.55 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[541])).
% 2.02/1.55 tff(543,plain,
% 2.02/1.55 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = tptp_fun_X1_13(X!1, X!1))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[542, 539])).
% 2.02/1.55 tff(544,plain,
% 2.02/1.55 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.02/1.55 inference(transitivity,[status(thm)],[543, 538])).
% 2.02/1.55 tff(545,plain,
% 2.02/1.55 ((tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.55 inference(symmetry,[status(thm)],[544])).
% 2.02/1.55 tff(546,plain,
% 2.02/1.55 ((X!1 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[539, 542])).
% 2.02/1.55 tff(547,plain,
% 2.02/1.55 ((X!1 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.55 inference(transitivity,[status(thm)],[546, 545])).
% 2.02/1.55 tff(548,plain,
% 2.02/1.55 ((~(X!1 = tptp_fun_Z1_9(W1!8))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[547])).
% 2.02/1.55 tff(549,plain,
% 2.02/1.55 (big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[496, 482])).
% 2.02/1.55 tff(550,plain,
% 2.02/1.55 (big_f(X!1, W1!8) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[539, 541])).
% 2.02/1.55 tff(551,plain,
% 2.02/1.55 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, W1!8)),
% 2.02/1.55 inference(symmetry,[status(thm)],[550])).
% 2.02/1.55 tff(552,plain,
% 2.02/1.55 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (~big_f(X!1, W1!8))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[551])).
% 2.02/1.55 tff(553,plain,
% 2.02/1.55 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[316, 296, 272])).
% 2.02/1.55 tff(554,plain,
% 2.02/1.55 (~big_f(X!1, W1!8)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[553, 552])).
% 2.02/1.55 tff(555,plain,
% 2.02/1.55 (~(X!1 = tptp_fun_Z1_9(W1!8))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[502, 554, 549])).
% 2.02/1.55 tff(556,plain,
% 2.02/1.55 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[555, 548])).
% 2.02/1.55 tff(557,plain,
% 2.02/1.55 ($false),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[522, 556, 537])).
% 2.02/1.55 tff(558,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) | (~(tptp_fun_Y_4(Y!0, Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))) | (tptp_fun_X_2(X!1) = X!1) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.55 tff(559,plain,
% 2.02/1.55 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[558, 98, 96, 30, 45, 91, 47, 87])).
% 2.02/1.55 tff(560,plain,
% 2.02/1.55 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[39, 559])).
% 2.02/1.55 tff(561,plain,
% 2.02/1.55 (((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))) | ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))),
% 2.02/1.55 inference(tautology,[status(thm)],[])).
% 2.02/1.55 tff(562,plain,
% 2.02/1.55 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[561, 85])).
% 2.02/1.55 tff(563,plain,
% 2.02/1.55 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.02/1.55 inference(tautology,[status(thm)],[])).
% 2.02/1.55 tff(564,plain,
% 2.02/1.55 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[563, 559, 562])).
% 2.02/1.55 tff(565,plain,
% 2.02/1.55 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.55 inference(monotonicity,[status(thm)],[527, 560])).
% 2.02/1.55 tff(566,plain,
% 2.02/1.55 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.02/1.55 inference(symmetry,[status(thm)],[565])).
% 2.02/1.55 tff(567,plain,
% 2.02/1.55 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[566])).
% 2.02/1.55 tff(568,plain,
% 2.02/1.55 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.55 inference(monotonicity,[status(thm)],[531, 96])).
% 2.02/1.55 tff(569,plain,
% 2.02/1.55 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), X!1))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[568])).
% 2.02/1.55 tff(570,plain,
% 2.02/1.55 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[98, 569])).
% 2.02/1.55 tff(571,plain,
% 2.02/1.55 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[570, 567])).
% 2.02/1.55 tff(572,plain,
% 2.02/1.55 ((tptp_fun_Z1_12(Y!0) = X!1) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.02/1.55 inference(commutativity,[status(thm)],[])).
% 2.02/1.55 tff(573,plain,
% 2.02/1.55 ((X!1 = tptp_fun_Z1_12(Y!0)) <=> (tptp_fun_Z1_12(Y!0) = X!1)),
% 2.02/1.55 inference(symmetry,[status(thm)],[572])).
% 2.02/1.55 tff(574,plain,
% 2.02/1.55 ((~(X!1 = tptp_fun_Z1_12(Y!0))) <=> (~(tptp_fun_Z1_12(Y!0) = X!1))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[573])).
% 2.02/1.55 tff(575,assumption,(![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))), introduced(assumption)).
% 2.02/1.55 tff(576,plain,
% 2.02/1.55 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))) | (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0)))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(577,plain,
% 2.02/1.55 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[576, 575])).
% 2.02/1.55 tff(578,plain,
% 2.02/1.55 ((~(big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0)))) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(X!1 = tptp_fun_Z1_12(Y!0)))),
% 2.02/1.55 inference(tautology,[status(thm)],[])).
% 2.02/1.55 tff(579,plain,
% 2.02/1.55 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[578, 577, 42])).
% 2.02/1.55 tff(580,plain,
% 2.02/1.55 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[579, 574])).
% 2.02/1.55 tff(581,plain,
% 2.02/1.55 ((Y!0 = tptp_fun_Z1_12(Y!0)) <=> (tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.02/1.55 inference(commutativity,[status(thm)],[])).
% 2.02/1.55 tff(582,plain,
% 2.02/1.55 ((~(Y!0 = tptp_fun_Z1_12(Y!0))) <=> (~(tptp_fun_Z1_12(Y!0) = Y!0))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[581])).
% 2.02/1.55 tff(583,plain,
% 2.02/1.55 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))) | (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0)))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(584,plain,
% 2.02/1.55 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[583, 575])).
% 2.02/1.55 tff(585,plain,
% 2.02/1.55 ((~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0)))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(Y!0 = tptp_fun_Z1_12(Y!0)))),
% 2.02/1.55 inference(tautology,[status(thm)],[])).
% 2.02/1.55 tff(586,plain,
% 2.02/1.55 (~(Y!0 = tptp_fun_Z1_12(Y!0))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[585, 584, 41])).
% 2.02/1.55 tff(587,plain,
% 2.02/1.55 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[586, 582])).
% 2.02/1.55 tff(588,plain,
% 2.02/1.55 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_12(Y!0) = X!1) | (tptp_fun_Z1_12(Y!0) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Z1_12(Y!0) = X!1) | (tptp_fun_Z1_12(Y!0) = Y!0))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(589,plain,
% 2.02/1.55 (((tptp_fun_Z1_12(Y!0) = Y!0) | (tptp_fun_Z1_12(Y!0) = X!1)) <=> ((tptp_fun_Z1_12(Y!0) = X!1) | (tptp_fun_Z1_12(Y!0) = Y!0))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(590,plain,
% 2.02/1.55 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_12(Y!0) = Y!0) | (tptp_fun_Z1_12(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_12(Y!0) = X!1) | (tptp_fun_Z1_12(Y!0) = Y!0)))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[589])).
% 2.02/1.55 tff(591,plain,
% 2.02/1.55 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_12(Y!0) = Y!0) | (tptp_fun_Z1_12(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Z1_12(Y!0) = X!1) | (tptp_fun_Z1_12(Y!0) = Y!0))),
% 2.02/1.55 inference(transitivity,[status(thm)],[590, 588])).
% 2.02/1.55 tff(592,plain,
% 2.02/1.55 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Z1_12(Y!0) = Y!0) | (tptp_fun_Z1_12(Y!0) = X!1))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(593,plain,
% 2.02/1.55 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Z1_12(Y!0) = X!1) | (tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[592, 591])).
% 2.02/1.55 tff(594,plain,
% 2.02/1.55 ((tptp_fun_Z1_12(Y!0) = X!1) | (tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[593, 12])).
% 2.02/1.55 tff(595,plain,
% 2.02/1.55 ($false),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[594, 587, 580])).
% 2.02/1.55 tff(596,plain,((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(X!1, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.55 tff(597,plain,
% 2.02/1.55 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[596, 571, 564])).
% 2.02/1.55 tff(598,assumption,(tptp_fun_Y1_11(Y!0) = X!1), introduced(assumption)).
% 2.02/1.55 tff(599,plain,
% 2.02/1.55 (X!1 = tptp_fun_Y1_11(Y!0)),
% 2.02/1.55 inference(symmetry,[status(thm)],[598])).
% 2.02/1.55 tff(600,assumption,((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)), introduced(assumption)).
% 2.02/1.55 tff(601,assumption,(~(tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)), introduced(assumption)).
% 2.02/1.55 tff(602,plain,
% 2.02/1.55 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(603,plain,
% 2.02/1.55 (((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)) <=> ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(604,plain,
% 2.02/1.55 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0)))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[603])).
% 2.02/1.55 tff(605,plain,
% 2.02/1.55 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0))),
% 2.02/1.55 inference(transitivity,[status(thm)],[604, 602])).
% 2.02/1.55 tff(606,plain,
% 2.02/1.55 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(607,plain,
% 2.02/1.55 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[606, 605])).
% 2.02/1.55 tff(608,plain,
% 2.02/1.55 ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[607, 12])).
% 2.02/1.55 tff(609,plain,
% 2.02/1.55 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = Y!0),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[608, 601])).
% 2.02/1.55 tff(610,plain,
% 2.02/1.55 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))) <=> big_f(X!1, Y!0)),
% 2.02/1.55 inference(monotonicity,[status(thm)],[598, 609])).
% 2.02/1.55 tff(611,plain,
% 2.02/1.55 (big_f(X!1, Y!0) <=> big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.02/1.55 inference(symmetry,[status(thm)],[610])).
% 2.02/1.55 tff(612,plain,
% 2.02/1.55 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[611])).
% 2.02/1.55 tff(613,plain,
% 2.02/1.55 (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[45, 612])).
% 2.02/1.55 tff(614,plain,
% 2.02/1.55 ((~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) | big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)),
% 2.02/1.55 inference(tautology,[status(thm)],[])).
% 2.02/1.55 tff(615,plain,
% 2.02/1.55 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[614, 601, 600])).
% 2.02/1.55 tff(616,plain,
% 2.02/1.55 ($false),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[615, 613])).
% 2.02/1.55 tff(617,plain,((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | big_f(X!1, Y!0) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.55 tff(618,plain,
% 2.02/1.55 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[617, 600, 45, 598])).
% 2.02/1.55 tff(619,plain,
% 2.02/1.55 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = tptp_fun_Y1_11(Y!0)),
% 2.02/1.55 inference(transitivity,[status(thm)],[618, 599])).
% 2.02/1.55 tff(620,plain,
% 2.02/1.55 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[598, 619])).
% 2.02/1.55 tff(621,plain,
% 2.02/1.55 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.02/1.55 inference(symmetry,[status(thm)],[620])).
% 2.02/1.55 tff(622,assumption,(big_f(X!1, tptp_fun_Y1_11(Y!0))), introduced(assumption)).
% 2.02/1.55 tff(623,plain,
% 2.02/1.55 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[622, 621])).
% 2.02/1.55 tff(624,plain,
% 2.02/1.55 ((~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) | (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) | (~(tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.02/1.55 inference(tautology,[status(thm)],[])).
% 2.02/1.55 tff(625,plain,
% 2.02/1.55 (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[624, 618, 600])).
% 2.02/1.55 tff(626,plain,
% 2.02/1.55 ($false),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[625, 623])).
% 2.02/1.55 tff(627,plain,((~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.56 tff(628,plain,
% 2.02/1.56 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[627, 597, 45, 560])).
% 2.02/1.56 tff(629,plain,
% 2.02/1.56 ((~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))) | ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.02/1.56 inference(quant_inst,[status(thm)],[])).
% 2.02/1.56 tff(630,plain,
% 2.02/1.56 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[629, 628])).
% 2.02/1.56 tff(631,plain,
% 2.02/1.56 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[269, 277, 143])).
% 2.02/1.56 tff(632,plain,
% 2.02/1.56 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[271, 631])).
% 2.02/1.56 tff(633,plain,
% 2.02/1.56 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[286])).
% 2.02/1.56 tff(634,plain,
% 2.02/1.56 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(symmetry,[status(thm)],[633])).
% 2.02/1.56 tff(635,plain,
% 2.02/1.56 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0)))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[634])).
% 2.02/1.56 tff(636,plain,
% 2.02/1.56 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[41, 635])).
% 2.02/1.56 tff(637,plain,
% 2.02/1.56 (tptp_fun_Y1_11(X!1) = tptp_fun_Y1_11(Y!0)),
% 2.02/1.56 inference(transitivity,[status(thm)],[277, 599])).
% 2.02/1.56 tff(638,plain,
% 2.02/1.56 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[637])).
% 2.02/1.56 tff(639,plain,
% 2.02/1.56 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[292, 638])).
% 2.02/1.56 tff(640,plain,
% 2.02/1.56 ($false),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[639, 636])).
% 2.02/1.56 tff(641,plain,((tptp_fun_X1_13(X!1, X!1) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.56 tff(642,plain,
% 2.02/1.56 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[641, 277, 41, 598, 632])).
% 2.02/1.56 tff(643,plain,
% 2.02/1.56 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[642])).
% 2.02/1.56 tff(644,plain,
% 2.02/1.56 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(symmetry,[status(thm)],[643])).
% 2.02/1.56 tff(645,plain,
% 2.02/1.56 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[622, 644])).
% 2.02/1.56 tff(646,plain,
% 2.02/1.56 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0)))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[638])).
% 2.02/1.56 tff(647,plain,
% 2.02/1.56 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[316, 642, 632])).
% 2.02/1.56 tff(648,plain,
% 2.02/1.56 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(Y!0))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[647, 646])).
% 2.02/1.56 tff(649,plain,
% 2.02/1.56 ($false),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[648, 645])).
% 2.02/1.56 tff(650,plain,((~(tptp_fun_Y1_11(X!1) = X!1)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.56 tff(651,plain,
% 2.02/1.56 (~(tptp_fun_Y1_11(X!1) = X!1)),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[650, 597, 91, 560, 571])).
% 2.02/1.56 tff(652,plain,
% 2.02/1.56 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[187, 183])).
% 2.02/1.56 tff(653,plain,
% 2.02/1.56 (tptp_fun_Z1_12(X!1) = tptp_fun_X_2(Y!0)),
% 2.02/1.56 inference(transitivity,[status(thm)],[652, 31])).
% 2.02/1.56 tff(654,plain,
% 2.02/1.56 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.02/1.56 inference(monotonicity,[status(thm)],[653, 154])).
% 2.02/1.56 tff(655,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.02/1.56 inference(symmetry,[status(thm)],[654])).
% 2.02/1.56 tff(656,plain,
% 2.02/1.56 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[655])).
% 2.02/1.56 tff(657,plain,
% 2.02/1.56 (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[35, 656])).
% 2.02/1.56 tff(658,plain,
% 2.02/1.56 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[161, 145, 144])).
% 2.02/1.56 tff(659,plain,
% 2.02/1.56 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[171, 658])).
% 2.02/1.56 tff(660,plain,
% 2.02/1.56 ($false),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[659, 657])).
% 2.02/1.56 tff(661,plain,((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.56 tff(662,plain,
% 2.02/1.56 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[661, 35, 30, 144, 45])).
% 2.02/1.56 tff(663,plain,
% 2.02/1.56 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[191, 662])).
% 2.02/1.56 tff(664,plain,
% 2.02/1.56 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[88, 663])).
% 2.02/1.56 tff(665,plain,
% 2.02/1.56 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[82, 664])).
% 2.02/1.56 tff(666,plain,
% 2.02/1.56 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[56, 665])).
% 2.02/1.56 tff(667,plain,
% 2.02/1.56 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[54, 666])).
% 2.02/1.56 tff(668,plain,
% 2.02/1.56 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[52, 667, 30])).
% 2.02/1.56 tff(669,plain,
% 2.02/1.56 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[198, 668])).
% 2.02/1.56 tff(670,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.02/1.56 inference(monotonicity,[status(thm)],[208])).
% 2.02/1.56 tff(671,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.02/1.56 inference(symmetry,[status(thm)],[670])).
% 2.02/1.56 tff(672,plain,
% 2.02/1.56 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[671])).
% 2.02/1.56 tff(673,plain,
% 2.02/1.56 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[35, 672])).
% 2.02/1.56 tff(674,plain,
% 2.02/1.56 ($false),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[216, 673])).
% 2.02/1.56 tff(675,plain,((tptp_fun_Y_4(X!1, Y!0) = X!1) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.56 tff(676,plain,
% 2.02/1.56 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[675, 669, 35])).
% 2.02/1.56 tff(677,plain,
% 2.02/1.56 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[236, 676, 669])).
% 2.02/1.56 tff(678,plain,
% 2.02/1.56 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[220, 665])).
% 2.02/1.56 tff(679,plain,
% 2.02/1.56 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[222, 678])).
% 2.02/1.56 tff(680,plain,
% 2.02/1.56 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[224, 679, 47])).
% 2.02/1.56 tff(681,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[234, 680])).
% 2.02/1.56 tff(682,plain,
% 2.02/1.56 (~(tptp_fun_W_3(X!1) = X!1)),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[265, 681, 677, 676, 30, 106])).
% 2.02/1.56 tff(683,plain,
% 2.02/1.56 (tptp_fun_W_3(X!1) = Y!0),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[252, 682])).
% 2.02/1.56 tff(684,plain,
% 2.02/1.56 (tptp_fun_X_2(X!1) = tptp_fun_X_2(Y!0)),
% 2.02/1.56 inference(transitivity,[status(thm)],[106, 31])).
% 2.02/1.56 tff(685,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.02/1.56 inference(monotonicity,[status(thm)],[684, 683])).
% 2.02/1.56 tff(686,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.02/1.56 inference(symmetry,[status(thm)],[685])).
% 2.02/1.56 tff(687,plain,
% 2.02/1.56 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[686])).
% 2.02/1.56 tff(688,plain,
% 2.02/1.56 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[35, 687])).
% 2.02/1.56 tff(689,plain,
% 2.02/1.56 ($false),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[681, 688])).
% 2.02/1.56 tff(690,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.56 tff(691,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[690, 651, 30, 47, 45])).
% 2.02/1.56 tff(692,assumption,(big_f(tptp_fun_X_2(Y!0), Y!0)), introduced(assumption)).
% 2.02/1.56 tff(693,assumption,((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)), introduced(assumption)).
% 2.02/1.56 tff(694,assumption,(tptp_fun_Y_7(Y!0, Y!0) = Y!0), introduced(assumption)).
% 2.02/1.56 tff(695,plain,
% 2.02/1.56 (Y!0 = tptp_fun_Y_7(Y!0, Y!0)),
% 2.02/1.56 inference(symmetry,[status(thm)],[694])).
% 2.02/1.56 tff(696,plain,
% 2.02/1.56 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[30, 695])).
% 2.02/1.56 tff(697,plain,
% 2.02/1.56 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.02/1.56 inference(symmetry,[status(thm)],[696])).
% 2.02/1.56 tff(698,plain,
% 2.02/1.56 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (~big_f(tptp_fun_X_2(Y!0), Y!0))),
% 2.02/1.56 inference(monotonicity,[status(thm)],[697])).
% 2.02/1.56 tff(699,plain,
% 2.02/1.56 ((~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) | (~(tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.02/1.56 inference(tautology,[status(thm)],[])).
% 2.02/1.56 tff(700,plain,
% 2.02/1.56 (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[699, 694, 693])).
% 2.02/1.56 tff(701,plain,
% 2.02/1.56 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[700, 698])).
% 2.02/1.57 tff(702,plain,
% 2.02/1.57 ($false),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[692, 701])).
% 2.02/1.57 tff(703,plain,((~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.57 tff(704,plain,
% 2.02/1.57 (~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[703, 693, 30, 692])).
% 2.02/1.57 tff(705,plain,
% 2.02/1.57 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(Y!0, Y!0) = Y!0) | (tptp_fun_Y_7(Y!0, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(Y!0, Y!0) = Y!0) | (tptp_fun_Y_7(Y!0, Y!0) = X!1))),
% 2.02/1.57 inference(rewrite,[status(thm)],[])).
% 2.02/1.57 tff(706,plain,
% 2.02/1.57 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(Y!0, Y!0) = Y!0) | (tptp_fun_Y_7(Y!0, Y!0) = X!1))),
% 2.02/1.57 inference(quant_inst,[status(thm)],[])).
% 2.02/1.57 tff(707,plain,
% 2.02/1.57 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(Y!0, Y!0) = Y!0) | (tptp_fun_Y_7(Y!0, Y!0) = X!1)),
% 2.02/1.57 inference(modus_ponens,[status(thm)],[706, 705])).
% 2.02/1.57 tff(708,plain,
% 2.02/1.57 ((tptp_fun_Y_7(Y!0, Y!0) = Y!0) | (tptp_fun_Y_7(Y!0, Y!0) = X!1)),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[707, 12])).
% 2.02/1.57 tff(709,plain,
% 2.02/1.57 (tptp_fun_Y_7(Y!0, Y!0) = X!1),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[708, 704])).
% 2.02/1.57 tff(710,plain,
% 2.02/1.57 (X!1 = tptp_fun_Y_7(Y!0, Y!0)),
% 2.02/1.57 inference(symmetry,[status(thm)],[709])).
% 2.02/1.57 tff(711,plain,
% 2.02/1.57 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y_7(Y!0, Y!0)),
% 2.02/1.57 inference(transitivity,[status(thm)],[598, 710])).
% 2.02/1.57 tff(712,plain,
% 2.02/1.57 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.02/1.57 inference(monotonicity,[status(thm)],[711])).
% 2.02/1.57 tff(713,plain,
% 2.02/1.57 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.02/1.57 inference(symmetry,[status(thm)],[712])).
% 2.02/1.57 tff(714,plain,
% 2.02/1.57 ((~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) | (tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.02/1.57 inference(tautology,[status(thm)],[])).
% 2.02/1.57 tff(715,plain,
% 2.02/1.57 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[714, 704, 693])).
% 2.02/1.57 tff(716,plain,
% 2.02/1.57 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.02/1.57 inference(modus_ponens,[status(thm)],[715, 713])).
% 2.02/1.57 tff(717,plain,
% 2.02/1.57 ($false),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[41, 716])).
% 2.02/1.57 tff(718,plain,((~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.02/1.57 tff(719,plain,
% 2.02/1.57 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[718, 691, 560, 30, 571])).
% 2.02/1.57 tff(720,plain,
% 2.02/1.57 ((~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))) | ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.02/1.57 inference(quant_inst,[status(thm)],[])).
% 2.02/1.57 tff(721,plain,
% 2.02/1.57 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[720, 719])).
% 2.02/1.57 tff(722,assumption,(~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))), introduced(assumption)).
% 2.02/1.57 tff(723,plain,
% 2.02/1.57 (((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))) | ((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))),
% 2.02/1.57 inference(tautology,[status(thm)],[])).
% 2.02/1.57 tff(724,plain,
% 2.02/1.57 ((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[723, 429])).
% 2.02/1.57 tff(725,plain,
% 2.02/1.57 ((~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))) | (Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.02/1.57 inference(tautology,[status(thm)],[])).
% 2.02/1.57 tff(726,plain,
% 2.02/1.57 (Y!0 = Z!5),
% 2.02/1.57 inference(unit_resolution,[status(thm)],[725, 724, 722])).
% 2.02/1.57 tff(727,plain,
% 2.02/1.57 (Z!5 = Y!0),
% 2.02/1.57 inference(symmetry,[status(thm)],[726])).
% 2.02/1.57 tff(728,assumption,(~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))), introduced(assumption)).
% 2.02/1.57 tff(729,plain,
% 2.02/1.57 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))))))),
% 2.02/1.57 inference(rewrite,[status(thm)],[])).
% 2.02/1.57 tff(730,plain,
% 2.02/1.57 ((~((~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))) | (~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))))) <=> (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))))))),
% 2.02/1.57 inference(rewrite,[status(thm)],[])).
% 2.02/1.57 tff(731,plain,
% 2.02/1.57 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))) | (~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))))))),
% 2.02/1.57 inference(monotonicity,[status(thm)],[730])).
% 2.02/1.57 tff(732,plain,
% 2.02/1.57 (((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))) | (~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))))))) <=> ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))))))),
% 2.06/1.57 inference(transitivity,[status(thm)],[731, 729])).
% 2.06/1.57 tff(733,plain,
% 2.06/1.57 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))) | (~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))))))),
% 2.06/1.57 inference(quant_inst,[status(thm)],[])).
% 2.06/1.57 tff(734,plain,
% 2.06/1.57 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))))))),
% 2.06/1.57 inference(modus_ponens,[status(thm)],[733, 732])).
% 2.06/1.57 tff(735,plain,
% 2.06/1.57 (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[734, 341])).
% 2.06/1.57 tff(736,plain,
% 2.06/1.57 (((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))))) | ((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))),
% 2.06/1.57 inference(tautology,[status(thm)],[])).
% 2.06/1.57 tff(737,plain,
% 2.06/1.57 ((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[736, 735])).
% 2.06/1.57 tff(738,plain,
% 2.06/1.57 ((~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))) | (tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.06/1.57 inference(tautology,[status(thm)],[])).
% 2.06/1.57 tff(739,plain,
% 2.06/1.57 (tptp_fun_Y1_11(Y!0) = Z!5),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[738, 737, 728])).
% 2.06/1.57 tff(740,plain,
% 2.06/1.57 (X!1 = Y!0),
% 2.06/1.57 inference(transitivity,[status(thm)],[599, 739, 727])).
% 2.06/1.57 tff(741,plain,
% 2.06/1.57 (~(X!1 = Y!0)),
% 2.06/1.57 inference(and_elim,[status(thm)],[11])).
% 2.06/1.57 tff(742,plain,
% 2.06/1.57 ($false),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[741, 740])).
% 2.06/1.57 tff(743,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.57 tff(744,plain,
% 2.06/1.57 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[743, 721, 560, 630])).
% 2.06/1.57 tff(745,plain,
% 2.06/1.57 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[462, 744])).
% 2.06/1.57 tff(746,plain,
% 2.06/1.57 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))))))),
% 2.06/1.57 inference(quant_inst,[status(thm)],[])).
% 2.06/1.57 tff(747,plain,
% 2.06/1.57 (~((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[746, 745])).
% 2.06/1.57 tff(748,plain,
% 2.06/1.57 (((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))))) | ((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))),
% 2.06/1.57 inference(tautology,[status(thm)],[])).
% 2.06/1.57 tff(749,plain,
% 2.06/1.57 ((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[748, 747])).
% 2.06/1.57 tff(750,plain,
% 2.06/1.57 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[576, 564])).
% 2.06/1.57 tff(751,plain,
% 2.06/1.57 ((~(big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0)))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.57 inference(tautology,[status(thm)],[])).
% 2.06/1.57 tff(752,plain,
% 2.06/1.57 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[751, 597, 750])).
% 2.06/1.57 tff(753,plain,
% 2.06/1.57 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.06/1.57 inference(symmetry,[status(thm)],[752])).
% 2.06/1.57 tff(754,plain,
% 2.06/1.57 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.06/1.57 inference(monotonicity,[status(thm)],[753])).
% 2.06/1.57 tff(755,plain,
% 2.06/1.57 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.06/1.57 inference(transitivity,[status(thm)],[754, 24])).
% 2.06/1.57 tff(756,plain,
% 2.06/1.57 ((W1!8 = X!1) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.06/1.57 inference(symmetry,[status(thm)],[755])).
% 2.06/1.57 tff(757,plain,
% 2.06/1.57 (tptp_fun_Y1_11(X!1) = Y!0),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[153, 651])).
% 2.06/1.57 tff(758,plain,
% 2.06/1.57 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[191, 89])).
% 2.06/1.57 tff(759,plain,
% 2.06/1.57 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))),
% 2.06/1.57 inference(quant_inst,[status(thm)],[])).
% 2.06/1.57 tff(760,plain,
% 2.06/1.57 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.06/1.57 inference(unit_resolution,[status(thm)],[759, 658])).
% 2.06/1.57 tff(761,assumption,((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)), introduced(assumption)).
% 2.06/1.57 tff(762,plain,
% 2.06/1.57 (Y!0 = tptp_fun_Z1_12(X!1)),
% 2.06/1.57 inference(symmetry,[status(thm)],[156])).
% 2.06/1.57 tff(763,assumption,(~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))), introduced(assumption)).
% 2.06/1.57 tff(764,plain,
% 2.06/1.57 ((~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))) | big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.06/1.58 inference(tautology,[status(thm)],[])).
% 2.06/1.58 tff(765,plain,
% 2.06/1.58 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[764, 763, 761])).
% 2.06/1.58 tff(766,plain,
% 2.06/1.58 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)),
% 2.06/1.58 inference(transitivity,[status(thm)],[765, 762])).
% 2.06/1.58 tff(767,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[766])).
% 2.06/1.58 tff(768,plain,
% 2.06/1.58 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.58 inference(symmetry,[status(thm)],[767])).
% 2.06/1.58 tff(769,assumption,(big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))), introduced(assumption)).
% 2.06/1.58 tff(770,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.58 inference(modus_ponens,[status(thm)],[769, 768])).
% 2.06/1.58 tff(771,plain,
% 2.06/1.58 ($false),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[763, 770])).
% 2.06/1.58 tff(772,plain,(big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Z1_12(X!1) = Y!0)) | (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.58 tff(773,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[772, 652, 761, 659])).
% 2.06/1.58 tff(774,plain,
% 2.06/1.58 ((~(big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.06/1.58 inference(tautology,[status(thm)],[])).
% 2.06/1.58 tff(775,plain,
% 2.06/1.58 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[774, 773, 760])).
% 2.06/1.58 tff(776,plain,
% 2.06/1.58 ((~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))) | (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) | (~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.06/1.58 inference(tautology,[status(thm)],[])).
% 2.06/1.58 tff(777,plain,
% 2.06/1.58 (~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[776, 773, 761])).
% 2.06/1.58 tff(778,plain,
% 2.06/1.58 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.06/1.58 inference(rewrite,[status(thm)],[])).
% 2.06/1.58 tff(779,plain,
% 2.06/1.58 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.06/1.58 inference(quant_inst,[status(thm)],[])).
% 2.06/1.58 tff(780,plain,
% 2.06/1.58 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.06/1.58 inference(modus_ponens,[status(thm)],[779, 778])).
% 2.06/1.58 tff(781,plain,
% 2.06/1.58 ((tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[780, 12])).
% 2.06/1.58 tff(782,plain,
% 2.06/1.58 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[781, 777])).
% 2.06/1.58 tff(783,plain,
% 2.06/1.58 (X!1 = tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1))),
% 2.06/1.58 inference(symmetry,[status(thm)],[782])).
% 2.06/1.58 tff(784,plain,
% 2.06/1.58 (X!1 = Y!0),
% 2.06/1.58 inference(transitivity,[status(thm)],[783, 775, 652])).
% 2.06/1.58 tff(785,plain,
% 2.06/1.58 ($false),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[741, 784])).
% 2.06/1.58 tff(786,plain,((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.58 tff(787,plain,
% 2.06/1.58 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[786, 651, 45, 758])).
% 2.06/1.58 tff(788,plain,
% 2.06/1.58 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))) | ((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.06/1.58 inference(quant_inst,[status(thm)],[])).
% 2.06/1.58 tff(789,plain,
% 2.06/1.58 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[788, 787])).
% 2.06/1.58 tff(790,plain,
% 2.06/1.58 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))))))),
% 2.06/1.58 inference(quant_inst,[status(thm)],[])).
% 2.06/1.58 tff(791,plain,
% 2.06/1.58 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[790, 745])).
% 2.06/1.58 tff(792,plain,
% 2.06/1.58 (((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))))) | ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))),
% 2.06/1.58 inference(tautology,[status(thm)],[])).
% 2.06/1.58 tff(793,plain,
% 2.06/1.58 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[792, 791])).
% 2.06/1.58 tff(794,plain,
% 2.06/1.58 ((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.06/1.58 inference(tautology,[status(thm)],[])).
% 2.06/1.58 tff(795,plain,
% 2.06/1.58 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[794, 793, 789])).
% 2.06/1.58 tff(796,assumption,(tptp_fun_Y1_11(X!1) = Y!0), introduced(assumption)).
% 2.06/1.58 tff(797,plain,
% 2.06/1.58 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (Y!0 = W1!8)),
% 2.06/1.58 inference(monotonicity,[status(thm)],[796])).
% 2.06/1.58 tff(798,plain,
% 2.06/1.58 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (W1!8 = Y!0)),
% 2.06/1.58 inference(transitivity,[status(thm)],[797, 1])).
% 2.06/1.58 tff(799,assumption,(tptp_fun_Y1_11(X!1) = W1!8), introduced(assumption)).
% 2.06/1.58 tff(800,plain,
% 2.06/1.58 (W1!8 = Y!0),
% 2.06/1.58 inference(modus_ponens,[status(thm)],[799, 798])).
% 2.06/1.58 tff(801,assumption,(~(W1!8 = Y!0)), introduced(assumption)).
% 2.06/1.58 tff(802,plain,
% 2.06/1.58 ($false),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[801, 800])).
% 2.06/1.58 tff(803,plain,((~(tptp_fun_Y1_11(X!1) = W1!8)) | (W1!8 = Y!0) | (~(tptp_fun_Y1_11(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.58 tff(804,plain,
% 2.06/1.58 (W1!8 = Y!0),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[803, 795, 757])).
% 2.06/1.58 tff(805,plain,
% 2.06/1.58 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.06/1.58 inference(monotonicity,[status(thm)],[804])).
% 2.06/1.58 tff(806,plain,
% 2.06/1.58 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.06/1.58 inference(transitivity,[status(thm)],[805, 46])).
% 2.06/1.58 tff(807,plain,
% 2.06/1.58 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.06/1.58 inference(symmetry,[status(thm)],[806])).
% 2.06/1.58 tff(808,plain,
% 2.06/1.58 ((X!1 = Y!0) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.06/1.58 inference(transitivity,[status(thm)],[807, 756])).
% 2.06/1.58 tff(809,plain,
% 2.06/1.58 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Z1_12(Y!0) = W1!8))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[808])).
% 2.06/1.58 tff(810,plain,
% 2.06/1.58 (~(tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.06/1.58 inference(modus_ponens,[status(thm)],[741, 809])).
% 2.06/1.58 tff(811,plain,
% 2.06/1.58 ((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.06/1.58 inference(tautology,[status(thm)],[])).
% 2.06/1.58 tff(812,plain,
% 2.06/1.58 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[811, 810, 749])).
% 2.06/1.58 tff(813,plain,
% 2.06/1.58 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))) | ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.06/1.58 inference(quant_inst,[status(thm)],[])).
% 2.06/1.58 tff(814,plain,
% 2.06/1.58 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[813, 812])).
% 2.06/1.58 tff(815,assumption,(~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)), introduced(assumption)).
% 2.06/1.58 tff(816,plain,
% 2.06/1.58 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0))),
% 2.06/1.58 inference(rewrite,[status(thm)],[])).
% 2.06/1.58 tff(817,plain,
% 2.06/1.58 (((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)) <=> ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0))),
% 2.06/1.58 inference(rewrite,[status(thm)],[])).
% 2.06/1.58 tff(818,plain,
% 2.06/1.58 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0)))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[817])).
% 2.06/1.58 tff(819,plain,
% 2.06/1.58 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0))),
% 2.06/1.58 inference(transitivity,[status(thm)],[818, 816])).
% 2.06/1.58 tff(820,plain,
% 2.06/1.58 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.06/1.58 inference(quant_inst,[status(thm)],[])).
% 2.06/1.58 tff(821,plain,
% 2.06/1.58 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0)),
% 2.06/1.58 inference(modus_ponens,[status(thm)],[820, 819])).
% 2.06/1.58 tff(822,plain,
% 2.06/1.58 ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0)),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[821, 12])).
% 2.06/1.58 tff(823,plain,
% 2.06/1.58 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[822, 815])).
% 2.06/1.58 tff(824,plain,
% 2.06/1.58 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_X_2(X!1)),
% 2.06/1.58 inference(transitivity,[status(thm)],[823, 273])).
% 2.06/1.58 tff(825,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.58 inference(monotonicity,[status(thm)],[824, 598])).
% 2.06/1.58 tff(826,plain,
% 2.06/1.58 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.58 inference(symmetry,[status(thm)],[825])).
% 2.06/1.58 tff(827,plain,
% 2.06/1.58 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[826])).
% 2.06/1.58 tff(828,assumption,(~big_f(tptp_fun_X_2(X!1), X!1)), introduced(assumption)).
% 2.06/1.58 tff(829,plain,
% 2.06/1.58 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.58 inference(modus_ponens,[status(thm)],[828, 827])).
% 2.06/1.58 tff(830,assumption,(X!1 = tptp_fun_Z1_12(Y!0)), introduced(assumption)).
% 2.06/1.58 tff(831,plain,
% 2.06/1.58 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.06/1.58 inference(symmetry,[status(thm)],[830])).
% 2.06/1.58 tff(832,plain,
% 2.06/1.58 (tptp_fun_Z1_12(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.06/1.58 inference(transitivity,[status(thm)],[831, 599])).
% 2.06/1.58 tff(833,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[832])).
% 2.06/1.58 tff(834,assumption,((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)), introduced(assumption)).
% 2.06/1.58 tff(835,plain,
% 2.06/1.58 ((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))) | big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.06/1.58 inference(tautology,[status(thm)],[])).
% 2.06/1.58 tff(836,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[835, 815, 834])).
% 2.06/1.58 tff(837,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.58 inference(modus_ponens,[status(thm)],[836, 833])).
% 2.06/1.58 tff(838,plain,
% 2.06/1.58 ($false),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[837, 829])).
% 2.06/1.58 tff(839,plain,((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) | big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(X!1 = tptp_fun_Z1_12(Y!0))) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.58 tff(840,plain,
% 2.06/1.58 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1),
% 2.06/1.58 inference(unit_resolution,[status(thm)],[839, 570, 560, 106, 752, 814])).
% 2.06/1.58 tff(841,plain,
% 2.06/1.58 (X!1 = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.06/1.58 inference(symmetry,[status(thm)],[840])).
% 2.06/1.58 tff(842,plain,
% 2.06/1.58 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[841])).
% 2.06/1.58 tff(843,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.58 inference(symmetry,[status(thm)],[842])).
% 2.06/1.58 tff(844,plain,
% 2.06/1.58 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))) <=> (~big_f(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[843])).
% 2.06/1.58 tff(845,plain,
% 2.06/1.58 (X!1 = tptp_fun_Y1_11(Y!0)),
% 2.06/1.58 inference(symmetry,[status(thm)],[560])).
% 2.06/1.58 tff(846,plain,
% 2.06/1.58 (tptp_fun_Z1_12(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.06/1.58 inference(transitivity,[status(thm)],[753, 845])).
% 2.06/1.58 tff(847,plain,
% 2.06/1.58 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[846])).
% 2.06/1.58 tff(848,plain,
% 2.06/1.58 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)))),
% 2.06/1.58 inference(monotonicity,[status(thm)],[847])).
% 2.06/1.58 tff(849,plain,
% 2.06/1.58 ((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))) | (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) | (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.06/1.59 inference(tautology,[status(thm)],[])).
% 2.06/1.59 tff(850,plain,
% 2.06/1.59 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[849, 840, 814])).
% 2.06/1.59 tff(851,plain,
% 2.06/1.59 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[850, 848])).
% 2.06/1.59 tff(852,plain,
% 2.06/1.59 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[851, 844])).
% 2.06/1.59 tff(853,plain,
% 2.06/1.59 ($false),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[597, 852])).
% 2.06/1.59 tff(854,plain,(((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1) | big_f(X!1, Y!0) | (tptp_fun_Y_4(Y!0, Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.59 tff(855,plain,
% 2.06/1.59 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[854, 48, 47, 45, 30])).
% 2.06/1.59 tff(856,plain,
% 2.06/1.59 ((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) | (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.06/1.59 inference(tautology,[status(thm)],[])).
% 2.06/1.59 tff(857,plain,
% 2.06/1.59 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[856, 855, 48])).
% 2.06/1.59 tff(858,plain,
% 2.06/1.59 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[857, 568])).
% 2.06/1.59 tff(859,plain,
% 2.06/1.59 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[675, 214, 35])).
% 2.06/1.59 tff(860,plain,
% 2.06/1.59 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.59 inference(monotonicity,[status(thm)],[274, 859])).
% 2.06/1.59 tff(861,plain,
% 2.06/1.59 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.06/1.59 inference(symmetry,[status(thm)],[860])).
% 2.06/1.59 tff(862,assumption,(big_f(tptp_fun_X_2(X!1), X!1)), introduced(assumption)).
% 2.06/1.59 tff(863,plain,
% 2.06/1.59 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[862, 861])).
% 2.06/1.59 tff(864,plain,
% 2.06/1.59 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[236, 214, 859])).
% 2.06/1.59 tff(865,plain,
% 2.06/1.59 ($false),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[864, 863])).
% 2.06/1.59 tff(866,plain,((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.59 tff(867,plain,
% 2.06/1.59 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[866, 35, 30, 106, 858])).
% 2.06/1.59 tff(868,plain,
% 2.06/1.59 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[198, 867])).
% 2.06/1.59 tff(869,plain,
% 2.06/1.59 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[52, 868, 30])).
% 2.06/1.59 tff(870,plain,
% 2.06/1.59 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[54, 869])).
% 2.06/1.59 tff(871,plain,
% 2.06/1.59 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[56, 870])).
% 2.06/1.59 tff(872,plain,
% 2.06/1.59 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[82, 871])).
% 2.06/1.59 tff(873,plain,
% 2.06/1.59 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[84, 872])).
% 2.06/1.59 tff(874,plain,
% 2.06/1.59 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[86, 873])).
% 2.06/1.59 tff(875,plain,
% 2.06/1.59 (tptp_fun_Y1_11(X!1) = X!1),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[690, 35, 30, 47, 45])).
% 2.06/1.59 tff(876,plain,
% 2.06/1.59 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[88, 872])).
% 2.06/1.59 tff(877,plain,
% 2.06/1.59 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[90, 876])).
% 2.06/1.59 tff(878,plain,
% 2.06/1.59 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[269, 877, 875])).
% 2.06/1.59 tff(879,plain,
% 2.06/1.59 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))) | ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))),
% 2.06/1.59 inference(quant_inst,[status(thm)],[])).
% 2.06/1.59 tff(880,plain,
% 2.06/1.59 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[879, 878])).
% 2.06/1.59 tff(881,plain,
% 2.06/1.59 (~(W1!8 = Y!0)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[524, 495, 30, 45, 35])).
% 2.06/1.59 tff(882,plain,
% 2.06/1.59 (W1!8 = X!1),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[19, 881])).
% 2.06/1.59 tff(883,plain,
% 2.06/1.59 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.59 inference(monotonicity,[status(thm)],[273, 882])).
% 2.06/1.59 tff(884,plain,
% 2.06/1.59 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, W1!8)),
% 2.06/1.59 inference(symmetry,[status(thm)],[883])).
% 2.06/1.59 tff(885,plain,
% 2.06/1.59 (big_f(Y!0, W1!8)),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[862, 884])).
% 2.06/1.59 tff(886,plain,
% 2.06/1.59 ((~(big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8)))) | (~big_f(Y!0, W1!8)) | (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.06/1.59 inference(tautology,[status(thm)],[])).
% 2.06/1.59 tff(887,plain,
% 2.06/1.59 (Y!0 = tptp_fun_Z1_9(W1!8)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[886, 885, 511])).
% 2.06/1.59 tff(888,plain,
% 2.06/1.59 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.06/1.59 inference(symmetry,[status(thm)],[887])).
% 2.06/1.59 tff(889,plain,
% 2.06/1.59 (X!1 = tptp_fun_Y1_11(X!1)),
% 2.06/1.59 inference(symmetry,[status(thm)],[277])).
% 2.06/1.59 tff(890,plain,
% 2.06/1.59 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.06/1.59 inference(transitivity,[status(thm)],[882, 889])).
% 2.06/1.59 tff(891,plain,
% 2.06/1.59 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[866, 35, 30, 240, 862])).
% 2.06/1.59 tff(892,plain,
% 2.06/1.59 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[198, 891])).
% 2.06/1.59 tff(893,plain,
% 2.06/1.59 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[52, 892, 30])).
% 2.06/1.59 tff(894,plain,
% 2.06/1.59 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[54, 893])).
% 2.06/1.59 tff(895,plain,
% 2.06/1.59 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[56, 894])).
% 2.06/1.59 tff(896,plain,
% 2.06/1.59 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[82, 895])).
% 2.06/1.59 tff(897,plain,
% 2.06/1.59 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[88, 896])).
% 2.06/1.59 tff(898,plain,
% 2.06/1.59 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[90, 897])).
% 2.06/1.59 tff(899,plain,
% 2.06/1.59 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[269, 898, 277])).
% 2.06/1.59 tff(900,plain,
% 2.06/1.59 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[879, 899])).
% 2.06/1.59 tff(901,assumption,(tptp_fun_X1_13(Y!0, X!1) = Y!0), introduced(assumption)).
% 2.06/1.59 tff(902,plain,
% 2.06/1.59 (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_X_2(X!1)),
% 2.06/1.59 inference(transitivity,[status(thm)],[901, 273])).
% 2.06/1.59 tff(903,plain,
% 2.06/1.59 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.59 inference(monotonicity,[status(thm)],[902, 277])).
% 2.06/1.59 tff(904,plain,
% 2.06/1.59 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.59 inference(symmetry,[status(thm)],[903])).
% 2.06/1.59 tff(905,plain,
% 2.06/1.59 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[862, 904])).
% 2.06/1.59 tff(906,assumption,((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)), introduced(assumption)).
% 2.06/1.59 tff(907,plain,
% 2.06/1.59 ((~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) | (~(tptp_fun_X1_13(Y!0, X!1) = Y!0))),
% 2.06/1.59 inference(tautology,[status(thm)],[])).
% 2.06/1.59 tff(908,plain,
% 2.06/1.59 (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[907, 901, 906])).
% 2.06/1.59 tff(909,plain,
% 2.06/1.59 ($false),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[908, 905])).
% 2.06/1.59 tff(910,plain,((~(tptp_fun_X1_13(Y!0, X!1) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.59 tff(911,plain,
% 2.06/1.59 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[910, 277, 862, 240, 900])).
% 2.06/1.59 tff(912,plain,
% 2.06/1.59 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(Y!0, X!1) = Y!0) | (tptp_fun_X1_13(Y!0, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(Y!0, X!1) = Y!0) | (tptp_fun_X1_13(Y!0, X!1) = X!1))),
% 2.06/1.59 inference(rewrite,[status(thm)],[])).
% 2.06/1.59 tff(913,plain,
% 2.06/1.59 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(Y!0, X!1) = Y!0) | (tptp_fun_X1_13(Y!0, X!1) = X!1))),
% 2.06/1.59 inference(quant_inst,[status(thm)],[])).
% 2.06/1.59 tff(914,plain,
% 2.06/1.59 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(Y!0, X!1) = Y!0) | (tptp_fun_X1_13(Y!0, X!1) = X!1)),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[913, 912])).
% 2.06/1.59 tff(915,plain,
% 2.06/1.59 ((tptp_fun_X1_13(Y!0, X!1) = Y!0) | (tptp_fun_X1_13(Y!0, X!1) = X!1)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[914, 12])).
% 2.06/1.59 tff(916,plain,
% 2.06/1.59 (tptp_fun_X1_13(Y!0, X!1) = X!1),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[915, 911])).
% 2.06/1.59 tff(917,plain,
% 2.06/1.59 (X!1 = tptp_fun_X1_13(Y!0, X!1)),
% 2.06/1.59 inference(symmetry,[status(thm)],[916])).
% 2.06/1.59 tff(918,plain,
% 2.06/1.59 (big_f(X!1, W1!8) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.59 inference(monotonicity,[status(thm)],[917, 890])).
% 2.06/1.59 tff(919,plain,
% 2.06/1.59 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, W1!8)),
% 2.06/1.59 inference(symmetry,[status(thm)],[918])).
% 2.06/1.59 tff(920,plain,
% 2.06/1.59 ((~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) | (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.59 inference(tautology,[status(thm)],[])).
% 2.06/1.59 tff(921,plain,
% 2.06/1.59 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[920, 911, 900])).
% 2.06/1.59 tff(922,plain,
% 2.06/1.59 (big_f(X!1, W1!8)),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[921, 919])).
% 2.06/1.59 tff(923,plain,
% 2.06/1.59 ((~(big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8)))) | (~big_f(X!1, W1!8)) | (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.06/1.59 inference(tautology,[status(thm)],[])).
% 2.06/1.59 tff(924,plain,
% 2.06/1.59 (X!1 = tptp_fun_Z1_9(W1!8)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[923, 922, 497])).
% 2.06/1.59 tff(925,plain,
% 2.06/1.59 (X!1 = Y!0),
% 2.06/1.59 inference(transitivity,[status(thm)],[924, 888])).
% 2.06/1.59 tff(926,plain,
% 2.06/1.59 ($false),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[741, 925])).
% 2.06/1.59 tff(927,plain,((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.59 tff(928,plain,
% 2.06/1.59 (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[927, 875, 858, 106, 30, 45, 35])).
% 2.06/1.59 tff(929,plain,
% 2.06/1.59 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[481, 928])).
% 2.06/1.59 tff(930,plain,
% 2.06/1.59 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[462, 929])).
% 2.06/1.59 tff(931,assumption,(~(tptp_fun_Y1_11(Y!0) = X!1)), introduced(assumption)).
% 2.06/1.59 tff(932,plain,
% 2.06/1.59 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[39, 931])).
% 2.06/1.59 tff(933,plain,
% 2.06/1.59 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[113, 932, 112])).
% 2.06/1.59 tff(934,plain,
% 2.06/1.59 ((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0)),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[115, 933])).
% 2.06/1.59 tff(935,plain,
% 2.06/1.59 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.59 inference(unit_resolution,[status(thm)],[140, 934, 45, 932])).
% 2.06/1.59 tff(936,plain,
% 2.06/1.59 (tptp_fun_Y_7(X!1, Y!0) = tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.59 inference(monotonicity,[status(thm)],[146])).
% 2.06/1.59 tff(937,plain,
% 2.06/1.59 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = tptp_fun_Y_7(X!1, Y!0)),
% 2.06/1.59 inference(symmetry,[status(thm)],[936])).
% 2.06/1.59 tff(938,plain,
% 2.06/1.59 (Y!0 = tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.59 inference(symmetry,[status(thm)],[609])).
% 2.06/1.59 tff(939,plain,
% 2.06/1.59 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y_7(X!1, Y!0)),
% 2.06/1.59 inference(transitivity,[status(thm)],[109, 938, 937])).
% 2.06/1.59 tff(940,plain,
% 2.06/1.59 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.59 inference(monotonicity,[status(thm)],[939])).
% 2.06/1.59 tff(941,plain,
% 2.06/1.59 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.59 inference(symmetry,[status(thm)],[940])).
% 2.06/1.59 tff(942,plain,
% 2.06/1.59 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.59 inference(monotonicity,[status(thm)],[109, 937])).
% 2.06/1.59 tff(943,plain,
% 2.06/1.59 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.59 inference(modus_ponens,[status(thm)],[615, 942])).
% 2.06/1.59 tff(944,plain,
% 2.06/1.59 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[943, 941])).
% 2.06/1.60 tff(945,plain,
% 2.06/1.60 ($false),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[41, 944])).
% 2.06/1.60 tff(946,plain,((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.60 tff(947,plain,
% 2.06/1.60 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[946, 600, 109, 41])).
% 2.06/1.60 tff(948,plain,
% 2.06/1.60 (tptp_fun_Y_7(X!1, Y!0) = X!1),
% 2.06/1.60 inference(transitivity,[status(thm)],[936, 947])).
% 2.06/1.60 tff(949,plain,
% 2.06/1.60 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.60 inference(monotonicity,[status(thm)],[273, 948])).
% 2.06/1.60 tff(950,plain,
% 2.06/1.60 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.60 inference(symmetry,[status(thm)],[949])).
% 2.06/1.60 tff(951,plain,
% 2.06/1.60 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[862, 950])).
% 2.06/1.60 tff(952,plain,
% 2.06/1.60 ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)))),
% 2.06/1.60 inference(monotonicity,[status(thm)],[942])).
% 2.06/1.60 tff(953,plain,
% 2.06/1.60 (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[624, 600, 947])).
% 2.06/1.60 tff(954,plain,
% 2.06/1.60 (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[953, 952])).
% 2.06/1.60 tff(955,plain,
% 2.06/1.60 ($false),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[954, 951])).
% 2.06/1.60 tff(956,plain,((~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.60 tff(957,plain,
% 2.06/1.60 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[956, 935, 862, 240, 932])).
% 2.06/1.60 tff(958,plain,
% 2.06/1.60 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))) | ((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.06/1.60 inference(quant_inst,[status(thm)],[])).
% 2.06/1.60 tff(959,plain,
% 2.06/1.60 ((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1)),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[958, 933])).
% 2.06/1.60 tff(960,assumption,(~(tptp_fun_X1_13(X!1, Y!0) = X!1)), introduced(assumption)).
% 2.06/1.60 tff(961,plain,
% 2.06/1.60 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, Y!0) = X!1) | (tptp_fun_X1_13(X!1, Y!0) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(X!1, Y!0) = X!1) | (tptp_fun_X1_13(X!1, Y!0) = Y!0))),
% 2.06/1.60 inference(rewrite,[status(thm)],[])).
% 2.06/1.60 tff(962,plain,
% 2.06/1.60 (((tptp_fun_X1_13(X!1, Y!0) = Y!0) | (tptp_fun_X1_13(X!1, Y!0) = X!1)) <=> ((tptp_fun_X1_13(X!1, Y!0) = X!1) | (tptp_fun_X1_13(X!1, Y!0) = Y!0))),
% 2.06/1.60 inference(rewrite,[status(thm)],[])).
% 2.06/1.60 tff(963,plain,
% 2.06/1.60 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, Y!0) = Y!0) | (tptp_fun_X1_13(X!1, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, Y!0) = X!1) | (tptp_fun_X1_13(X!1, Y!0) = Y!0)))),
% 2.06/1.60 inference(monotonicity,[status(thm)],[962])).
% 2.06/1.60 tff(964,plain,
% 2.06/1.60 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, Y!0) = Y!0) | (tptp_fun_X1_13(X!1, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(X!1, Y!0) = X!1) | (tptp_fun_X1_13(X!1, Y!0) = Y!0))),
% 2.06/1.60 inference(transitivity,[status(thm)],[963, 961])).
% 2.06/1.60 tff(965,plain,
% 2.06/1.60 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_13(X!1, Y!0) = Y!0) | (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.06/1.60 inference(quant_inst,[status(thm)],[])).
% 2.06/1.60 tff(966,plain,
% 2.06/1.60 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_13(X!1, Y!0) = X!1) | (tptp_fun_X1_13(X!1, Y!0) = Y!0)),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[965, 964])).
% 2.06/1.60 tff(967,plain,
% 2.06/1.60 ((tptp_fun_X1_13(X!1, Y!0) = X!1) | (tptp_fun_X1_13(X!1, Y!0) = Y!0)),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[966, 12])).
% 2.06/1.60 tff(968,plain,
% 2.06/1.60 (tptp_fun_X1_13(X!1, Y!0) = Y!0),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[967, 960])).
% 2.06/1.60 tff(969,plain,
% 2.06/1.60 (big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.60 inference(monotonicity,[status(thm)],[968])).
% 2.06/1.60 tff(970,plain,
% 2.06/1.60 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))),
% 2.06/1.60 inference(symmetry,[status(thm)],[969])).
% 2.06/1.60 tff(971,plain,
% 2.06/1.60 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0)))),
% 2.06/1.60 inference(monotonicity,[status(thm)],[970])).
% 2.06/1.60 tff(972,plain,
% 2.06/1.60 (~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[41, 971])).
% 2.06/1.60 tff(973,assumption,((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1)), introduced(assumption)).
% 2.06/1.60 tff(974,plain,
% 2.06/1.60 ((~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))) | big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0)) | (tptp_fun_X1_13(X!1, Y!0) = X!1)),
% 2.06/1.60 inference(tautology,[status(thm)],[])).
% 2.06/1.60 tff(975,plain,
% 2.06/1.60 (big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[974, 960, 973])).
% 2.06/1.60 tff(976,plain,
% 2.06/1.60 ($false),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[975, 972])).
% 2.06/1.60 tff(977,plain,((tptp_fun_X1_13(X!1, Y!0) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.60 tff(978,plain,
% 2.06/1.60 (tptp_fun_X1_13(X!1, Y!0) = X!1),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[977, 935, 959])).
% 2.06/1.60 tff(979,assumption,(tptp_fun_X1_13(X!1, Y!0) = X!1), introduced(assumption)).
% 2.06/1.60 tff(980,plain,
% 2.06/1.60 (((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))))) | ((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))),
% 2.06/1.60 inference(tautology,[status(thm)],[])).
% 2.06/1.60 tff(981,plain,
% 2.06/1.60 ((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[980, 343])).
% 2.06/1.60 tff(982,assumption,(![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))), introduced(assumption)).
% 2.06/1.60 tff(983,plain,
% 2.06/1.60 ((~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))) | (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5)))),
% 2.06/1.60 inference(quant_inst,[status(thm)],[])).
% 2.06/1.60 tff(984,plain,
% 2.06/1.60 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[983, 982])).
% 2.06/1.60 tff(985,plain,
% 2.06/1.60 (Z!5 = tptp_fun_X_2(X!1)),
% 2.06/1.60 inference(transitivity,[status(thm)],[412, 273])).
% 2.06/1.60 tff(986,plain,
% 2.06/1.60 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.60 inference(monotonicity,[status(thm)],[985])).
% 2.06/1.60 tff(987,plain,
% 2.06/1.60 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Z!5, X!1)),
% 2.06/1.60 inference(symmetry,[status(thm)],[986])).
% 2.06/1.60 tff(988,plain,
% 2.06/1.60 (big_f(Z!5, X!1)),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[862, 987])).
% 2.06/1.60 tff(989,plain,
% 2.06/1.60 ((~(big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5)))) | (~big_f(Z!5, X!1)) | (X!1 = tptp_fun_W_6(Z!5))),
% 2.06/1.60 inference(tautology,[status(thm)],[])).
% 2.06/1.60 tff(990,plain,
% 2.06/1.60 (X!1 = tptp_fun_W_6(Z!5)),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[989, 988, 984])).
% 2.06/1.60 tff(991,plain,
% 2.06/1.60 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[910, 277, 862, 240, 906])).
% 2.06/1.60 tff(992,plain,
% 2.06/1.60 (Y!0 = Z!5),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[438, 412])).
% 2.06/1.60 tff(993,assumption,((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))), introduced(assumption)).
% 2.06/1.60 tff(994,plain,
% 2.06/1.60 ((tptp_fun_X1_13(X!1, Y!0) = Z!5) <=> (X!1 = Z!5)),
% 2.06/1.60 inference(monotonicity,[status(thm)],[979])).
% 2.06/1.60 tff(995,plain,
% 2.06/1.60 ((~(tptp_fun_X1_13(X!1, Y!0) = Z!5)) <=> (~(X!1 = Z!5))),
% 2.06/1.60 inference(monotonicity,[status(thm)],[994])).
% 2.06/1.60 tff(996,plain,
% 2.06/1.60 ((tptp_fun_X1_13(X!1, Y!0) = Y!0) <=> (X!1 = Y!0)),
% 2.06/1.60 inference(monotonicity,[status(thm)],[979])).
% 2.06/1.60 tff(997,plain,
% 2.06/1.60 ((X!1 = Y!0) <=> (tptp_fun_X1_13(X!1, Y!0) = Y!0)),
% 2.06/1.60 inference(symmetry,[status(thm)],[996])).
% 2.06/1.60 tff(998,plain,
% 2.06/1.60 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X1_13(X!1, Y!0) = Y!0))),
% 2.06/1.60 inference(monotonicity,[status(thm)],[997])).
% 2.06/1.60 tff(999,plain,
% 2.06/1.60 (~(tptp_fun_X1_13(X!1, Y!0) = Y!0)),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[741, 998])).
% 2.06/1.60 tff(1000,plain,
% 2.06/1.60 ((tptp_fun_X1_13(X!1, Y!0) = Z!5) <=> (tptp_fun_X1_13(X!1, Y!0) = Y!0)),
% 2.06/1.60 inference(monotonicity,[status(thm)],[412])).
% 2.06/1.60 tff(1001,assumption,(tptp_fun_X1_13(X!1, Y!0) = Z!5), introduced(assumption)).
% 2.06/1.60 tff(1002,plain,
% 2.06/1.60 (tptp_fun_X1_13(X!1, Y!0) = Y!0),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 2.06/1.60 tff(1003,assumption,(~(tptp_fun_X1_13(X!1, Y!0) = Y!0)), introduced(assumption)).
% 2.06/1.60 tff(1004,plain,
% 2.06/1.60 ($false),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[1003, 1002])).
% 2.06/1.60 tff(1005,plain,((~(tptp_fun_X1_13(X!1, Y!0) = Z!5)) | (tptp_fun_X1_13(X!1, Y!0) = Y!0) | (~(Z!5 = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.60 tff(1006,plain,
% 2.06/1.60 (~(tptp_fun_X1_13(X!1, Y!0) = Z!5)),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[1005, 412, 999])).
% 2.06/1.60 tff(1007,plain,
% 2.06/1.60 (~(X!1 = Z!5)),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[1006, 995])).
% 2.06/1.60 tff(1008,plain,
% 2.06/1.60 ((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.06/1.60 inference(tautology,[status(thm)],[])).
% 2.06/1.60 tff(1009,plain,
% 2.06/1.60 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[1008, 1007, 993])).
% 2.06/1.60 tff(1010,plain,
% 2.06/1.60 ((~![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))) | ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)))),
% 2.06/1.60 inference(quant_inst,[status(thm)],[])).
% 2.06/1.60 tff(1011,plain,
% 2.06/1.60 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[1010, 1009])).
% 2.06/1.60 tff(1012,assumption,(X!1 = tptp_fun_W_6(Z!5)), introduced(assumption)).
% 2.06/1.60 tff(1013,plain,
% 2.06/1.60 (tptp_fun_W_6(Z!5) = X!1),
% 2.06/1.60 inference(symmetry,[status(thm)],[1012])).
% 2.06/1.60 tff(1014,assumption,(Y!0 = Z!5), introduced(assumption)).
% 2.06/1.60 tff(1015,plain,
% 2.06/1.60 (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Z!5)),
% 2.06/1.60 inference(monotonicity,[status(thm)],[1014])).
% 2.06/1.60 tff(1016,plain,
% 2.06/1.60 (tptp_fun_W_6(Y!0) = X!1),
% 2.06/1.60 inference(transitivity,[status(thm)],[1015, 1013])).
% 2.06/1.60 tff(1017,plain,
% 2.06/1.60 ((tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.06/1.60 inference(monotonicity,[status(thm)],[1016])).
% 2.06/1.60 tff(1018,plain,
% 2.06/1.60 ((~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))) <=> (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1))),
% 2.06/1.60 inference(monotonicity,[status(thm)],[1017])).
% 2.06/1.60 tff(1019,assumption,((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))), introduced(assumption)).
% 2.06/1.60 tff(1020,assumption,(big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))), introduced(assumption)).
% 2.06/1.60 tff(1021,plain,
% 2.06/1.60 ((~((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)))) | (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) | (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)))),
% 2.06/1.60 inference(tautology,[status(thm)],[])).
% 2.06/1.60 tff(1022,plain,
% 2.06/1.60 (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.06/1.60 inference(unit_resolution,[status(thm)],[1021, 1020, 1019])).
% 2.06/1.60 tff(1023,plain,
% 2.06/1.60 (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.06/1.60 inference(modus_ponens,[status(thm)],[1022, 1018])).
% 2.06/1.60 tff(1024,plain,
% 2.06/1.60 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1))),
% 2.06/1.61 inference(rewrite,[status(thm)],[])).
% 2.06/1.61 tff(1025,plain,
% 2.06/1.61 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1))),
% 2.06/1.61 inference(quant_inst,[status(thm)],[])).
% 2.06/1.61 tff(1026,plain,
% 2.06/1.61 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.06/1.61 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 2.06/1.61 tff(1027,plain,
% 2.06/1.61 ((tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1026, 12])).
% 2.06/1.61 tff(1028,plain,
% 2.06/1.61 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1027, 1023])).
% 2.06/1.61 tff(1029,plain,
% 2.06/1.61 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(X!1, Y!0)),
% 2.06/1.61 inference(monotonicity,[status(thm)],[1028])).
% 2.06/1.61 tff(1030,plain,
% 2.06/1.61 (big_f(X!1, Y!0) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.06/1.61 inference(symmetry,[status(thm)],[1029])).
% 2.06/1.61 tff(1031,plain,
% 2.06/1.61 ((~big_f(X!1, Y!0)) <=> (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)))),
% 2.06/1.61 inference(monotonicity,[status(thm)],[1030])).
% 2.06/1.61 tff(1032,plain,
% 2.06/1.61 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.06/1.61 inference(modus_ponens,[status(thm)],[45, 1031])).
% 2.06/1.61 tff(1033,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1020, 1032])).
% 2.06/1.61 tff(1034,plain,((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) | big_f(X!1, Y!0) | (~(X!1 = tptp_fun_W_6(Z!5))) | (~(Y!0 = Z!5)) | (~((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1035,plain,
% 2.06/1.61 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1034, 990, 1011, 992, 45])).
% 2.06/1.61 tff(1036,plain,
% 2.06/1.61 ((~((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)))) | big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) | (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.06/1.61 inference(tautology,[status(thm)],[])).
% 2.06/1.61 tff(1037,plain,
% 2.06/1.61 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1036, 1035, 1011])).
% 2.06/1.61 tff(1038,assumption,(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)), introduced(assumption)).
% 2.06/1.61 tff(1039,plain,
% 2.06/1.61 (tptp_fun_W_6(Y!0) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.06/1.61 inference(symmetry,[status(thm)],[1038])).
% 2.06/1.61 tff(1040,plain,
% 2.06/1.61 (Y!0 = Z!5),
% 2.06/1.61 inference(symmetry,[status(thm)],[412])).
% 2.06/1.61 tff(1041,plain,
% 2.06/1.61 (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Z!5)),
% 2.06/1.61 inference(monotonicity,[status(thm)],[1040])).
% 2.06/1.61 tff(1042,plain,
% 2.06/1.61 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.06/1.61 inference(symmetry,[status(thm)],[1041])).
% 2.06/1.61 tff(1043,plain,
% 2.06/1.61 (tptp_fun_Y1_11(X!1) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.06/1.61 inference(transitivity,[status(thm)],[277, 1012, 1042, 1039])).
% 2.06/1.61 tff(1044,assumption,(~(tptp_fun_X1_13(Y!0, X!1) = Y!0)), introduced(assumption)).
% 2.06/1.61 tff(1045,plain,
% 2.06/1.61 (tptp_fun_X1_13(Y!0, X!1) = X!1),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[915, 1044])).
% 2.06/1.61 tff(1046,plain,
% 2.06/1.61 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.06/1.61 inference(monotonicity,[status(thm)],[1045, 1043])).
% 2.06/1.61 tff(1047,plain,
% 2.06/1.61 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.61 inference(symmetry,[status(thm)],[1046])).
% 2.06/1.61 tff(1048,plain,
% 2.06/1.61 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)))),
% 2.06/1.61 inference(monotonicity,[status(thm)],[1047])).
% 2.06/1.61 tff(1049,assumption,(~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))), introduced(assumption)).
% 2.06/1.61 tff(1050,plain,
% 2.06/1.61 (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.61 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 2.06/1.61 tff(1051,plain,
% 2.06/1.61 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[920, 1044, 906])).
% 2.06/1.61 tff(1052,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1051, 1050])).
% 2.06/1.61 tff(1053,plain,((tptp_fun_X1_13(Y!0, X!1) = Y!0) | big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))) | (~(X!1 = tptp_fun_W_6(Z!5))) | (~(Z!5 = Y!0)) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1054,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1053, 1037, 1035, 277, 991, 990, 412, 906])).
% 2.06/1.61 tff(1055,plain,((~(Z!5 = Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | big_f(X!1, Y!0) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))) | (~(tptp_fun_X1_13(X!1, Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1056,plain,
% 2.06/1.61 (~(Z!5 = Y!0)),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1055, 981, 906, 45, 862, 240, 277, 386, 979])).
% 2.06/1.61 tff(1057,plain,
% 2.06/1.61 (Z!5 = X!1),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[361, 1056])).
% 2.06/1.61 tff(1058,plain,
% 2.06/1.61 ((tptp_fun_Y1_11(Y!0) = Z!5) <=> (tptp_fun_Y1_11(Y!0) = X!1)),
% 2.06/1.61 inference(monotonicity,[status(thm)],[349])).
% 2.06/1.61 tff(1059,assumption,(tptp_fun_Y1_11(Y!0) = Z!5), introduced(assumption)).
% 2.06/1.61 tff(1060,plain,
% 2.06/1.61 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.06/1.61 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 2.06/1.61 tff(1061,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[931, 1060])).
% 2.06/1.61 tff(1062,plain,((~(tptp_fun_Y1_11(Y!0) = Z!5)) | (tptp_fun_Y1_11(Y!0) = X!1) | (~(Z!5 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1063,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1062, 1057, 739, 931])).
% 2.06/1.61 tff(1064,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (tptp_fun_Y1_11(Y!0) = X!1) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | big_f(X!1, Y!0) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X1_13(X!1, Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1065,plain,
% 2.06/1.61 (![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1064, 978, 341, 906, 45, 862, 240, 277, 931])).
% 2.06/1.61 tff(1066,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[629, 1065, 957])).
% 2.06/1.61 tff(1067,plain,((tptp_fun_Y1_11(Y!0) = X!1) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | big_f(X!1, Y!0) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1068,plain,
% 2.06/1.61 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1067, 930, 880, 45, 858, 106, 875, 874])).
% 2.06/1.61 tff(1069,plain,
% 2.06/1.61 (tptp_fun_Y_4(Y!0, Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.06/1.61 inference(transitivity,[status(thm)],[96, 599])).
% 2.06/1.61 tff(1070,plain,
% 2.06/1.61 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.61 inference(monotonicity,[status(thm)],[30, 1069])).
% 2.06/1.61 tff(1071,plain,
% 2.06/1.61 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.61 inference(symmetry,[status(thm)],[1070])).
% 2.06/1.61 tff(1072,plain,
% 2.06/1.61 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)))),
% 2.06/1.61 inference(monotonicity,[status(thm)],[1071])).
% 2.06/1.61 tff(1073,plain,
% 2.06/1.61 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.61 inference(modus_ponens,[status(thm)],[41, 1072])).
% 2.06/1.61 tff(1074,assumption,((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)), introduced(assumption)).
% 2.06/1.61 tff(1075,plain,
% 2.06/1.61 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[856, 48, 1074])).
% 2.06/1.61 tff(1076,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1075, 1073])).
% 2.06/1.61 tff(1077,plain,((tptp_fun_Y_4(Y!0, Y!0) = Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1078,plain,
% 2.06/1.61 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1077, 1068, 48, 30, 855])).
% 2.06/1.61 tff(1079,assumption,((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1)), introduced(assumption)).
% 2.06/1.61 tff(1080,assumption,(~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))), introduced(assumption)).
% 2.06/1.61 tff(1081,assumption,(tptp_fun_Y_7(X!1, Y!0) = X!1), introduced(assumption)).
% 2.06/1.61 tff(1082,plain,
% 2.06/1.61 (tptp_fun_Y_7(X!1, Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.06/1.61 inference(transitivity,[status(thm)],[1081, 599])).
% 2.06/1.61 tff(1083,plain,
% 2.06/1.61 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.61 inference(monotonicity,[status(thm)],[1082])).
% 2.06/1.61 tff(1084,plain,
% 2.06/1.61 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.61 inference(symmetry,[status(thm)],[1083])).
% 2.06/1.61 tff(1085,plain,
% 2.06/1.61 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.61 inference(modus_ponens,[status(thm)],[135, 1084])).
% 2.06/1.61 tff(1086,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1080, 1085])).
% 2.06/1.61 tff(1087,plain,((~(tptp_fun_Y_7(X!1, Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1088,plain,
% 2.06/1.61 (~(tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1087, 1080, 135, 598])).
% 2.06/1.61 tff(1089,plain,
% 2.06/1.61 ((~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) | (tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.06/1.61 inference(tautology,[status(thm)],[])).
% 2.06/1.61 tff(1090,plain,
% 2.06/1.61 ($false),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1089, 1088, 1080, 1079])).
% 2.06/1.61 tff(1091,plain,(big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) | (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.61 tff(1092,plain,
% 2.06/1.61 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1091, 1079, 135, 598])).
% 2.06/1.61 tff(1093,plain,
% 2.06/1.61 ((~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) | (~(tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.06/1.61 inference(tautology,[status(thm)],[])).
% 2.06/1.61 tff(1094,plain,
% 2.06/1.61 (~(tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.06/1.61 inference(unit_resolution,[status(thm)],[1093, 1092, 1079])).
% 2.06/1.61 tff(1095,plain,
% 2.06/1.61 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, Y!0) = X!1) | (tptp_fun_Y_7(X!1, Y!0) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(X!1, Y!0) = X!1) | (tptp_fun_Y_7(X!1, Y!0) = Y!0))),
% 2.06/1.61 inference(rewrite,[status(thm)],[])).
% 2.06/1.61 tff(1096,plain,
% 2.06/1.61 (((tptp_fun_Y_7(X!1, Y!0) = Y!0) | (tptp_fun_Y_7(X!1, Y!0) = X!1)) <=> ((tptp_fun_Y_7(X!1, Y!0) = X!1) | (tptp_fun_Y_7(X!1, Y!0) = Y!0))),
% 2.06/1.61 inference(rewrite,[status(thm)],[])).
% 2.06/1.61 tff(1097,plain,
% 2.06/1.61 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, Y!0) = Y!0) | (tptp_fun_Y_7(X!1, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, Y!0) = X!1) | (tptp_fun_Y_7(X!1, Y!0) = Y!0)))),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1096])).
% 2.06/1.62 tff(1098,plain,
% 2.06/1.62 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, Y!0) = Y!0) | (tptp_fun_Y_7(X!1, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(X!1, Y!0) = X!1) | (tptp_fun_Y_7(X!1, Y!0) = Y!0))),
% 2.06/1.62 inference(transitivity,[status(thm)],[1097, 1095])).
% 2.06/1.62 tff(1099,plain,
% 2.06/1.62 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(X!1, Y!0) = Y!0) | (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.06/1.62 inference(quant_inst,[status(thm)],[])).
% 2.06/1.62 tff(1100,plain,
% 2.06/1.62 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(X!1, Y!0) = X!1) | (tptp_fun_Y_7(X!1, Y!0) = Y!0)),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 2.06/1.62 tff(1101,plain,
% 2.06/1.62 ((tptp_fun_Y_7(X!1, Y!0) = X!1) | (tptp_fun_Y_7(X!1, Y!0) = Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1100, 12])).
% 2.06/1.62 tff(1102,plain,
% 2.06/1.62 (tptp_fun_Y_7(X!1, Y!0) = Y!0),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1101, 1094])).
% 2.06/1.62 tff(1103,plain,
% 2.06/1.62 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.62 inference(monotonicity,[status(thm)],[31, 1102])).
% 2.06/1.62 tff(1104,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.62 inference(symmetry,[status(thm)],[1103])).
% 2.06/1.62 tff(1105,plain,
% 2.06/1.62 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)))),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1104])).
% 2.06/1.62 tff(1106,plain,
% 2.06/1.62 (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[35, 1105])).
% 2.06/1.62 tff(1107,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1092, 1106])).
% 2.06/1.62 tff(1108,plain,((~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1109,plain,
% 2.06/1.62 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1108, 1078, 30, 35, 1068])).
% 2.06/1.62 tff(1110,plain,
% 2.06/1.62 ((~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))) | ((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.06/1.62 inference(quant_inst,[status(thm)],[])).
% 2.06/1.62 tff(1111,plain,
% 2.06/1.62 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1110, 1109])).
% 2.06/1.62 tff(1112,plain,
% 2.06/1.62 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[910, 875, 858, 106, 880])).
% 2.06/1.62 tff(1113,plain,
% 2.06/1.62 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1045, 637])).
% 2.06/1.62 tff(1114,plain,
% 2.06/1.62 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.62 inference(symmetry,[status(thm)],[1113])).
% 2.06/1.62 tff(1115,plain,
% 2.06/1.62 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)))),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1114])).
% 2.06/1.62 tff(1116,plain,
% 2.06/1.62 (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[42, 1115])).
% 2.06/1.62 tff(1117,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1051, 1116])).
% 2.06/1.62 tff(1118,plain,((tptp_fun_X1_13(Y!0, X!1) = Y!0) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1119,plain,
% 2.06/1.62 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1118, 1068, 875, 1112, 880])).
% 2.06/1.62 tff(1120,plain,
% 2.06/1.62 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[627, 1119, 45, 1068])).
% 2.06/1.62 tff(1121,plain,
% 2.06/1.62 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[629, 1120])).
% 2.06/1.62 tff(1122,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[743, 1121, 1111, 930, 1068])).
% 2.06/1.62 tff(1123,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y_4(Y!0, Y!0) = Y!0) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1124,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1123, 48, 30, 45, 47])).
% 2.06/1.62 tff(1125,plain,
% 2.06/1.62 (tptp_fun_Y_4(Y!0, Y!0) = Y!0),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1077, 1074, 598, 30, 41])).
% 2.06/1.62 tff(1126,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1125])).
% 2.06/1.62 tff(1127,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.62 inference(symmetry,[status(thm)],[1126])).
% 2.06/1.62 tff(1128,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[692, 1127])).
% 2.06/1.62 tff(1129,plain,
% 2.06/1.62 ((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))) | (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) | (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.06/1.62 inference(tautology,[status(thm)],[])).
% 2.06/1.62 tff(1130,plain,
% 2.06/1.62 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1129, 1125, 1074])).
% 2.06/1.62 tff(1131,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1130, 1128])).
% 2.06/1.62 tff(1132,plain,((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1133,plain,
% 2.06/1.62 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1132, 41, 1074, 30, 692])).
% 2.06/1.62 tff(1134,plain,
% 2.06/1.62 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[39, 1133])).
% 2.06/1.62 tff(1135,plain,
% 2.06/1.62 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.62 inference(monotonicity,[status(thm)],[31, 1134])).
% 2.06/1.62 tff(1136,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(symmetry,[status(thm)],[1135])).
% 2.06/1.62 tff(1137,plain,
% 2.06/1.62 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[692, 1136])).
% 2.06/1.62 tff(1138,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[41, 1137])).
% 2.06/1.62 tff(1139,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1140,plain,
% 2.06/1.62 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1139, 1124, 30, 855])).
% 2.06/1.62 tff(1141,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.62 inference(monotonicity,[status(thm)],[684])).
% 2.06/1.62 tff(1142,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.06/1.62 inference(symmetry,[status(thm)],[1141])).
% 2.06/1.62 tff(1143,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[1124, 1142])).
% 2.06/1.62 tff(1144,assumption,(big_f(tptp_fun_X_2(X!1), Y!0)), introduced(assumption)).
% 2.06/1.62 tff(1145,assumption,(![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))), introduced(assumption)).
% 2.06/1.62 tff(1146,plain,
% 2.06/1.62 ((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | (big_f(tptp_fun_X_2(X!1), Y!0) <=> (Y!0 = tptp_fun_W_3(X!1)))),
% 2.06/1.62 inference(quant_inst,[status(thm)],[])).
% 2.06/1.62 tff(1147,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(X!1), Y!0) <=> (Y!0 = tptp_fun_W_3(X!1))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1146, 1145])).
% 2.06/1.62 tff(1148,plain,
% 2.06/1.62 ((~(big_f(tptp_fun_X_2(X!1), Y!0) <=> (Y!0 = tptp_fun_W_3(X!1)))) | (~big_f(tptp_fun_X_2(X!1), Y!0)) | (Y!0 = tptp_fun_W_3(X!1))),
% 2.06/1.62 inference(tautology,[status(thm)],[])).
% 2.06/1.62 tff(1149,plain,
% 2.06/1.62 (Y!0 = tptp_fun_W_3(X!1)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1148, 1147, 1144])).
% 2.06/1.62 tff(1150,plain,
% 2.06/1.62 (tptp_fun_W_3(X!1) = Y!0),
% 2.06/1.62 inference(symmetry,[status(thm)],[1149])).
% 2.06/1.62 tff(1151,plain,
% 2.06/1.62 ((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | (big_f(tptp_fun_X_2(X!1), X!1) <=> (X!1 = tptp_fun_W_3(X!1)))),
% 2.06/1.62 inference(quant_inst,[status(thm)],[])).
% 2.06/1.62 tff(1152,plain,
% 2.06/1.62 (big_f(tptp_fun_X_2(X!1), X!1) <=> (X!1 = tptp_fun_W_3(X!1))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1151, 1145])).
% 2.06/1.62 tff(1153,plain,
% 2.06/1.62 ((~(big_f(tptp_fun_X_2(X!1), X!1) <=> (X!1 = tptp_fun_W_3(X!1)))) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (X!1 = tptp_fun_W_3(X!1))),
% 2.06/1.62 inference(tautology,[status(thm)],[])).
% 2.06/1.62 tff(1154,plain,
% 2.06/1.62 (X!1 = tptp_fun_W_3(X!1)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1153, 1152, 862])).
% 2.06/1.62 tff(1155,plain,
% 2.06/1.62 (X!1 = Y!0),
% 2.06/1.62 inference(transitivity,[status(thm)],[1154, 1150])).
% 2.06/1.62 tff(1156,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[741, 1155])).
% 2.06/1.62 tff(1157,plain,((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~big_f(tptp_fun_X_2(X!1), Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1158,plain,
% 2.06/1.62 (~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1157, 858, 1143])).
% 2.06/1.62 tff(1159,plain,
% 2.06/1.62 (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[224, 1158, 47])).
% 2.06/1.62 tff(1160,plain,
% 2.06/1.62 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[222, 1159])).
% 2.06/1.62 tff(1161,plain,
% 2.06/1.62 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[220, 1160])).
% 2.06/1.62 tff(1162,plain,
% 2.06/1.62 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[82, 1161])).
% 2.06/1.62 tff(1163,plain,
% 2.06/1.62 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[84, 1162])).
% 2.06/1.62 tff(1164,plain,
% 2.06/1.62 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[561, 1163])).
% 2.06/1.62 tff(1165,plain,
% 2.06/1.62 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[86, 1163])).
% 2.06/1.62 tff(1166,plain,
% 2.06/1.62 (~((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[140, 109, 45, 135])).
% 2.06/1.62 tff(1167,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[115, 1166, 114])).
% 2.06/1.62 tff(1168,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(X!1, Y!0) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1169,plain,
% 2.06/1.62 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1168, 1140, 45, 1165])).
% 2.06/1.62 tff(1170,plain,
% 2.06/1.62 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[563, 1169, 1164])).
% 2.06/1.62 tff(1171,plain,
% 2.06/1.62 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[88, 1162])).
% 2.06/1.62 tff(1172,plain,
% 2.06/1.62 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[90, 1171])).
% 2.06/1.62 tff(1173,plain,
% 2.06/1.62 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[267, 109, 30, 47, 144, 45])).
% 2.06/1.62 tff(1174,plain,
% 2.06/1.62 (~((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[140, 109, 45, 1173])).
% 2.06/1.62 tff(1175,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[115, 114, 1174])).
% 2.06/1.62 tff(1176,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1177,plain,
% 2.06/1.62 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1176, 144, 45, 30, 47, 1165])).
% 2.06/1.62 tff(1178,plain,
% 2.06/1.62 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[39, 1177])).
% 2.06/1.62 tff(1179,plain,
% 2.06/1.62 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1077, 1178, 48, 30, 855])).
% 2.06/1.62 tff(1180,plain,
% 2.06/1.62 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[563, 1177, 1164])).
% 2.06/1.62 tff(1181,plain,
% 2.06/1.62 ((~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0)))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (Y!0 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.62 inference(tautology,[status(thm)],[])).
% 2.06/1.62 tff(1182,plain,
% 2.06/1.62 (Y!0 = tptp_fun_Z1_12(Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1181, 584, 135])).
% 2.06/1.62 tff(1183,plain,
% 2.06/1.62 (tptp_fun_Z1_12(Y!0) = Y!0),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[1182, 581])).
% 2.06/1.62 tff(1184,plain,
% 2.06/1.62 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[751, 577, 622])).
% 2.06/1.62 tff(1185,assumption,(tptp_fun_Z1_12(Y!0) = Y!0), introduced(assumption)).
% 2.06/1.62 tff(1186,plain,
% 2.06/1.62 ((X!1 = tptp_fun_Z1_12(Y!0)) <=> (X!1 = Y!0)),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1185])).
% 2.06/1.62 tff(1187,plain,
% 2.06/1.62 ((X!1 = Y!0) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.62 inference(symmetry,[status(thm)],[1186])).
% 2.06/1.62 tff(1188,plain,
% 2.06/1.62 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1187])).
% 2.06/1.62 tff(1189,plain,
% 2.06/1.62 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.62 inference(modus_ponens,[status(thm)],[741, 1188])).
% 2.06/1.62 tff(1190,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[830, 1189])).
% 2.06/1.62 tff(1191,plain,((~(tptp_fun_Z1_12(Y!0) = Y!0)) | (~(X!1 = tptp_fun_Z1_12(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1192,plain,
% 2.06/1.62 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1191, 1184])).
% 2.06/1.62 tff(1193,plain,
% 2.06/1.62 ($false),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1192, 1183])).
% 2.06/1.62 tff(1194,plain,((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.62 tff(1195,plain,
% 2.06/1.62 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.62 inference(unit_resolution,[status(thm)],[1194, 1180, 1179])).
% 2.06/1.62 tff(1196,plain,
% 2.06/1.62 ((Y!0 = tptp_fun_W_6(X!1)) <=> (tptp_fun_W_6(X!1) = Y!0)),
% 2.06/1.62 inference(symmetry,[status(thm)],[325])).
% 2.06/1.62 tff(1197,plain,
% 2.06/1.62 ((~(Y!0 = tptp_fun_W_6(X!1))) <=> (~(tptp_fun_W_6(X!1) = Y!0))),
% 2.06/1.62 inference(monotonicity,[status(thm)],[1196])).
% 2.06/1.62 tff(1198,plain,
% 2.06/1.62 (~(tptp_fun_W_6(X!1) = Y!0)),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[324, 1197])).
% 2.06/1.63 tff(1199,plain,
% 2.06/1.63 (tptp_fun_W_6(X!1) = X!1),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[335, 1198])).
% 2.06/1.63 tff(1200,plain,
% 2.06/1.63 (tptp_fun_W_6(X!1) = tptp_fun_Y1_11(Y!0)),
% 2.06/1.63 inference(transitivity,[status(thm)],[1199, 599])).
% 2.06/1.63 tff(1201,plain,
% 2.06/1.63 (big_f(X!1, tptp_fun_W_6(X!1)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1200])).
% 2.06/1.63 tff(1202,plain,
% 2.06/1.63 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_W_6(X!1))),
% 2.06/1.63 inference(symmetry,[status(thm)],[1201])).
% 2.06/1.63 tff(1203,plain,
% 2.06/1.63 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(X!1, tptp_fun_W_6(X!1)))),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1202])).
% 2.06/1.63 tff(1204,plain,
% 2.06/1.63 (~big_f(X!1, tptp_fun_W_6(X!1))),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[42, 1203])).
% 2.06/1.63 tff(1205,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[308, 1204])).
% 2.06/1.63 tff(1206,plain,((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1207,plain,
% 2.06/1.63 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1206, 1195, 1178, 45])).
% 2.06/1.63 tff(1208,plain,
% 2.06/1.63 (big_f(Z!5, Y!0)),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[692, 391])).
% 2.06/1.63 tff(1209,plain,
% 2.06/1.63 ((~(big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5)))) | (~big_f(Z!5, Y!0)) | (Y!0 = tptp_fun_W_6(Z!5))),
% 2.06/1.63 inference(tautology,[status(thm)],[])).
% 2.06/1.63 tff(1210,plain,
% 2.06/1.63 (Y!0 = tptp_fun_W_6(Z!5)),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1209, 1208, 388])).
% 2.06/1.63 tff(1211,plain,
% 2.06/1.63 (tptp_fun_W_6(Z!5) = Y!0),
% 2.06/1.63 inference(symmetry,[status(thm)],[1210])).
% 2.06/1.63 tff(1212,plain,
% 2.06/1.63 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[983, 386])).
% 2.06/1.63 tff(1213,plain,
% 2.06/1.63 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.63 inference(monotonicity,[status(thm)],[362, 599])).
% 2.06/1.63 tff(1214,plain,
% 2.06/1.63 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, X!1)),
% 2.06/1.63 inference(symmetry,[status(thm)],[1213])).
% 2.06/1.63 tff(1215,plain,
% 2.06/1.63 (big_f(Z!5, X!1)),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[135, 1214])).
% 2.06/1.63 tff(1216,plain,
% 2.06/1.63 (X!1 = tptp_fun_W_6(Z!5)),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[989, 1215, 1212])).
% 2.06/1.63 tff(1217,plain,
% 2.06/1.63 (X!1 = Y!0),
% 2.06/1.63 inference(transitivity,[status(thm)],[1216, 1211])).
% 2.06/1.63 tff(1218,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[741, 1217])).
% 2.06/1.63 tff(1219,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1220,plain,
% 2.06/1.63 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1219, 1207, 1124, 1178, 30, 1179])).
% 2.06/1.63 tff(1221,plain,
% 2.06/1.63 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[191, 1171])).
% 2.06/1.63 tff(1222,plain,
% 2.06/1.63 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[786, 144, 45, 1221])).
% 2.06/1.63 tff(1223,plain,
% 2.06/1.63 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[788, 1222])).
% 2.06/1.63 tff(1224,assumption,((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0)), introduced(assumption)).
% 2.06/1.63 tff(1225,assumption,(tptp_fun_X1_10(Y!0, X!1) = Y!0), introduced(assumption)).
% 2.06/1.63 tff(1226,plain,
% 2.06/1.63 (Y!0 = tptp_fun_X1_10(Y!0, X!1)),
% 2.06/1.63 inference(symmetry,[status(thm)],[1225])).
% 2.06/1.63 tff(1227,plain,
% 2.06/1.63 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1226, 598])).
% 2.06/1.63 tff(1228,plain,
% 2.06/1.63 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.63 inference(symmetry,[status(thm)],[1227])).
% 2.06/1.63 tff(1229,plain,
% 2.06/1.63 ((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1228])).
% 2.06/1.63 tff(1230,plain,
% 2.06/1.63 ((~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))) | (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) | (~(tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.06/1.63 inference(tautology,[status(thm)],[])).
% 2.06/1.63 tff(1231,plain,
% 2.06/1.63 (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1230, 1225, 1224])).
% 2.06/1.63 tff(1232,plain,
% 2.06/1.63 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[1231, 1229])).
% 2.06/1.63 tff(1233,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[135, 1232])).
% 2.06/1.63 tff(1234,plain,((~(tptp_fun_X1_10(Y!0, X!1) = Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1235,plain,
% 2.06/1.63 (~(tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1234, 1224, 598, 135])).
% 2.06/1.63 tff(1236,assumption,(~(tptp_fun_X1_10(Y!0, X!1) = Y!0)), introduced(assumption)).
% 2.06/1.63 tff(1237,plain,
% 2.06/1.63 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, X!1) = X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(Y!0, X!1) = X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.06/1.63 inference(rewrite,[status(thm)],[])).
% 2.06/1.63 tff(1238,plain,
% 2.06/1.63 (((tptp_fun_X1_10(Y!0, X!1) = Y!0) | (tptp_fun_X1_10(Y!0, X!1) = X!1)) <=> ((tptp_fun_X1_10(Y!0, X!1) = X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.06/1.63 inference(rewrite,[status(thm)],[])).
% 2.06/1.63 tff(1239,plain,
% 2.06/1.63 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, X!1) = Y!0) | (tptp_fun_X1_10(Y!0, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, X!1) = X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0)))),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1238])).
% 2.06/1.63 tff(1240,plain,
% 2.06/1.63 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, X!1) = Y!0) | (tptp_fun_X1_10(Y!0, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(Y!0, X!1) = X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.06/1.63 inference(transitivity,[status(thm)],[1239, 1237])).
% 2.06/1.63 tff(1241,plain,
% 2.06/1.63 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, X!1) = Y!0) | (tptp_fun_X1_10(Y!0, X!1) = X!1))),
% 2.06/1.63 inference(quant_inst,[status(thm)],[])).
% 2.06/1.63 tff(1242,plain,
% 2.06/1.63 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(Y!0, X!1) = X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 2.06/1.63 tff(1243,plain,
% 2.06/1.63 ((tptp_fun_X1_10(Y!0, X!1) = X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1242, 12])).
% 2.06/1.63 tff(1244,plain,
% 2.06/1.63 (tptp_fun_X1_10(Y!0, X!1) = X!1),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1243, 1236])).
% 2.06/1.63 tff(1245,plain,
% 2.06/1.63 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1244, 599])).
% 2.06/1.63 tff(1246,plain,
% 2.06/1.63 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.06/1.63 inference(symmetry,[status(thm)],[1245])).
% 2.06/1.63 tff(1247,plain,
% 2.06/1.63 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1))),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1246])).
% 2.06/1.63 tff(1248,plain,
% 2.06/1.63 (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[42, 1247])).
% 2.06/1.63 tff(1249,plain,
% 2.06/1.63 ((~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))) | big_f(tptp_fun_X1_10(Y!0, X!1), X!1) | (tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.06/1.63 inference(tautology,[status(thm)],[])).
% 2.06/1.63 tff(1250,plain,
% 2.06/1.63 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1249, 1236, 1224])).
% 2.06/1.63 tff(1251,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1250, 1248])).
% 2.06/1.63 tff(1252,plain,((tptp_fun_X1_10(Y!0, X!1) = Y!0) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1253,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1252, 1235, 1224, 598, 42])).
% 2.06/1.63 tff(1254,plain,((~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1255,plain,
% 2.06/1.63 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1254, 1195, 1178, 1179])).
% 2.06/1.63 tff(1256,plain,
% 2.06/1.63 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))) | ((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.06/1.63 inference(quant_inst,[status(thm)],[])).
% 2.06/1.63 tff(1257,plain,
% 2.06/1.63 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1256, 1255])).
% 2.06/1.63 tff(1258,plain,
% 2.06/1.63 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[576, 1180])).
% 2.06/1.63 tff(1259,plain,
% 2.06/1.63 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[578, 1258, 1195])).
% 2.06/1.63 tff(1260,assumption,(tptp_fun_Z1_12(Y!0) = X!1), introduced(assumption)).
% 2.06/1.63 tff(1261,plain,
% 2.06/1.63 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[1260, 572])).
% 2.06/1.63 tff(1262,assumption,(~(X!1 = tptp_fun_Z1_12(Y!0))), introduced(assumption)).
% 2.06/1.63 tff(1263,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1262, 1261])).
% 2.06/1.63 tff(1264,plain,((~(tptp_fun_Z1_12(Y!0) = X!1)) | (X!1 = tptp_fun_Z1_12(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1265,plain,
% 2.06/1.63 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1264, 1259])).
% 2.06/1.63 tff(1266,assumption,(~(tptp_fun_Z1_12(Y!0) = X!1)), introduced(assumption)).
% 2.06/1.63 tff(1267,assumption,(~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))), introduced(assumption)).
% 2.06/1.63 tff(1268,assumption,(![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))), introduced(assumption)).
% 2.06/1.63 tff(1269,plain,
% 2.06/1.63 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1)))))))),
% 2.06/1.63 inference(quant_inst,[status(thm)],[])).
% 2.06/1.63 tff(1270,plain,
% 2.06/1.63 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1269, 1268])).
% 2.06/1.63 tff(1271,plain,
% 2.06/1.63 (((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1)))))) | ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))),
% 2.06/1.63 inference(tautology,[status(thm)],[])).
% 2.06/1.63 tff(1272,plain,
% 2.06/1.63 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1271, 1270])).
% 2.06/1.63 tff(1273,plain,
% 2.06/1.63 ((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.06/1.63 inference(tautology,[status(thm)],[])).
% 2.06/1.63 tff(1274,plain,
% 2.06/1.63 (X!1 = W1!8),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1273, 1272, 1267])).
% 2.06/1.63 tff(1275,plain,
% 2.06/1.63 (W1!8 = X!1),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[28, 1274])).
% 2.06/1.63 tff(1276,plain,
% 2.06/1.63 (tptp_fun_Z1_12(Y!0) = Y!0),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[594, 1266])).
% 2.06/1.63 tff(1277,assumption,(~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))), introduced(assumption)).
% 2.06/1.63 tff(1278,plain,
% 2.06/1.63 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[790, 1268])).
% 2.06/1.63 tff(1279,plain,
% 2.06/1.63 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[792, 1278])).
% 2.06/1.63 tff(1280,plain,
% 2.06/1.63 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[794, 1279, 1277])).
% 2.06/1.63 tff(1281,plain,
% 2.06/1.63 (W1!8 = Y!0),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[803, 1280, 796])).
% 2.06/1.63 tff(1282,plain,
% 2.06/1.63 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.06/1.63 inference(monotonicity,[status(thm)],[486])).
% 2.06/1.63 tff(1283,plain,
% 2.06/1.63 ((tptp_fun_Z1_12(Y!0) = Y!0) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.06/1.63 inference(symmetry,[status(thm)],[1282])).
% 2.06/1.63 tff(1284,plain,
% 2.06/1.63 (tptp_fun_Z1_12(Y!0) = W1!8),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[1185, 1283])).
% 2.06/1.63 tff(1285,assumption,(~(tptp_fun_Z1_12(Y!0) = W1!8)), introduced(assumption)).
% 2.06/1.63 tff(1286,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1285, 1284])).
% 2.06/1.63 tff(1287,plain,((~(tptp_fun_Z1_12(Y!0) = Y!0)) | (tptp_fun_Z1_12(Y!0) = W1!8) | (~(W1!8 = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1288,plain,
% 2.06/1.63 (tptp_fun_Z1_12(Y!0) = W1!8),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1287, 1281, 1276])).
% 2.06/1.63 tff(1289,assumption,(W1!8 = X!1), introduced(assumption)).
% 2.06/1.63 tff(1290,plain,
% 2.06/1.63 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (tptp_fun_Z1_12(Y!0) = X!1)),
% 2.06/1.63 inference(monotonicity,[status(thm)],[1289])).
% 2.06/1.63 tff(1291,plain,
% 2.06/1.63 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.63 inference(transitivity,[status(thm)],[1290, 572])).
% 2.06/1.63 tff(1292,plain,
% 2.06/1.63 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (tptp_fun_Z1_12(Y!0) = X!1)),
% 2.06/1.63 inference(transitivity,[status(thm)],[1291, 573])).
% 2.06/1.63 tff(1293,assumption,(tptp_fun_Z1_12(Y!0) = W1!8), introduced(assumption)).
% 2.06/1.63 tff(1294,plain,
% 2.06/1.63 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.06/1.63 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 2.06/1.63 tff(1295,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1266, 1294])).
% 2.06/1.63 tff(1296,plain,((~(tptp_fun_Z1_12(Y!0) = W1!8)) | (tptp_fun_Z1_12(Y!0) = X!1) | (~(W1!8 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1297,plain,
% 2.06/1.63 ($false),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1296, 1288, 1275, 1266])).
% 2.06/1.63 tff(1298,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (tptp_fun_Z1_12(Y!0) = X!1) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.63 tff(1299,plain,
% 2.06/1.63 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.06/1.63 inference(unit_resolution,[status(thm)],[1298, 1265, 154, 1257, 1223])).
% 2.06/1.63 tff(1300,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[462, 1299, 1220])).
% 2.06/1.64 tff(1301,plain,((tptp_fun_Y1_11(X!1) = X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | (tptp_fun_Y_4(Y!0, Y!0) = Y!0) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1302,plain,
% 2.06/1.64 (tptp_fun_Y1_11(X!1) = X!1),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1301, 48, 45, 30, 47])).
% 2.06/1.64 tff(1303,plain,
% 2.06/1.64 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[269, 1302, 1172])).
% 2.06/1.64 tff(1304,plain,
% 2.06/1.64 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[879, 1303])).
% 2.06/1.64 tff(1305,plain,
% 2.06/1.64 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[910, 1304, 858, 106, 1302])).
% 2.06/1.64 tff(1306,plain,
% 2.06/1.64 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[39, 1169])).
% 2.06/1.64 tff(1307,plain,
% 2.06/1.64 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1118, 1306, 1302, 1305, 1304])).
% 2.06/1.64 tff(1308,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1194, 1307, 1170, 1140])).
% 2.06/1.64 tff(1309,plain,((tptp_fun_Y_4(Y!0, Y!0) = Y!0) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1310,plain,
% 2.06/1.64 (tptp_fun_Y_4(Y!0, Y!0) = Y!0),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1309, 47, 30, 45])).
% 2.06/1.64 tff(1311,plain,
% 2.06/1.64 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[41, 111])).
% 2.06/1.64 tff(1312,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[690, 144, 30, 47, 45])).
% 2.06/1.64 tff(1313,assumption,(~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)), introduced(assumption)).
% 2.06/1.64 tff(1314,plain,
% 2.06/1.64 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[781, 1313])).
% 2.06/1.64 tff(1315,plain,
% 2.06/1.64 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1314, 796])).
% 2.06/1.64 tff(1316,plain,
% 2.06/1.64 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.64 inference(symmetry,[status(thm)],[1315])).
% 2.06/1.64 tff(1317,plain,
% 2.06/1.64 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)))),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1316])).
% 2.06/1.64 tff(1318,plain,
% 2.06/1.64 (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[45, 1317])).
% 2.06/1.64 tff(1319,plain,
% 2.06/1.64 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[764, 1313, 761])).
% 2.06/1.64 tff(1320,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1319, 1318])).
% 2.06/1.64 tff(1321,plain,((tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0) | big_f(X!1, Y!0) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1322,plain,
% 2.06/1.64 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1321, 761, 796, 45])).
% 2.06/1.64 tff(1323,plain,
% 2.06/1.64 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(Y!0)),
% 2.06/1.64 inference(transitivity,[status(thm)],[1322, 31])).
% 2.06/1.64 tff(1324,plain,
% 2.06/1.64 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1323, 796])).
% 2.06/1.64 tff(1325,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.64 inference(symmetry,[status(thm)],[1324])).
% 2.06/1.64 tff(1326,plain,
% 2.06/1.64 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[692, 1325])).
% 2.06/1.64 tff(1327,plain,
% 2.06/1.64 (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[776, 1322, 761])).
% 2.06/1.64 tff(1328,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1327, 1326])).
% 2.06/1.64 tff(1329,plain,((~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1330,plain,
% 2.06/1.64 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1329, 154, 45, 30, 1312])).
% 2.06/1.64 tff(1331,plain,
% 2.06/1.64 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[788, 1330])).
% 2.06/1.64 tff(1332,assumption,(tptp_fun_Y_4(Y!0, Y!0) = Y!0), introduced(assumption)).
% 2.06/1.64 tff(1333,plain,
% 2.06/1.64 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1129, 1074, 1332])).
% 2.06/1.64 tff(1334,plain,
% 2.06/1.64 (tptp_fun_Y_4(Y!0, Y!0) = Y!0),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[856, 107, 1074])).
% 2.06/1.64 tff(1335,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1334])).
% 2.06/1.64 tff(1336,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.64 inference(symmetry,[status(thm)],[1335])).
% 2.06/1.64 tff(1337,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[692, 1336])).
% 2.06/1.64 tff(1338,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[107, 1337])).
% 2.06/1.64 tff(1339,plain,(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1340,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1339, 1333, 1074, 692])).
% 2.06/1.64 tff(1341,plain,((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1342,plain,
% 2.06/1.64 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1341, 1312, 1310])).
% 2.06/1.64 tff(1343,plain,
% 2.06/1.64 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[50, 1342])).
% 2.06/1.64 tff(1344,plain,
% 2.06/1.64 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[52, 1343, 30])).
% 2.06/1.64 tff(1345,plain,
% 2.06/1.64 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[54, 1344])).
% 2.06/1.64 tff(1346,plain,
% 2.06/1.64 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[56, 1345])).
% 2.06/1.64 tff(1347,plain,
% 2.06/1.64 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[82, 1346])).
% 2.06/1.64 tff(1348,plain,
% 2.06/1.64 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[84, 1347])).
% 2.06/1.64 tff(1349,plain,
% 2.06/1.64 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[86, 1348])).
% 2.06/1.64 tff(1350,plain,
% 2.06/1.64 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1176, 1349, 45, 30, 47, 144])).
% 2.06/1.64 tff(1351,plain,
% 2.06/1.64 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[39, 1350])).
% 2.06/1.64 tff(1352,plain,
% 2.06/1.64 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.64 inference(monotonicity,[status(thm)],[527, 1351])).
% 2.06/1.64 tff(1353,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(symmetry,[status(thm)],[1352])).
% 2.06/1.64 tff(1354,plain,
% 2.06/1.64 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[267, 41, 30, 47, 144, 45])).
% 2.06/1.64 tff(1355,plain,
% 2.06/1.64 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1139, 41, 30, 1312])).
% 2.06/1.64 tff(1356,plain,
% 2.06/1.64 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[50, 1355])).
% 2.06/1.64 tff(1357,plain,
% 2.06/1.64 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[52, 1356, 30])).
% 2.06/1.64 tff(1358,plain,
% 2.06/1.64 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[54, 1357])).
% 2.06/1.64 tff(1359,plain,
% 2.06/1.64 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[56, 1358])).
% 2.06/1.64 tff(1360,plain,
% 2.06/1.64 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[82, 1359])).
% 2.06/1.64 tff(1361,plain,
% 2.06/1.64 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[84, 1360])).
% 2.06/1.64 tff(1362,plain,
% 2.06/1.64 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[561, 1361])).
% 2.06/1.64 tff(1363,plain,
% 2.06/1.64 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[563, 1362, 1354])).
% 2.06/1.64 tff(1364,plain,
% 2.06/1.64 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[576, 1363])).
% 2.06/1.64 tff(1365,plain,
% 2.06/1.64 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[596, 1363, 41])).
% 2.06/1.64 tff(1366,plain,
% 2.06/1.64 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[751, 1365, 1364])).
% 2.06/1.64 tff(1367,plain,
% 2.06/1.64 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[39, 1354])).
% 2.06/1.64 tff(1368,plain,
% 2.06/1.64 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[718, 1367, 1312, 30, 41])).
% 2.06/1.64 tff(1369,plain,
% 2.06/1.64 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[720, 1368])).
% 2.06/1.64 tff(1370,plain,
% 2.06/1.64 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[627, 1365, 45, 1367])).
% 2.06/1.64 tff(1371,plain,
% 2.06/1.64 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[629, 1370])).
% 2.06/1.64 tff(1372,plain,
% 2.06/1.64 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[743, 1371, 1369, 1367])).
% 2.06/1.64 tff(1373,plain,
% 2.06/1.64 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[462, 1372])).
% 2.06/1.64 tff(1374,plain,
% 2.06/1.64 (~((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[746, 1373])).
% 2.06/1.64 tff(1375,plain,
% 2.06/1.64 ((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[748, 1374])).
% 2.06/1.64 tff(1376,plain,
% 2.06/1.64 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1191, 1366])).
% 2.06/1.64 tff(1377,plain,
% 2.06/1.64 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[594, 1376])).
% 2.06/1.64 tff(1378,plain,
% 2.06/1.64 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1377])).
% 2.06/1.64 tff(1379,plain,
% 2.06/1.64 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.06/1.64 inference(transitivity,[status(thm)],[1378, 24])).
% 2.06/1.64 tff(1380,plain,
% 2.06/1.64 ((W1!8 = X!1) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.06/1.64 inference(symmetry,[status(thm)],[1379])).
% 2.06/1.64 tff(1381,plain,
% 2.06/1.64 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[790, 1373])).
% 2.06/1.64 tff(1382,plain,
% 2.06/1.64 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[792, 1381])).
% 2.06/1.64 tff(1383,plain,
% 2.06/1.64 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[794, 1382, 1331])).
% 2.06/1.64 tff(1384,plain,
% 2.06/1.64 (W1!8 = Y!0),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[803, 1383, 154])).
% 2.06/1.64 tff(1385,plain,
% 2.06/1.64 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1384])).
% 2.06/1.64 tff(1386,plain,
% 2.06/1.64 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.06/1.64 inference(transitivity,[status(thm)],[1385, 46])).
% 2.06/1.64 tff(1387,plain,
% 2.06/1.64 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.06/1.64 inference(symmetry,[status(thm)],[1386])).
% 2.06/1.64 tff(1388,plain,
% 2.06/1.64 ((X!1 = Y!0) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.06/1.64 inference(transitivity,[status(thm)],[1387, 1380])).
% 2.06/1.64 tff(1389,plain,
% 2.06/1.64 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Z1_12(Y!0) = W1!8))),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1388])).
% 2.06/1.64 tff(1390,plain,
% 2.06/1.64 (~(tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[741, 1389])).
% 2.06/1.64 tff(1391,plain,
% 2.06/1.64 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[811, 1390, 1375])).
% 2.06/1.64 tff(1392,plain,
% 2.06/1.64 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[813, 1391])).
% 2.06/1.64 tff(1393,plain,
% 2.06/1.64 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[839, 1392, 828, 106, 1367, 1366])).
% 2.06/1.64 tff(1394,plain,
% 2.06/1.64 (X!1 = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.06/1.64 inference(symmetry,[status(thm)],[1393])).
% 2.06/1.64 tff(1395,plain,
% 2.06/1.64 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1394])).
% 2.06/1.64 tff(1396,plain,
% 2.06/1.64 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(symmetry,[status(thm)],[1395])).
% 2.06/1.64 tff(1397,plain,
% 2.06/1.64 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))) <=> (~big_f(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1396])).
% 2.06/1.64 tff(1398,plain,
% 2.06/1.64 (X!1 = tptp_fun_Y1_11(Y!0)),
% 2.06/1.64 inference(symmetry,[status(thm)],[1367])).
% 2.06/1.64 tff(1399,plain,
% 2.06/1.64 (tptp_fun_Z1_12(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.06/1.64 inference(transitivity,[status(thm)],[1377, 1398])).
% 2.06/1.64 tff(1400,plain,
% 2.06/1.64 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1399])).
% 2.06/1.64 tff(1401,plain,
% 2.06/1.64 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)))),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1400])).
% 2.06/1.64 tff(1402,plain,
% 2.06/1.64 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[849, 1393, 1392])).
% 2.06/1.64 tff(1403,plain,
% 2.06/1.64 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 2.06/1.64 tff(1404,plain,
% 2.06/1.64 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[1403, 1397])).
% 2.06/1.64 tff(1405,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1365, 1404])).
% 2.06/1.64 tff(1406,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(tptp_fun_X_2(X!1), X!1) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1407,plain,
% 2.06/1.64 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1406, 828, 45, 30, 47, 144])).
% 2.06/1.64 tff(1408,plain,
% 2.06/1.64 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.64 inference(monotonicity,[status(thm)],[273, 598])).
% 2.06/1.64 tff(1409,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(symmetry,[status(thm)],[1408])).
% 2.06/1.64 tff(1410,plain,
% 2.06/1.64 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.06/1.64 inference(monotonicity,[status(thm)],[1409])).
% 2.06/1.64 tff(1411,plain,
% 2.06/1.64 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[828, 1410])).
% 2.06/1.64 tff(1412,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[135, 1411])).
% 2.06/1.64 tff(1413,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1414,plain,
% 2.06/1.64 ($false),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1413, 1407, 828, 1351, 106])).
% 2.06/1.64 tff(1415,plain,(big_f(tptp_fun_X_2(X!1), X!1) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.64 tff(1416,plain,
% 2.06/1.64 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1415, 144, 30, 47, 45])).
% 2.06/1.64 tff(1417,plain,
% 2.06/1.64 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(modus_ponens,[status(thm)],[1416, 1353])).
% 2.06/1.64 tff(1418,plain,
% 2.06/1.64 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[561, 1348])).
% 2.06/1.64 tff(1419,plain,
% 2.06/1.64 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[563, 1350, 1418])).
% 2.06/1.64 tff(1420,plain,
% 2.06/1.64 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.06/1.64 inference(unit_resolution,[status(thm)],[1194, 1417, 1419])).
% 2.06/1.64 tff(1421,plain,
% 2.06/1.64 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1254, 1420, 1351, 1417])).
% 2.06/1.65 tff(1422,plain,
% 2.06/1.65 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1256, 1421])).
% 2.06/1.65 tff(1423,plain,
% 2.06/1.65 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[576, 1419])).
% 2.06/1.65 tff(1424,plain,
% 2.06/1.65 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[578, 1420, 1423])).
% 2.06/1.65 tff(1425,plain,
% 2.06/1.65 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1264, 1424])).
% 2.06/1.65 tff(1426,plain,
% 2.06/1.65 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1206, 1420, 1351, 45])).
% 2.06/1.65 tff(1427,plain,
% 2.06/1.65 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1219, 1426, 1312, 1351, 30, 1417])).
% 2.06/1.65 tff(1428,plain,
% 2.06/1.65 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[462, 1427])).
% 2.06/1.65 tff(1429,plain,
% 2.06/1.65 ($false),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1298, 1428, 1425, 154, 1422, 1331])).
% 2.06/1.65 tff(1430,plain,((tptp_fun_Y1_11(X!1) = X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.65 tff(1431,plain,
% 2.06/1.65 (tptp_fun_Y1_11(X!1) = X!1),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1430, 47, 45, 30])).
% 2.06/1.65 tff(1432,plain,
% 2.06/1.65 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.65 inference(symmetry,[status(thm)],[110])).
% 2.06/1.65 tff(1433,plain,
% 2.06/1.65 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.06/1.65 inference(monotonicity,[status(thm)],[1432])).
% 2.06/1.65 tff(1434,plain,
% 2.06/1.65 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.06/1.65 inference(modus_ponens,[status(thm)],[35, 1433])).
% 2.06/1.65 tff(1435,assumption,(![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))), introduced(assumption)).
% 2.06/1.65 tff(1436,plain,
% 2.06/1.65 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[220, 1435])).
% 2.06/1.65 tff(1437,plain,
% 2.06/1.65 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[222, 1436])).
% 2.06/1.65 tff(1438,plain,
% 2.06/1.65 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[224, 1437, 47])).
% 2.06/1.65 tff(1439,plain,
% 2.06/1.65 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[234, 1438])).
% 2.06/1.65 tff(1440,plain,
% 2.06/1.65 (~(tptp_fun_W_3(X!1) = Y!0)),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[247, 1439, 106, 1434, 109])).
% 2.06/1.65 tff(1441,plain,
% 2.06/1.65 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[56, 1435])).
% 2.06/1.65 tff(1442,plain,
% 2.06/1.65 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[54, 1441])).
% 2.06/1.65 tff(1443,plain,
% 2.06/1.65 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[52, 1442, 30])).
% 2.06/1.65 tff(1444,plain,
% 2.06/1.65 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[198, 1443])).
% 2.06/1.65 tff(1445,plain,
% 2.06/1.65 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[675, 1444, 35])).
% 2.06/1.65 tff(1446,plain,
% 2.06/1.65 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[236, 1444, 1445])).
% 2.06/1.65 tff(1447,plain,
% 2.06/1.65 (~(tptp_fun_W_3(X!1) = X!1)),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[265, 1446, 30, 106, 1439, 1445])).
% 2.06/1.65 tff(1448,plain,
% 2.06/1.65 ($false),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[252, 1447, 1440])).
% 2.06/1.65 tff(1449,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.65 tff(1450,plain,
% 2.06/1.65 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1449, 1311, 30, 109, 47])).
% 2.06/1.65 tff(1451,plain,
% 2.06/1.65 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[82, 1450])).
% 2.06/1.65 tff(1452,plain,
% 2.06/1.65 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[88, 1451])).
% 2.06/1.65 tff(1453,plain,
% 2.06/1.65 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[90, 1452])).
% 2.06/1.65 tff(1454,plain,
% 2.06/1.65 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[269, 1453, 1431])).
% 2.06/1.65 tff(1455,plain,
% 2.06/1.65 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[271, 1454])).
% 2.06/1.65 tff(1456,plain,
% 2.06/1.65 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[481, 1268])).
% 2.06/1.65 tff(1457,plain,
% 2.06/1.65 (~(W1!8 = Y!0)),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[524, 1456, 30, 45, 35])).
% 2.06/1.65 tff(1458,plain,
% 2.06/1.65 (W1!8 = X!1),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[19, 1457])).
% 2.06/1.65 tff(1459,plain,
% 2.06/1.65 (((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))))) | ((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))),
% 2.06/1.65 inference(tautology,[status(thm)],[])).
% 2.06/1.65 tff(1460,plain,
% 2.06/1.65 ((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1459, 1278])).
% 2.06/1.65 tff(1461,plain,
% 2.06/1.65 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (X!1 = W1!8)),
% 2.06/1.65 inference(monotonicity,[status(thm)],[277])).
% 2.06/1.65 tff(1462,plain,
% 2.06/1.65 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (W1!8 = X!1)),
% 2.06/1.65 inference(transitivity,[status(thm)],[1461, 24])).
% 2.06/1.65 tff(1463,plain,
% 2.06/1.65 ((W1!8 = X!1) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.06/1.65 inference(symmetry,[status(thm)],[1462])).
% 2.06/1.65 tff(1464,plain,
% 2.06/1.65 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.06/1.65 inference(modus_ponens,[status(thm)],[1458, 1463])).
% 2.06/1.65 tff(1465,plain,
% 2.06/1.65 ((~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))) | (~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.06/1.65 inference(tautology,[status(thm)],[])).
% 2.06/1.65 tff(1466,plain,
% 2.06/1.65 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1465, 1464, 1460])).
% 2.06/1.65 tff(1467,plain,
% 2.06/1.65 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.06/1.65 inference(quant_inst,[status(thm)],[])).
% 2.06/1.65 tff(1468,plain,
% 2.06/1.65 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1467, 1466])).
% 2.06/1.65 tff(1469,plain,
% 2.06/1.65 (X!1 = W1!8),
% 2.06/1.65 inference(symmetry,[status(thm)],[1289])).
% 2.06/1.65 tff(1470,plain,
% 2.06/1.65 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.06/1.65 inference(transitivity,[status(thm)],[277, 1469])).
% 2.06/1.65 tff(1471,plain,
% 2.06/1.65 (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_9(W1!8)),
% 2.06/1.65 inference(monotonicity,[status(thm)],[1470])).
% 2.06/1.65 tff(1472,plain,
% 2.06/1.65 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.06/1.65 inference(symmetry,[status(thm)],[1471])).
% 2.06/1.65 tff(1473,assumption,(tptp_fun_Z1_9(W1!8) = X!1), introduced(assumption)).
% 2.06/1.65 tff(1474,plain,
% 2.06/1.65 (X!1 = tptp_fun_Z1_9(W1!8)),
% 2.06/1.65 inference(symmetry,[status(thm)],[1473])).
% 2.06/1.65 tff(1475,plain,
% 2.06/1.65 (X!1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.06/1.65 inference(transitivity,[status(thm)],[1474, 1472])).
% 2.06/1.65 tff(1476,plain,
% 2.06/1.65 ((tptp_fun_X1_13(X!1, X!1) = X!1) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.06/1.65 inference(monotonicity,[status(thm)],[1475])).
% 2.06/1.65 tff(1477,assumption,(big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))), introduced(assumption)).
% 2.06/1.65 tff(1478,plain,
% 2.06/1.65 ((~(tptp_fun_X1_13(X!1, X!1) = X!1)) <=> (~(tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.06/1.65 inference(monotonicity,[status(thm)],[1476])).
% 2.06/1.65 tff(1479,plain,
% 2.06/1.65 (~(tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.06/1.65 inference(modus_ponens,[status(thm)],[278, 1478])).
% 2.06/1.65 tff(1480,plain,
% 2.06/1.65 ((~(big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) | (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.06/1.65 inference(tautology,[status(thm)],[])).
% 2.06/1.65 tff(1481,plain,
% 2.06/1.65 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1480, 292, 1477])).
% 2.06/1.65 tff(1482,plain,
% 2.06/1.65 ($false),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1481, 1479])).
% 2.06/1.65 tff(1483,plain,((tptp_fun_X1_13(X!1, X!1) = X!1) | (~(tptp_fun_Z1_9(W1!8) = X!1)) | (~(W1!8 = X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.65 tff(1484,plain,
% 2.06/1.65 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[1483, 1473, 1289, 277, 1477, 290])).
% 2.06/1.65 tff(1485,plain,
% 2.06/1.65 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.06/1.65 inference(modus_ponens,[status(thm)],[1484, 1476])).
% 2.06/1.65 tff(1486,plain,
% 2.06/1.65 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.06/1.65 inference(unit_resolution,[status(thm)],[316, 1484, 290])).
% 2.06/1.65 tff(1487,plain,
% 2.06/1.65 ((~(big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) | (~(tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.14/1.65 inference(tautology,[status(thm)],[])).
% 2.14/1.65 tff(1488,plain,
% 2.14/1.65 (~(tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.14/1.65 inference(unit_resolution,[status(thm)],[1487, 1486, 1477])).
% 2.14/1.65 tff(1489,plain,
% 2.14/1.65 ($false),
% 2.14/1.65 inference(unit_resolution,[status(thm)],[1488, 1485])).
% 2.14/1.65 tff(1490,plain,((~(tptp_fun_Z1_9(W1!8) = X!1)) | (~(W1!8 = X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.65 tff(1491,plain,
% 2.14/1.65 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.14/1.65 inference(unit_resolution,[status(thm)],[1490, 1458, 277, 1468, 290])).
% 2.14/1.65 tff(1492,plain,
% 2.14/1.65 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.14/1.65 inference(unit_resolution,[status(thm)],[522, 1491])).
% 2.14/1.65 tff(1493,plain,
% 2.14/1.65 (tptp_fun_Z1_9(W1!8) = tptp_fun_X_2(X!1)),
% 2.14/1.65 inference(transitivity,[status(thm)],[1492, 273])).
% 2.14/1.65 tff(1494,plain,
% 2.14/1.65 (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.14/1.65 inference(monotonicity,[status(thm)],[1493, 1458])).
% 2.14/1.65 tff(1495,plain,
% 2.14/1.65 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.14/1.65 inference(symmetry,[status(thm)],[1494])).
% 2.14/1.65 tff(1496,plain,
% 2.14/1.65 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.14/1.65 inference(monotonicity,[status(thm)],[1495])).
% 2.14/1.65 tff(1497,plain,
% 2.14/1.65 (~big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.14/1.65 inference(modus_ponens,[status(thm)],[828, 1496])).
% 2.14/1.65 tff(1498,plain,
% 2.14/1.65 (((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | big_f(tptp_fun_Z1_9(W1!8), W1!8)) <=> ((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.14/1.65 inference(rewrite,[status(thm)],[])).
% 2.14/1.65 tff(1499,plain,
% 2.14/1.65 ((big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> $true) <=> big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.14/1.65 inference(rewrite,[status(thm)],[])).
% 2.14/1.65 tff(1500,plain,
% 2.14/1.65 ((tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(W1!8)) <=> $true),
% 2.14/1.65 inference(rewrite,[status(thm)],[])).
% 2.14/1.65 tff(1501,plain,
% 2.14/1.65 ((big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(W1!8))) <=> (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> $true)),
% 2.14/1.65 inference(monotonicity,[status(thm)],[1500])).
% 2.14/1.65 tff(1502,plain,
% 2.14/1.65 ((big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(W1!8))) <=> big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.14/1.65 inference(transitivity,[status(thm)],[1501, 1499])).
% 2.14/1.65 tff(1503,plain,
% 2.14/1.65 (((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(W1!8)))) <=> ((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.14/1.65 inference(monotonicity,[status(thm)],[1502])).
% 2.14/1.65 tff(1504,plain,
% 2.14/1.65 (((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(W1!8)))) <=> ((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.14/1.65 inference(transitivity,[status(thm)],[1503, 1498])).
% 2.14/1.65 tff(1505,plain,
% 2.14/1.65 ((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(W1!8)))),
% 2.14/1.65 inference(quant_inst,[status(thm)],[])).
% 2.14/1.65 tff(1506,plain,
% 2.14/1.65 ((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.14/1.65 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 2.14/1.65 tff(1507,plain,
% 2.14/1.65 (big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.14/1.65 inference(unit_resolution,[status(thm)],[1506, 1456])).
% 2.14/1.65 tff(1508,plain,
% 2.14/1.65 ($false),
% 2.14/1.65 inference(unit_resolution,[status(thm)],[1507, 1497])).
% 2.14/1.65 tff(1509,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1510,plain,
% 2.14/1.66 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1509, 1455, 106, 1431, 828, 30, 45, 1311])).
% 2.14/1.66 tff(1511,plain,
% 2.14/1.66 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[462, 1510])).
% 2.14/1.66 tff(1512,plain,
% 2.14/1.66 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[342, 1511])).
% 2.14/1.66 tff(1513,plain,
% 2.14/1.66 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[344, 1512])).
% 2.14/1.66 tff(1514,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.14/1.66 inference(symmetry,[status(thm)],[288])).
% 2.14/1.66 tff(1515,plain,
% 2.14/1.66 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1514])).
% 2.14/1.66 tff(1516,plain,
% 2.14/1.66 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[828, 1515])).
% 2.14/1.66 tff(1517,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[292, 1516])).
% 2.14/1.66 tff(1518,plain,((tptp_fun_X1_13(X!1, X!1) = X!1) | big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1519,plain,
% 2.14/1.66 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1518, 1455, 1431, 106, 828])).
% 2.14/1.66 tff(1520,plain,
% 2.14/1.66 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[337, 1519, 1431, 1455, 45])).
% 2.14/1.66 tff(1521,plain,
% 2.14/1.66 (~(X!1 = Z!5)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[346, 1520, 1513])).
% 2.14/1.66 tff(1522,plain,
% 2.14/1.66 (~(Z!5 = X!1)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[353, 1521])).
% 2.14/1.66 tff(1523,plain,
% 2.14/1.66 (Z!5 = Y!0),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[361, 1522])).
% 2.14/1.66 tff(1524,plain,
% 2.14/1.66 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1523])).
% 2.14/1.66 tff(1525,plain,
% 2.14/1.66 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1524])).
% 2.14/1.66 tff(1526,plain,
% 2.14/1.66 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.14/1.66 inference(transitivity,[status(thm)],[1525, 339])).
% 2.14/1.66 tff(1527,plain,
% 2.14/1.66 ((~(Y!0 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1526])).
% 2.14/1.66 tff(1528,plain,
% 2.14/1.66 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[385, 1511])).
% 2.14/1.66 tff(1529,plain,
% 2.14/1.66 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[387, 1528])).
% 2.14/1.66 tff(1530,plain,
% 2.14/1.66 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.14/1.66 inference(transitivity,[status(thm)],[1523, 31])).
% 2.14/1.66 tff(1531,plain,
% 2.14/1.66 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1530])).
% 2.14/1.66 tff(1532,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.14/1.66 inference(symmetry,[status(thm)],[1531])).
% 2.14/1.66 tff(1533,plain,
% 2.14/1.66 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Z!5, Y!0))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1532])).
% 2.14/1.66 tff(1534,plain,
% 2.14/1.66 (~big_f(Z!5, Y!0)),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[1311, 1533])).
% 2.14/1.66 tff(1535,plain,
% 2.14/1.66 (~(Y!0 = tptp_fun_W_6(Z!5))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[394, 1534, 1529])).
% 2.14/1.66 tff(1536,plain,
% 2.14/1.66 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[1535, 1527])).
% 2.14/1.66 tff(1537,plain,
% 2.14/1.66 ((X!1 = tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.14/1.66 inference(commutativity,[status(thm)],[])).
% 2.14/1.66 tff(1538,plain,
% 2.14/1.66 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1524])).
% 2.14/1.66 tff(1539,plain,
% 2.14/1.66 ((X!1 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.14/1.66 inference(transitivity,[status(thm)],[1538, 1537])).
% 2.14/1.66 tff(1540,plain,
% 2.14/1.66 ((~(X!1 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1539])).
% 2.14/1.66 tff(1541,plain,
% 2.14/1.66 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[983, 1528])).
% 2.14/1.66 tff(1542,plain,
% 2.14/1.66 (Z!5 = tptp_fun_X_2(X!1)),
% 2.14/1.66 inference(transitivity,[status(thm)],[1523, 527])).
% 2.14/1.66 tff(1543,plain,
% 2.14/1.66 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1542])).
% 2.14/1.66 tff(1544,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Z!5, X!1)),
% 2.14/1.66 inference(symmetry,[status(thm)],[1543])).
% 2.14/1.66 tff(1545,plain,
% 2.14/1.66 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Z!5, X!1))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1544])).
% 2.14/1.66 tff(1546,plain,
% 2.14/1.66 (~big_f(Z!5, X!1)),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[828, 1545])).
% 2.14/1.66 tff(1547,plain,
% 2.14/1.66 ((~(big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5)))) | big_f(Z!5, X!1) | (~(X!1 = tptp_fun_W_6(Z!5)))),
% 2.14/1.66 inference(tautology,[status(thm)],[])).
% 2.14/1.66 tff(1548,plain,
% 2.14/1.66 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1547, 1546, 1541])).
% 2.14/1.66 tff(1549,plain,
% 2.14/1.66 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[1548, 1540])).
% 2.14/1.66 tff(1550,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[403, 1549, 1536])).
% 2.14/1.66 tff(1551,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | (tptp_fun_X_2(X!1) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1552,plain,
% 2.14/1.66 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1551, 41, 30, 45, 47, 828])).
% 2.14/1.66 tff(1553,plain,
% 2.14/1.66 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[39, 1552])).
% 2.14/1.66 tff(1554,assumption,(![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))), introduced(assumption)).
% 2.14/1.66 tff(1555,plain,
% 2.14/1.66 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[88, 1554])).
% 2.14/1.66 tff(1556,plain,
% 2.14/1.66 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[90, 1555])).
% 2.14/1.66 tff(1557,plain,
% 2.14/1.66 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[650, 1556, 277, 41, 40])).
% 2.14/1.66 tff(1558,plain,
% 2.14/1.66 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[84, 1554])).
% 2.14/1.66 tff(1559,plain,
% 2.14/1.66 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[561, 1558])).
% 2.14/1.66 tff(1560,plain,
% 2.14/1.66 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[563, 1559, 34])).
% 2.14/1.66 tff(1561,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[596, 1560, 1557, 41])).
% 2.14/1.66 tff(1562,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_Y1_11(Y!0) = Y!0) | (~(tptp_fun_Y1_11(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1563,plain,
% 2.14/1.66 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1562, 41, 1552, 1431])).
% 2.14/1.66 tff(1564,plain,
% 2.14/1.66 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[82, 1563])).
% 2.14/1.66 tff(1565,plain,
% 2.14/1.66 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[220, 1564])).
% 2.14/1.66 tff(1566,plain,
% 2.14/1.66 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[222, 1565])).
% 2.14/1.66 tff(1567,plain,
% 2.14/1.66 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[224, 1566, 47])).
% 2.14/1.66 tff(1568,assumption,(~big_f(tptp_fun_X_2(X!1), Y!0)), introduced(assumption)).
% 2.14/1.66 tff(1569,plain,
% 2.14/1.66 ((~(big_f(tptp_fun_X_2(X!1), Y!0) <=> (Y!0 = tptp_fun_W_3(X!1)))) | big_f(tptp_fun_X_2(X!1), Y!0) | (~(Y!0 = tptp_fun_W_3(X!1)))),
% 2.14/1.66 inference(tautology,[status(thm)],[])).
% 2.14/1.66 tff(1570,plain,
% 2.14/1.66 (~(Y!0 = tptp_fun_W_3(X!1))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1569, 1147, 1568])).
% 2.14/1.66 tff(1571,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[234, 1145])).
% 2.14/1.66 tff(1572,plain,
% 2.14/1.66 (tptp_fun_W_3(X!1) = tptp_fun_Y1_11(Y!0)),
% 2.14/1.66 inference(transitivity,[status(thm)],[256, 599])).
% 2.14/1.66 tff(1573,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[240, 1572])).
% 2.14/1.66 tff(1574,plain,
% 2.14/1.66 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.14/1.66 inference(symmetry,[status(thm)],[1573])).
% 2.14/1.66 tff(1575,plain,
% 2.14/1.66 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 2.14/1.66 inference(monotonicity,[status(thm)],[1574])).
% 2.14/1.66 tff(1576,plain,
% 2.14/1.66 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[41, 1575])).
% 2.14/1.66 tff(1577,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[245, 1576])).
% 2.14/1.66 tff(1578,plain,((~(tptp_fun_W_3(X!1) = X!1)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1579,plain,
% 2.14/1.66 (~(tptp_fun_W_3(X!1) = X!1)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1578, 1571, 240, 598, 41])).
% 2.14/1.66 tff(1580,plain,
% 2.14/1.66 (tptp_fun_W_3(X!1) = Y!0),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[252, 1579])).
% 2.14/1.66 tff(1581,plain,
% 2.14/1.66 ((Y!0 = tptp_fun_W_3(X!1)) <=> (tptp_fun_W_3(X!1) = Y!0)),
% 2.14/1.66 inference(commutativity,[status(thm)],[])).
% 2.14/1.66 tff(1582,plain,
% 2.14/1.66 ((tptp_fun_W_3(X!1) = Y!0) <=> (Y!0 = tptp_fun_W_3(X!1))),
% 2.14/1.66 inference(symmetry,[status(thm)],[1581])).
% 2.14/1.66 tff(1583,plain,
% 2.14/1.66 (Y!0 = tptp_fun_W_3(X!1)),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[238, 1582])).
% 2.14/1.66 tff(1584,assumption,(~(Y!0 = tptp_fun_W_3(X!1))), introduced(assumption)).
% 2.14/1.66 tff(1585,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1584, 1583])).
% 2.14/1.66 tff(1586,plain,((~(tptp_fun_W_3(X!1) = Y!0)) | (Y!0 = tptp_fun_W_3(X!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1587,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1586, 1580, 1570])).
% 2.14/1.66 tff(1588,plain,((~![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))) | big_f(tptp_fun_X_2(X!1), Y!0) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1589,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1588, 1567, 106, 1553, 41])).
% 2.14/1.66 tff(1590,plain,
% 2.14/1.66 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[56, 1564])).
% 2.14/1.66 tff(1591,plain,
% 2.14/1.66 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[54, 1590])).
% 2.14/1.66 tff(1592,plain,
% 2.14/1.66 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[52, 1591, 30])).
% 2.14/1.66 tff(1593,plain,
% 2.14/1.66 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[50, 1592])).
% 2.14/1.66 tff(1594,plain,
% 2.14/1.66 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1129, 1593, 1310])).
% 2.14/1.66 tff(1595,plain,
% 2.14/1.66 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1339, 1593, 1594])).
% 2.14/1.66 tff(1596,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.66 inference(monotonicity,[status(thm)],[258])).
% 2.14/1.66 tff(1597,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.66 inference(modus_ponens,[status(thm)],[1144, 1596])).
% 2.14/1.66 tff(1598,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[35, 1597])).
% 2.14/1.66 tff(1599,plain,((~big_f(tptp_fun_X_2(X!1), Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1600,plain,
% 2.14/1.66 ($false),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1599, 1595, 1589, 30, 106])).
% 2.14/1.66 tff(1601,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(X!1), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/1.66 tff(1602,plain,
% 2.14/1.66 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1601, 828, 47, 45, 30])).
% 2.14/1.66 tff(1603,plain,
% 2.14/1.66 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1413, 1602, 828, 106])).
% 2.14/1.66 tff(1604,plain,
% 2.14/1.66 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[39, 1603])).
% 2.14/1.66 tff(1605,plain,
% 2.14/1.66 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[1168, 1604, 45, 1602])).
% 2.14/1.66 tff(1606,plain,
% 2.14/1.66 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[86, 1605])).
% 2.14/1.66 tff(1607,plain,
% 2.14/1.66 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[84, 1606])).
% 2.14/1.66 tff(1608,plain,
% 2.14/1.66 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.14/1.66 inference(unit_resolution,[status(thm)],[82, 1607])).
% 2.14/1.66 tff(1609,plain,
% 2.14/1.66 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1449, 1608, 30, 1604, 47])).
% 2.14/1.67 tff(1610,plain,
% 2.14/1.67 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1341, 1609, 1310])).
% 2.14/1.67 tff(1611,plain,
% 2.14/1.67 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[56, 1608])).
% 2.14/1.67 tff(1612,plain,
% 2.14/1.67 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[54, 1611])).
% 2.14/1.67 tff(1613,plain,
% 2.14/1.67 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[52, 1612, 30])).
% 2.14/1.67 tff(1614,plain,
% 2.14/1.67 ($false),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[50, 1613, 1610])).
% 2.14/1.67 tff(1615,plain,(big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_X_2(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.14/1.67 tff(1616,plain,
% 2.14/1.67 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1615, 47, 30, 45])).
% 2.14/1.67 tff(1617,plain,
% 2.14/1.67 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[84, 896])).
% 2.14/1.67 tff(1618,plain,
% 2.14/1.67 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[86, 1617])).
% 2.14/1.67 tff(1619,plain,
% 2.14/1.67 (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[927, 35, 862, 240, 30, 45, 277])).
% 2.14/1.67 tff(1620,plain,
% 2.14/1.67 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[481, 1619])).
% 2.14/1.67 tff(1621,plain,
% 2.14/1.67 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[462, 1620])).
% 2.14/1.67 tff(1622,plain,
% 2.14/1.67 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1067, 900, 862, 45, 1621, 240, 277, 1618])).
% 2.14/1.67 tff(1623,plain,
% 2.14/1.67 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[910, 900, 862, 240, 277])).
% 2.14/1.67 tff(1624,plain,
% 2.14/1.67 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1118, 1623, 277, 1622, 900])).
% 2.14/1.67 tff(1625,plain,
% 2.14/1.67 ($false),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[650, 1624, 1622, 277, 41, 898])).
% 2.14/1.67 tff(1626,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_Y1_11(X!1) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~big_f(tptp_fun_X_2(X!1), X!1)) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.67 tff(1627,plain,
% 2.14/1.67 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1626, 41, 277, 862, 45, 240, 30])).
% 2.14/1.67 tff(1628,plain,
% 2.14/1.67 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1341, 1627, 1332])).
% 2.14/1.67 tff(1629,plain,
% 2.14/1.67 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[50, 1628])).
% 2.14/1.67 tff(1630,plain,
% 2.14/1.67 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[52, 1629, 30])).
% 2.14/1.67 tff(1631,plain,
% 2.14/1.67 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[54, 1630])).
% 2.14/1.67 tff(1632,plain,
% 2.14/1.67 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[56, 1631])).
% 2.14/1.67 tff(1633,plain,
% 2.14/1.67 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[82, 1632])).
% 2.14/1.67 tff(1634,plain,
% 2.14/1.67 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1562, 1633, 41, 277])).
% 2.14/1.67 tff(1635,plain,
% 2.14/1.67 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.67 inference(monotonicity,[status(thm)],[31, 1634])).
% 2.14/1.67 tff(1636,plain,
% 2.14/1.67 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.14/1.67 inference(symmetry,[status(thm)],[1635])).
% 2.14/1.67 tff(1637,plain,
% 2.14/1.67 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.14/1.67 inference(modus_ponens,[status(thm)],[1627, 1636])).
% 2.14/1.67 tff(1638,plain,
% 2.14/1.67 ($false),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[41, 1637])).
% 2.14/1.67 tff(1639,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), X!1)) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.67 tff(1640,plain,
% 2.14/1.67 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1639, 1431, 30, 1310, 1616, 45, 106])).
% 2.14/1.67 tff(1641,plain,
% 2.14/1.67 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[86, 1558])).
% 2.14/1.67 tff(1642,plain,
% 2.14/1.67 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1168, 1641, 45, 135])).
% 2.14/1.67 tff(1643,plain,
% 2.14/1.67 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[563, 1642, 1559])).
% 2.14/1.67 tff(1644,plain,
% 2.14/1.67 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[269, 1556, 277])).
% 2.14/1.67 tff(1645,plain,
% 2.14/1.67 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[879, 1644])).
% 2.14/1.67 tff(1646,plain,
% 2.14/1.67 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[910, 1645, 862, 240, 277])).
% 2.14/1.67 tff(1647,plain,
% 2.14/1.67 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[39, 1642])).
% 2.14/1.67 tff(1648,plain,
% 2.14/1.67 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1118, 1647, 277, 1646, 1645])).
% 2.14/1.67 tff(1649,plain,
% 2.14/1.67 ($false),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1194, 1648, 1643, 135])).
% 2.14/1.67 tff(1650,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.14/1.67 tff(1651,plain,
% 2.14/1.67 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1650, 1640, 1431, 1616, 106, 45])).
% 2.14/1.67 tff(1652,plain,
% 2.14/1.67 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[82, 1651])).
% 2.14/1.67 tff(1653,plain,
% 2.14/1.67 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[56, 1652])).
% 2.14/1.67 tff(1654,plain,
% 2.14/1.67 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[54, 1653])).
% 2.14/1.67 tff(1655,plain,
% 2.14/1.67 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[52, 1654, 30])).
% 2.14/1.67 tff(1656,plain,
% 2.14/1.67 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[198, 1655])).
% 2.14/1.67 tff(1657,plain,
% 2.14/1.67 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[50, 1655])).
% 2.14/1.67 tff(1658,plain,
% 2.14/1.67 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1129, 1657, 1310])).
% 2.14/1.67 tff(1659,plain,
% 2.14/1.67 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1339, 1657, 1658])).
% 2.14/1.67 tff(1660,plain,
% 2.14/1.67 ($false),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[866, 1659, 1656, 30, 106, 1616])).
% 2.14/1.67 tff(1661,plain,((tptp_fun_X_2(X!1) = X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.14/1.67 tff(1662,plain,
% 2.14/1.67 (tptp_fun_X_2(X!1) = X!1),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1661, 45, 30])).
% 2.14/1.67 tff(1663,assumption,(tptp_fun_X_2(X!1) = X!1), introduced(assumption)).
% 2.14/1.67 tff(1664,plain,
% 2.14/1.67 (X!1 = tptp_fun_X_2(X!1)),
% 2.14/1.67 inference(symmetry,[status(thm)],[1663])).
% 2.14/1.67 tff(1665,plain,
% 2.14/1.67 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1663])).
% 2.14/1.67 tff(1666,plain,
% 2.14/1.67 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1665])).
% 2.14/1.67 tff(1667,plain,
% 2.14/1.67 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.14/1.67 inference(symmetry,[status(thm)],[1666])).
% 2.14/1.67 tff(1668,plain,
% 2.14/1.67 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1664, 154])).
% 2.14/1.67 tff(1669,plain,
% 2.14/1.67 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1668, 154])).
% 2.14/1.67 tff(1670,plain,
% 2.14/1.67 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.14/1.67 inference(symmetry,[status(thm)],[1669])).
% 2.14/1.67 tff(1671,plain,
% 2.14/1.67 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1664, 30])).
% 2.14/1.67 tff(1672,assumption,(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1), introduced(assumption)).
% 2.14/1.67 tff(1673,plain,
% 2.14/1.67 ((~(Y!0 = tptp_fun_W_6(Y!0))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.14/1.67 inference(monotonicity,[status(thm)],[339])).
% 2.14/1.67 tff(1674,plain,
% 2.14/1.67 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[441, 341, 422])).
% 2.14/1.67 tff(1675,assumption,((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)), introduced(assumption)).
% 2.14/1.67 tff(1676,assumption,(big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))), introduced(assumption)).
% 2.14/1.67 tff(1677,plain,
% 2.14/1.67 ((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) | (~(tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.14/1.67 inference(tautology,[status(thm)],[])).
% 2.14/1.67 tff(1678,plain,
% 2.14/1.67 (~(tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1677, 1676, 1675])).
% 2.14/1.67 tff(1679,plain,
% 2.14/1.67 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, X!1) = X!1) | (tptp_fun_Y_4(X!1, X!1) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(X!1, X!1) = X!1) | (tptp_fun_Y_4(X!1, X!1) = Y!0))),
% 2.14/1.67 inference(rewrite,[status(thm)],[])).
% 2.14/1.67 tff(1680,plain,
% 2.14/1.67 (((tptp_fun_Y_4(X!1, X!1) = Y!0) | (tptp_fun_Y_4(X!1, X!1) = X!1)) <=> ((tptp_fun_Y_4(X!1, X!1) = X!1) | (tptp_fun_Y_4(X!1, X!1) = Y!0))),
% 2.14/1.67 inference(rewrite,[status(thm)],[])).
% 2.14/1.67 tff(1681,plain,
% 2.14/1.67 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, X!1) = Y!0) | (tptp_fun_Y_4(X!1, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, X!1) = X!1) | (tptp_fun_Y_4(X!1, X!1) = Y!0)))),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1680])).
% 2.14/1.67 tff(1682,plain,
% 2.14/1.67 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, X!1) = Y!0) | (tptp_fun_Y_4(X!1, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(X!1, X!1) = X!1) | (tptp_fun_Y_4(X!1, X!1) = Y!0))),
% 2.14/1.67 inference(transitivity,[status(thm)],[1681, 1679])).
% 2.14/1.67 tff(1683,plain,
% 2.14/1.67 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(X!1, X!1) = Y!0) | (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.14/1.67 inference(quant_inst,[status(thm)],[])).
% 2.14/1.67 tff(1684,plain,
% 2.14/1.67 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(X!1, X!1) = X!1) | (tptp_fun_Y_4(X!1, X!1) = Y!0)),
% 2.14/1.67 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 2.14/1.67 tff(1685,plain,
% 2.14/1.67 ((tptp_fun_Y_4(X!1, X!1) = X!1) | (tptp_fun_Y_4(X!1, X!1) = Y!0)),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1684, 12])).
% 2.14/1.67 tff(1686,plain,
% 2.14/1.67 (tptp_fun_Y_4(X!1, X!1) = Y!0),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1685, 1678])).
% 2.14/1.67 tff(1687,plain,
% 2.14/1.67 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(X!1, Y!0)),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1663, 1686])).
% 2.14/1.67 tff(1688,plain,
% 2.14/1.67 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.14/1.67 inference(symmetry,[status(thm)],[1687])).
% 2.14/1.67 tff(1689,plain,
% 2.14/1.67 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)))),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1688])).
% 2.14/1.67 tff(1690,plain,
% 2.14/1.67 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.14/1.67 inference(modus_ponens,[status(thm)],[45, 1689])).
% 2.14/1.67 tff(1691,plain,
% 2.14/1.67 ($false),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1676, 1690])).
% 2.14/1.67 tff(1692,plain,((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.67 tff(1693,plain,
% 2.14/1.67 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1692, 1675, 1663, 45])).
% 2.14/1.67 tff(1694,plain,
% 2.14/1.67 ((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) | (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.14/1.67 inference(tautology,[status(thm)],[])).
% 2.14/1.67 tff(1695,plain,
% 2.14/1.67 (tptp_fun_Y_4(X!1, X!1) = X!1),
% 2.14/1.67 inference(unit_resolution,[status(thm)],[1694, 1675, 1693])).
% 2.14/1.67 tff(1696,assumption,(tptp_fun_Y_4(X!1, X!1) = X!1), introduced(assumption)).
% 2.14/1.67 tff(1697,plain,
% 2.14/1.67 (X!1 = tptp_fun_Y_4(X!1, X!1)),
% 2.14/1.67 inference(symmetry,[status(thm)],[1696])).
% 2.14/1.67 tff(1698,plain,
% 2.14/1.67 (tptp_fun_W_6(X!1) = tptp_fun_Y_4(X!1, X!1)),
% 2.14/1.67 inference(transitivity,[status(thm)],[1199, 1697])).
% 2.14/1.67 tff(1699,plain,
% 2.14/1.67 (big_f(X!1, tptp_fun_W_6(X!1)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.14/1.67 inference(monotonicity,[status(thm)],[1664, 1698])).
% 2.14/1.67 tff(1700,plain,
% 2.14/1.67 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(X!1, tptp_fun_W_6(X!1))),
% 2.14/1.67 inference(symmetry,[status(thm)],[1699])).
% 2.14/1.68 tff(1701,plain,
% 2.14/1.68 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (~big_f(X!1, tptp_fun_W_6(X!1)))),
% 2.14/1.68 inference(monotonicity,[status(thm)],[1700])).
% 2.14/1.68 tff(1702,assumption,(~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))), introduced(assumption)).
% 2.14/1.68 tff(1703,plain,
% 2.14/1.68 (~big_f(X!1, tptp_fun_W_6(X!1))),
% 2.14/1.68 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 2.14/1.68 tff(1704,plain,
% 2.14/1.68 ($false),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[308, 1703])).
% 2.14/1.68 tff(1705,plain,((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) | (~(tptp_fun_Y_4(X!1, X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.14/1.68 tff(1706,plain,
% 2.14/1.68 ($false),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[1705, 1695, 1693, 45, 1663, 298])).
% 2.14/1.68 tff(1707,plain,((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.68 tff(1708,plain,
% 2.14/1.68 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[1707, 1674, 1663, 45])).
% 2.14/1.68 tff(1709,plain,
% 2.14/1.68 ((~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))) | ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.14/1.68 inference(quant_inst,[status(thm)],[])).
% 2.14/1.68 tff(1710,plain,
% 2.14/1.68 (~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[1709, 1708])).
% 2.14/1.68 tff(1711,plain,
% 2.14/1.68 ((~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))) | (~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.14/1.68 inference(tautology,[status(thm)],[])).
% 2.14/1.68 tff(1712,plain,
% 2.14/1.68 (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[1711, 1710, 1663])).
% 2.14/1.68 tff(1713,plain,
% 2.14/1.68 (((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))) | ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.14/1.68 inference(tautology,[status(thm)],[])).
% 2.14/1.68 tff(1714,plain,
% 2.14/1.68 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[1713, 1712])).
% 2.14/1.68 tff(1715,plain,
% 2.14/1.68 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[220, 1714])).
% 2.14/1.68 tff(1716,plain,
% 2.14/1.68 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[82, 1715])).
% 2.14/1.68 tff(1717,plain,
% 2.14/1.68 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.14/1.68 inference(unit_resolution,[status(thm)],[88, 1716])).
% 2.14/1.68 tff(1718,plain,
% 2.14/1.68 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[191, 1717])).
% 2.17/1.68 tff(1719,plain,
% 2.17/1.68 (~(tptp_fun_Z1_12(X!1) = X!1)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[182, 1718, 144, 45])).
% 2.17/1.68 tff(1720,plain,
% 2.17/1.68 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[187, 1719])).
% 2.17/1.68 tff(1721,plain,
% 2.17/1.68 (tptp_fun_Z1_12(X!1) = tptp_fun_X_2(Y!0)),
% 2.17/1.68 inference(transitivity,[status(thm)],[1720, 31])).
% 2.17/1.68 tff(1722,plain,
% 2.17/1.68 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1721, 154])).
% 2.17/1.68 tff(1723,plain,
% 2.17/1.68 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.17/1.68 inference(symmetry,[status(thm)],[1722])).
% 2.17/1.68 tff(1724,plain,
% 2.17/1.68 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1723])).
% 2.17/1.68 tff(1725,assumption,(~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))), introduced(assumption)).
% 2.17/1.68 tff(1726,plain,
% 2.17/1.68 ((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[723, 1725])).
% 2.17/1.68 tff(1727,plain,
% 2.17/1.68 ((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[430, 1725])).
% 2.17/1.68 tff(1728,plain,
% 2.17/1.68 (~(Y!0 = Z!5)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[432, 1727, 422])).
% 2.17/1.68 tff(1729,plain,
% 2.17/1.68 ($false),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[725, 1728, 1726, 722])).
% 2.17/1.68 tff(1730,plain,(((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.68 tff(1731,plain,
% 2.17/1.68 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1730, 429, 422])).
% 2.17/1.68 tff(1732,plain,
% 2.17/1.68 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[720, 1731])).
% 2.17/1.68 tff(1733,plain,
% 2.17/1.68 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[718, 1732, 41, 30, 598])).
% 2.17/1.68 tff(1734,plain,
% 2.17/1.68 (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1733, 1724])).
% 2.17/1.68 tff(1735,plain,
% 2.17/1.68 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[161, 1718, 144])).
% 2.17/1.68 tff(1736,plain,
% 2.17/1.68 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[171, 1735])).
% 2.17/1.68 tff(1737,plain,
% 2.17/1.68 ($false),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1736, 1734])).
% 2.17/1.68 tff(1738,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.68 tff(1739,plain,
% 2.17/1.68 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1738, 341, 144, 45, 1663, 41, 422, 30])).
% 2.17/1.68 tff(1740,plain,
% 2.17/1.68 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[39, 1739])).
% 2.17/1.68 tff(1741,plain,
% 2.17/1.68 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[189, 1740, 144, 45, 41])).
% 2.17/1.68 tff(1742,plain,
% 2.17/1.68 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[191, 1741])).
% 2.17/1.68 tff(1743,plain,
% 2.17/1.68 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[88, 1742])).
% 2.17/1.68 tff(1744,plain,
% 2.17/1.68 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[82, 1743])).
% 2.17/1.68 tff(1745,plain,
% 2.17/1.68 ($false),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[220, 1744, 1714])).
% 2.17/1.68 tff(1746,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X_2(X!1) = X!1)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.68 tff(1747,plain,
% 2.17/1.68 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1746, 341, 144, 45, 41, 1663, 30])).
% 2.17/1.68 tff(1748,plain,
% 2.17/1.68 ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | (big_f(Y!0, Y!0) <=> (Y!0 = tptp_fun_W_6(Y!0)))),
% 2.17/1.68 inference(quant_inst,[status(thm)],[])).
% 2.17/1.68 tff(1749,plain,
% 2.17/1.68 (big_f(Y!0, Y!0) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1748, 1747])).
% 2.17/1.68 tff(1750,plain,
% 2.17/1.68 (big_f(Y!0, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[31])).
% 2.17/1.68 tff(1751,plain,
% 2.17/1.68 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, Y!0)),
% 2.17/1.68 inference(symmetry,[status(thm)],[1750])).
% 2.17/1.68 tff(1752,plain,
% 2.17/1.68 (big_f(Y!0, Y!0)),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[692, 1751])).
% 2.17/1.68 tff(1753,plain,
% 2.17/1.68 ((~(big_f(Y!0, Y!0) <=> (Y!0 = tptp_fun_W_6(Y!0)))) | (~big_f(Y!0, Y!0)) | (Y!0 = tptp_fun_W_6(Y!0))),
% 2.17/1.68 inference(tautology,[status(thm)],[])).
% 2.17/1.68 tff(1754,plain,
% 2.17/1.68 (Y!0 = tptp_fun_W_6(Y!0)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1753, 1752, 1749])).
% 2.17/1.68 tff(1755,plain,
% 2.17/1.68 (tptp_fun_W_6(Y!0) = Y!0),
% 2.17/1.68 inference(symmetry,[status(thm)],[1754])).
% 2.17/1.68 tff(1756,plain,
% 2.17/1.68 ((tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0)) <=> (tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1755])).
% 2.17/1.68 tff(1757,plain,
% 2.17/1.68 ((~(tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0))) <=> (~(tptp_fun_Y1_11(Y!0) = Y!0))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1756])).
% 2.17/1.68 tff(1758,plain,
% 2.17/1.68 ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0)))),
% 2.17/1.68 inference(quant_inst,[status(thm)],[])).
% 2.17/1.68 tff(1759,plain,
% 2.17/1.68 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1758, 1747])).
% 2.17/1.68 tff(1760,plain,
% 2.17/1.68 ((~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0)))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0)))),
% 2.17/1.68 inference(tautology,[status(thm)],[])).
% 2.17/1.68 tff(1761,plain,
% 2.17/1.68 ((~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0)))) | (~(tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0)))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1760, 41])).
% 2.17/1.68 tff(1762,plain,
% 2.17/1.68 (~(tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1761, 1759])).
% 2.17/1.68 tff(1763,plain,
% 2.17/1.68 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1762, 1757])).
% 2.17/1.68 tff(1764,plain,
% 2.17/1.68 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[39, 1763])).
% 2.17/1.68 tff(1765,plain,
% 2.17/1.68 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1663, 31])).
% 2.17/1.68 tff(1766,plain,
% 2.17/1.68 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1),
% 2.17/1.68 inference(transitivity,[status(thm)],[1765, 1672])).
% 2.17/1.68 tff(1767,plain,
% 2.17/1.68 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1766])).
% 2.17/1.68 tff(1768,plain,
% 2.17/1.68 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.17/1.68 inference(symmetry,[status(thm)],[1767])).
% 2.17/1.68 tff(1769,plain,
% 2.17/1.68 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1768])).
% 2.17/1.68 tff(1770,plain,
% 2.17/1.68 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[45, 1769])).
% 2.17/1.68 tff(1771,plain,
% 2.17/1.68 ((tptp_fun_Y1_11(Y!0) = Z!5) <=> (X!1 = Z!5)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1764])).
% 2.17/1.68 tff(1772,plain,
% 2.17/1.68 ((X!1 = Z!5) <=> (tptp_fun_Y1_11(Y!0) = Z!5)),
% 2.17/1.68 inference(symmetry,[status(thm)],[1771])).
% 2.17/1.68 tff(1773,plain,
% 2.17/1.68 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[718, 1764, 41, 30, 692])).
% 2.17/1.68 tff(1774,plain,
% 2.17/1.68 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[720, 1773])).
% 2.17/1.68 tff(1775,plain,
% 2.17/1.68 (Y!0 = Z!5),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[725, 1774, 724])).
% 2.17/1.68 tff(1776,plain,
% 2.17/1.68 (Z!5 = Y!0),
% 2.17/1.68 inference(symmetry,[status(thm)],[1775])).
% 2.17/1.68 tff(1777,plain,
% 2.17/1.68 ((X!1 = Z!5) <=> (X!1 = Y!0)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1776])).
% 2.17/1.68 tff(1778,plain,
% 2.17/1.68 ((X!1 = Y!0) <=> (X!1 = Z!5)),
% 2.17/1.68 inference(symmetry,[status(thm)],[1777])).
% 2.17/1.68 tff(1779,plain,
% 2.17/1.68 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(Y!0) = Z!5)),
% 2.17/1.68 inference(transitivity,[status(thm)],[1778, 1772])).
% 2.17/1.68 tff(1780,plain,
% 2.17/1.68 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(Y!0) = Z!5))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1779])).
% 2.17/1.68 tff(1781,plain,
% 2.17/1.68 (~(tptp_fun_Y1_11(Y!0) = Z!5)),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[741, 1780])).
% 2.17/1.68 tff(1782,plain,
% 2.17/1.68 (![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[738, 1781, 737])).
% 2.17/1.68 tff(1783,plain,
% 2.17/1.68 ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[629, 1782])).
% 2.17/1.68 tff(1784,assumption,(~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)), introduced(assumption)).
% 2.17/1.68 tff(1785,plain,
% 2.17/1.68 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1664, 796])).
% 2.17/1.68 tff(1786,plain,
% 2.17/1.68 (Y!0 = tptp_fun_Y1_11(X!1)),
% 2.17/1.68 inference(symmetry,[status(thm)],[796])).
% 2.17/1.68 tff(1787,plain,
% 2.17/1.68 (tptp_fun_X_2(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.17/1.68 inference(transitivity,[status(thm)],[30, 1786])).
% 2.17/1.68 tff(1788,plain,
% 2.17/1.68 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1787])).
% 2.17/1.68 tff(1789,plain,
% 2.17/1.68 (X!1 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.17/1.68 inference(symmetry,[status(thm)],[1672])).
% 2.17/1.68 tff(1790,plain,
% 2.17/1.68 (tptp_fun_Y1_11(Y!0) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.17/1.68 inference(transitivity,[status(thm)],[598, 1789, 1788, 1785])).
% 2.17/1.68 tff(1791,plain,
% 2.17/1.68 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1790, 609])).
% 2.17/1.68 tff(1792,plain,
% 2.17/1.68 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.17/1.68 inference(symmetry,[status(thm)],[1791])).
% 2.17/1.68 tff(1793,plain,
% 2.17/1.68 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1792])).
% 2.17/1.68 tff(1794,plain,
% 2.17/1.68 (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1784, 1793])).
% 2.17/1.69 tff(1795,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[615, 1794])).
% 2.17/1.69 tff(1796,plain,((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(1797,plain,
% 2.17/1.69 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1796, 600, 598, 1672, 796, 1663, 30, 1784])).
% 2.17/1.69 tff(1798,plain,
% 2.17/1.69 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = tptp_fun_Y1_11(Y!0)),
% 2.17/1.69 inference(transitivity,[status(thm)],[1797, 599])).
% 2.17/1.69 tff(1799,plain,
% 2.17/1.69 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[598, 1798])).
% 2.17/1.69 tff(1800,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.17/1.69 inference(symmetry,[status(thm)],[1799])).
% 2.17/1.69 tff(1801,plain,
% 2.17/1.69 (big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[622, 1800])).
% 2.17/1.69 tff(1802,plain,
% 2.17/1.69 (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[624, 1797, 600])).
% 2.17/1.69 tff(1803,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1802, 1801])).
% 2.17/1.69 tff(1804,plain,((~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(1805,plain,
% 2.17/1.69 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1804, 1783, 1672, 1764, 154, 1663, 30, 1770])).
% 2.17/1.69 tff(1806,plain,
% 2.17/1.69 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1206, 1805, 1764, 45])).
% 2.17/1.69 tff(1807,assumption,(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1), introduced(assumption)).
% 2.17/1.69 tff(1808,plain,
% 2.17/1.69 (X!1 = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.17/1.69 inference(symmetry,[status(thm)],[1807])).
% 2.17/1.69 tff(1809,plain,
% 2.17/1.69 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.17/1.69 inference(transitivity,[status(thm)],[598, 1808])).
% 2.17/1.69 tff(1810,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1809])).
% 2.17/1.69 tff(1811,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.17/1.69 inference(symmetry,[status(thm)],[1810])).
% 2.17/1.69 tff(1812,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1020, 1811])).
% 2.17/1.69 tff(1813,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[42, 1812])).
% 2.17/1.69 tff(1814,plain,((~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) | (~(tptp_fun_Y1_11(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(1815,plain,
% 2.17/1.69 (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1814, 1020, 42, 598])).
% 2.17/1.69 tff(1816,plain,
% 2.17/1.69 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1027, 1815])).
% 2.17/1.69 tff(1817,plain,
% 2.17/1.69 (Y!0 = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.17/1.69 inference(symmetry,[status(thm)],[1816])).
% 2.17/1.69 tff(1818,plain,
% 2.17/1.69 (big_f(X!1, Y!0) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1817])).
% 2.17/1.69 tff(1819,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(X!1, Y!0)),
% 2.17/1.69 inference(symmetry,[status(thm)],[1818])).
% 2.17/1.69 tff(1820,plain,
% 2.17/1.69 (big_f(X!1, Y!0)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1020, 1819])).
% 2.17/1.69 tff(1821,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[45, 1820])).
% 2.17/1.69 tff(1822,plain,((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) | big_f(X!1, Y!0) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(1823,plain,
% 2.17/1.69 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1822, 1805, 1764, 45])).
% 2.17/1.69 tff(1824,plain,
% 2.17/1.69 (((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (~(tptp_fun_X_2(Y!0) = Y!0))),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(1825,plain,
% 2.17/1.69 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1824, 30])).
% 2.17/1.69 tff(1826,plain,
% 2.17/1.69 (tptp_fun_W_6(Y!0) = Y!0),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1754, 339])).
% 2.17/1.69 tff(1827,assumption,(tptp_fun_W_6(Y!0) = Y!0), introduced(assumption)).
% 2.17/1.69 tff(1828,plain,
% 2.17/1.69 (Y!0 = tptp_fun_W_6(Y!0)),
% 2.17/1.69 inference(symmetry,[status(thm)],[1827])).
% 2.17/1.69 tff(1829,plain,
% 2.17/1.69 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1828])).
% 2.17/1.69 tff(1830,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1829])).
% 2.17/1.69 tff(1831,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.17/1.69 inference(symmetry,[status(thm)],[1830])).
% 2.17/1.69 tff(1832,plain,
% 2.17/1.69 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1)))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1831])).
% 2.17/1.69 tff(1833,plain,
% 2.17/1.69 (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1049, 1832])).
% 2.17/1.69 tff(1834,assumption,(~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))), introduced(assumption)).
% 2.17/1.69 tff(1835,plain,
% 2.17/1.69 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[344, 1834])).
% 2.17/1.69 tff(1836,assumption,(~![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))), introduced(assumption)).
% 2.17/1.69 tff(1837,plain,
% 2.17/1.69 ((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[980, 1834])).
% 2.17/1.69 tff(1838,plain,
% 2.17/1.69 (X!1 = Z!5),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1008, 1837, 1836])).
% 2.17/1.69 tff(1839,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[346, 1838, 1835, 340])).
% 2.17/1.69 tff(1840,plain,(((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))))) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(1841,plain,
% 2.17/1.69 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1840, 343, 340])).
% 2.17/1.69 tff(1842,plain,
% 2.17/1.69 ((~![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))) | ((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(1843,plain,
% 2.17/1.69 ((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1842, 1841])).
% 2.17/1.69 tff(1844,plain,
% 2.17/1.69 ((~((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0))) | big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) | (tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(1845,plain,
% 2.17/1.69 (tptp_fun_Y_7(Y!0, X!1) = Y!0),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1844, 1843, 1833])).
% 2.17/1.69 tff(1846,assumption,((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))), introduced(assumption)).
% 2.17/1.69 tff(1847,plain,
% 2.17/1.69 ((X!1 = Z!5) <=> (Z!5 = X!1)),
% 2.17/1.69 inference(symmetry,[status(thm)],[348])).
% 2.17/1.69 tff(1848,plain,
% 2.17/1.69 ((~(X!1 = Z!5)) <=> (~(Z!5 = X!1))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1847])).
% 2.17/1.69 tff(1849,plain,
% 2.17/1.69 (~(Z!5 = X!1)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[347, 1848])).
% 2.17/1.69 tff(1850,plain,
% 2.17/1.69 (Z!5 = Y!0),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[361, 1849])).
% 2.17/1.69 tff(1851,plain,
% 2.17/1.69 (Y!0 = Z!5),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1850, 434])).
% 2.17/1.69 tff(1852,plain,
% 2.17/1.69 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[432, 1851, 431])).
% 2.17/1.69 tff(1853,plain,
% 2.17/1.69 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[451, 1852])).
% 2.17/1.69 tff(1854,plain,
% 2.17/1.69 ((tptp_fun_W_3(Y!0) = Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(commutativity,[status(thm)],[])).
% 2.17/1.69 tff(1855,plain,
% 2.17/1.69 ((Y!0 = tptp_fun_W_3(Y!0)) <=> (tptp_fun_W_3(Y!0) = Y!0)),
% 2.17/1.69 inference(symmetry,[status(thm)],[1854])).
% 2.17/1.69 tff(1856,plain,
% 2.17/1.69 ((~(Y!0 = tptp_fun_W_3(Y!0))) <=> (~(tptp_fun_W_3(Y!0) = Y!0))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1855])).
% 2.17/1.69 tff(1857,assumption,(~(tptp_fun_X_2(Y!0) = Y!0)), introduced(assumption)).
% 2.17/1.69 tff(1858,plain,
% 2.17/1.69 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(1859,plain,
% 2.17/1.69 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1858, 1857, 1846])).
% 2.17/1.69 tff(1860,plain,
% 2.17/1.69 ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(1861,plain,
% 2.17/1.69 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1860, 1859])).
% 2.17/1.69 tff(1862,plain,
% 2.17/1.69 ((~(big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(Y!0 = tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(1863,plain,
% 2.17/1.69 (~(Y!0 = tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1862, 1861, 35])).
% 2.17/1.69 tff(1864,plain,
% 2.17/1.69 (~(tptp_fun_W_3(Y!0) = Y!0)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1863, 1856])).
% 2.17/1.69 tff(1865,plain,
% 2.17/1.69 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_3(Y!0) = X!1) | (tptp_fun_W_3(Y!0) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_3(Y!0) = X!1) | (tptp_fun_W_3(Y!0) = Y!0))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(1866,plain,
% 2.17/1.69 (((tptp_fun_W_3(Y!0) = Y!0) | (tptp_fun_W_3(Y!0) = X!1)) <=> ((tptp_fun_W_3(Y!0) = X!1) | (tptp_fun_W_3(Y!0) = Y!0))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(1867,plain,
% 2.17/1.69 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_3(Y!0) = Y!0) | (tptp_fun_W_3(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_3(Y!0) = X!1) | (tptp_fun_W_3(Y!0) = Y!0)))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1866])).
% 2.17/1.69 tff(1868,plain,
% 2.17/1.69 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_3(Y!0) = Y!0) | (tptp_fun_W_3(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_3(Y!0) = X!1) | (tptp_fun_W_3(Y!0) = Y!0))),
% 2.17/1.69 inference(transitivity,[status(thm)],[1867, 1865])).
% 2.17/1.69 tff(1869,plain,
% 2.17/1.69 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_W_3(Y!0) = Y!0) | (tptp_fun_W_3(Y!0) = X!1))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(1870,plain,
% 2.17/1.69 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_W_3(Y!0) = X!1) | (tptp_fun_W_3(Y!0) = Y!0)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 2.17/1.69 tff(1871,plain,
% 2.17/1.69 ((tptp_fun_W_3(Y!0) = X!1) | (tptp_fun_W_3(Y!0) = Y!0)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1870, 12])).
% 2.17/1.69 tff(1872,plain,
% 2.17/1.69 (tptp_fun_W_3(Y!0) = X!1),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1871, 1864])).
% 2.17/1.69 tff(1873,plain,
% 2.17/1.69 (tptp_fun_W_3(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.17/1.69 inference(transitivity,[status(thm)],[1872, 599])).
% 2.17/1.69 tff(1874,plain,
% 2.17/1.69 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_X_2(Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_X_2(Y!0) = X!1))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(1875,plain,
% 2.17/1.69 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_X_2(Y!0) = X!1))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(1876,plain,
% 2.17/1.69 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_X_2(Y!0) = X!1)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 2.17/1.69 tff(1877,plain,
% 2.17/1.69 ((tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_X_2(Y!0) = X!1)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1876, 12])).
% 2.17/1.69 tff(1878,plain,
% 2.17/1.69 (tptp_fun_X_2(Y!0) = X!1),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1877, 1857])).
% 2.17/1.69 tff(1879,plain,
% 2.17/1.69 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1878, 1873])).
% 2.17/1.69 tff(1880,plain,
% 2.17/1.69 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(symmetry,[status(thm)],[1879])).
% 2.17/1.69 tff(1881,plain,
% 2.17/1.69 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1880])).
% 2.17/1.69 tff(1882,plain,
% 2.17/1.69 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[42, 1881])).
% 2.17/1.69 tff(1883,plain,
% 2.17/1.69 (((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(1884,plain,
% 2.17/1.69 ((big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> $true) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(1885,plain,
% 2.17/1.69 ((tptp_fun_W_3(Y!0) = tptp_fun_W_3(Y!0)) <=> $true),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(1886,plain,
% 2.17/1.69 ((big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> (tptp_fun_W_3(Y!0) = tptp_fun_W_3(Y!0))) <=> (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> $true)),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1885])).
% 2.17/1.69 tff(1887,plain,
% 2.17/1.69 ((big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> (tptp_fun_W_3(Y!0) = tptp_fun_W_3(Y!0))) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(transitivity,[status(thm)],[1886, 1884])).
% 2.17/1.69 tff(1888,plain,
% 2.17/1.69 (((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> (tptp_fun_W_3(Y!0) = tptp_fun_W_3(Y!0)))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[1887])).
% 2.17/1.69 tff(1889,plain,
% 2.17/1.69 (((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> (tptp_fun_W_3(Y!0) = tptp_fun_W_3(Y!0)))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(transitivity,[status(thm)],[1888, 1883])).
% 2.17/1.69 tff(1890,plain,
% 2.17/1.69 ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> (tptp_fun_W_3(Y!0) = tptp_fun_W_3(Y!0)))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(1891,plain,
% 2.17/1.69 ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 2.17/1.69 tff(1892,plain,
% 2.17/1.69 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1891, 1859])).
% 2.17/1.69 tff(1893,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1892, 1882])).
% 2.17/1.69 tff(1894,plain,((tptp_fun_X_2(Y!0) = Y!0) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(1895,plain,
% 2.17/1.70 (tptp_fun_X_2(Y!0) = Y!0),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1894, 35, 598, 42, 1846])).
% 2.17/1.70 tff(1896,plain,
% 2.17/1.70 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1895, 1828])).
% 2.17/1.70 tff(1897,plain,
% 2.17/1.70 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1896])).
% 2.17/1.70 tff(1898,assumption,(big_f(Y!0, tptp_fun_W_6(Y!0))), introduced(assumption)).
% 2.17/1.70 tff(1899,plain,
% 2.17/1.70 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 2.17/1.70 tff(1900,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[35, 1899])).
% 2.17/1.70 tff(1901,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | (~big_f(Y!0, tptp_fun_W_6(Y!0))) | (~(tptp_fun_W_6(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(1902,plain,
% 2.17/1.70 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1901, 1853, 1827, 598, 42, 1846])).
% 2.17/1.70 tff(1903,assumption,(tptp_fun_Y_7(Y!0, X!1) = Y!0), introduced(assumption)).
% 2.17/1.70 tff(1904,plain,
% 2.17/1.70 (Y!0 = tptp_fun_Y_7(Y!0, X!1)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1903])).
% 2.17/1.70 tff(1905,plain,
% 2.17/1.70 (Y!0 = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.17/1.70 inference(transitivity,[status(thm)],[1904, 1829])).
% 2.17/1.70 tff(1906,assumption,(tptp_fun_X_2(Y!0) = X!1), introduced(assumption)).
% 2.17/1.70 tff(1907,plain,
% 2.17/1.70 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1906, 1905])).
% 2.17/1.70 tff(1908,plain,
% 2.17/1.70 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1907])).
% 2.17/1.70 tff(1909,plain,
% 2.17/1.70 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (~big_f(tptp_fun_X_2(Y!0), Y!0))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1908])).
% 2.17/1.70 tff(1910,plain,
% 2.17/1.70 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[1049, 1909])).
% 2.17/1.70 tff(1911,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[692, 1910])).
% 2.17/1.70 tff(1912,plain,((~(tptp_fun_X_2(Y!0) = X!1)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) | (~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) | (~(tptp_fun_W_6(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(1913,plain,
% 2.17/1.70 (~(tptp_fun_X_2(Y!0) = X!1)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1912, 1902, 1049, 1845, 1827])).
% 2.17/1.70 tff(1914,plain,
% 2.17/1.70 (tptp_fun_X_2(Y!0) = Y!0),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1877, 1913])).
% 2.17/1.70 tff(1915,assumption,((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))), introduced(assumption)).
% 2.17/1.70 tff(1916,plain,
% 2.17/1.70 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[52, 1914, 1915])).
% 2.17/1.70 tff(1917,plain,
% 2.17/1.70 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[50, 1916])).
% 2.17/1.70 tff(1918,plain,
% 2.17/1.70 (tptp_fun_Y_4(Y!0, Y!0) = Y!0),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1077, 1917, 598, 1914, 41])).
% 2.17/1.70 tff(1919,plain,
% 2.17/1.70 (tptp_fun_Y_4(Y!0, Y!0) = tptp_fun_W_6(Y!0)),
% 2.17/1.70 inference(transitivity,[status(thm)],[1918, 1828])).
% 2.17/1.70 tff(1920,plain,
% 2.17/1.70 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1914, 1919])).
% 2.17/1.70 tff(1921,plain,
% 2.17/1.70 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.17/1.70 inference(symmetry,[status(thm)],[1920])).
% 2.17/1.70 tff(1922,plain,
% 2.17/1.70 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[1853, 1921])).
% 2.17/1.70 tff(1923,plain,
% 2.17/1.70 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1129, 1918, 1917])).
% 2.17/1.70 tff(1924,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1923, 1922])).
% 2.17/1.70 tff(1925,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_W_6(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))) | big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(1926,plain,
% 2.17/1.70 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1925, 1805, 1826, 41, 1764, 341, 1825, 1823, 1806])).
% 2.17/1.70 tff(1927,plain,
% 2.17/1.70 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[54, 1926])).
% 2.17/1.70 tff(1928,plain,
% 2.17/1.70 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[56, 1927])).
% 2.17/1.70 tff(1929,plain,
% 2.17/1.70 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[596, 1805, 41])).
% 2.17/1.70 tff(1930,plain,
% 2.17/1.70 (~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[563, 1929, 1763])).
% 2.17/1.70 tff(1931,plain,
% 2.17/1.70 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[561, 1930])).
% 2.17/1.70 tff(1932,plain,
% 2.17/1.70 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[84, 1931])).
% 2.17/1.70 tff(1933,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[82, 1932, 1928])).
% 2.17/1.70 tff(1934,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(X!1, Y!0) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(1935,plain,
% 2.17/1.70 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1934, 692, 45, 1672, 1663, 30, 41, 144])).
% 2.17/1.70 tff(1936,plain,
% 2.17/1.70 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[462, 1935])).
% 2.17/1.70 tff(1937,plain,
% 2.17/1.70 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[790, 1936])).
% 2.17/1.70 tff(1938,plain,
% 2.17/1.70 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[792, 1937])).
% 2.17/1.70 tff(1939,plain,
% 2.17/1.70 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1269, 1936])).
% 2.17/1.70 tff(1940,plain,
% 2.17/1.70 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1271, 1939])).
% 2.17/1.70 tff(1941,assumption,((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))), introduced(assumption)).
% 2.17/1.70 tff(1942,plain,
% 2.17/1.70 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1132, 40, 692, 30, 41])).
% 2.17/1.70 tff(1943,plain,
% 2.17/1.70 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[50, 1942])).
% 2.17/1.70 tff(1944,plain,
% 2.17/1.70 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[52, 1943, 30])).
% 2.17/1.70 tff(1945,plain,
% 2.17/1.70 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[54, 1944])).
% 2.17/1.70 tff(1946,plain,
% 2.17/1.70 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[56, 1945])).
% 2.17/1.70 tff(1947,plain,
% 2.17/1.70 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[82, 1946])).
% 2.17/1.70 tff(1948,plain,
% 2.17/1.70 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[88, 1947])).
% 2.17/1.70 tff(1949,plain,
% 2.17/1.70 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[191, 1948])).
% 2.17/1.70 tff(1950,plain,
% 2.17/1.70 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[786, 1949, 144, 45])).
% 2.17/1.70 tff(1951,plain,
% 2.17/1.70 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[788, 1950])).
% 2.17/1.70 tff(1952,plain,
% 2.17/1.70 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[794, 1951, 1941])).
% 2.17/1.70 tff(1953,plain,
% 2.17/1.70 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1952])).
% 2.17/1.70 tff(1954,assumption,((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))), introduced(assumption)).
% 2.17/1.70 tff(1955,plain,
% 2.17/1.70 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[84, 1947])).
% 2.17/1.70 tff(1956,plain,
% 2.17/1.70 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[561, 1955])).
% 2.17/1.70 tff(1957,plain,
% 2.17/1.70 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[563, 1956, 34])).
% 2.17/1.70 tff(1958,plain,
% 2.17/1.70 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[596, 1957, 41])).
% 2.17/1.70 tff(1959,plain,
% 2.17/1.70 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[576, 1957])).
% 2.17/1.70 tff(1960,plain,
% 2.17/1.70 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[751, 1959, 1958])).
% 2.17/1.70 tff(1961,plain,
% 2.17/1.70 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1191, 1960])).
% 2.17/1.70 tff(1962,plain,
% 2.17/1.70 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[594, 1961])).
% 2.17/1.70 tff(1963,plain,
% 2.17/1.70 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1260])).
% 2.17/1.70 tff(1964,plain,
% 2.17/1.70 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1963])).
% 2.17/1.70 tff(1965,plain,
% 2.17/1.70 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1964])).
% 2.17/1.70 tff(1966,plain,
% 2.17/1.70 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1965, 1789])).
% 2.17/1.70 tff(1967,plain,
% 2.17/1.70 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1966])).
% 2.17/1.70 tff(1968,plain,
% 2.17/1.70 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1967])).
% 2.17/1.70 tff(1969,assumption,((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))), introduced(assumption)).
% 2.17/1.70 tff(1970,assumption,(~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)), introduced(assumption)).
% 2.17/1.70 tff(1971,plain,
% 2.17/1.70 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))) | big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.17/1.70 inference(tautology,[status(thm)],[])).
% 2.17/1.70 tff(1972,plain,
% 2.17/1.70 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1971, 1970, 1969])).
% 2.17/1.70 tff(1973,plain,
% 2.17/1.70 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = X!1),
% 2.17/1.70 inference(transitivity,[status(thm)],[1972, 1672])).
% 2.17/1.70 tff(1974,plain,
% 2.17/1.70 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[1973, 599])).
% 2.17/1.70 tff(1975,plain,
% 2.17/1.70 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.17/1.70 inference(symmetry,[status(thm)],[1974])).
% 2.17/1.70 tff(1976,plain,
% 2.17/1.70 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[622, 1975])).
% 2.17/1.71 tff(1977,plain,
% 2.17/1.71 ($false),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1970, 1976])).
% 2.17/1.71 tff(1978,plain,(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.71 tff(1979,plain,
% 2.17/1.71 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1978, 1672, 598, 622, 1969])).
% 2.17/1.71 tff(1980,plain,
% 2.17/1.71 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))) | (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) | (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))),
% 2.17/1.71 inference(tautology,[status(thm)],[])).
% 2.17/1.71 tff(1981,plain,
% 2.17/1.71 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1980, 1979, 1969])).
% 2.17/1.71 tff(1982,plain,
% 2.17/1.71 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[1981, 1968])).
% 2.17/1.71 tff(1983,plain,
% 2.17/1.71 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(1984,plain,
% 2.17/1.71 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.17/1.71 inference(quant_inst,[status(thm)],[])).
% 2.17/1.71 tff(1985,plain,
% 2.17/1.71 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 2.17/1.71 tff(1986,plain,
% 2.17/1.71 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1985, 12])).
% 2.17/1.71 tff(1987,plain,
% 2.17/1.71 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = Y!0),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1986, 1982])).
% 2.17/1.71 tff(1988,plain,
% 2.17/1.71 (Y!0 = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.17/1.71 inference(symmetry,[status(thm)],[1987])).
% 2.17/1.71 tff(1989,plain,
% 2.17/1.71 (Y!0 = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.17/1.71 inference(transitivity,[status(thm)],[1988, 1965])).
% 2.17/1.71 tff(1990,plain,
% 2.17/1.71 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.17/1.71 inference(monotonicity,[status(thm)],[1989, 598])).
% 2.17/1.71 tff(1991,plain,
% 2.17/1.71 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.71 inference(symmetry,[status(thm)],[1990])).
% 2.17/1.71 tff(1992,plain,
% 2.17/1.71 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[1979, 1991])).
% 2.17/1.71 tff(1993,plain,
% 2.17/1.71 ($false),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[41, 1992])).
% 2.17/1.71 tff(1994,plain,((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | (~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.71 tff(1995,plain,
% 2.17/1.71 (~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1994, 1962, 1672, 40, 41, 1958])).
% 2.17/1.71 tff(1996,plain,
% 2.17/1.71 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))) | ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))),
% 2.17/1.71 inference(quant_inst,[status(thm)],[])).
% 2.17/1.71 tff(1997,plain,
% 2.17/1.71 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1996, 1995])).
% 2.17/1.71 tff(1998,plain,
% 2.17/1.71 (X!1 = W1!8),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1273, 1997, 1954])).
% 2.17/1.71 tff(1999,plain,
% 2.17/1.71 (X!1 = Y!0),
% 2.17/1.71 inference(transitivity,[status(thm)],[1998, 1953, 154])).
% 2.17/1.71 tff(2000,plain,
% 2.17/1.71 ($false),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[741, 1999])).
% 2.17/1.71 tff(2001,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | (~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.71 tff(2002,plain,
% 2.17/1.71 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2001, 1940, 1672, 41, 1938, 144, 45, 30, 692])).
% 2.17/1.71 tff(2003,plain,
% 2.17/1.71 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.71 inference(monotonicity,[status(thm)],[31, 2002])).
% 2.17/1.71 tff(2004,plain,
% 2.17/1.71 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.71 inference(symmetry,[status(thm)],[2003])).
% 2.17/1.71 tff(2005,plain,
% 2.17/1.71 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[692, 2004])).
% 2.17/1.71 tff(2006,plain,
% 2.17/1.71 ($false),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[41, 2005])).
% 2.17/1.71 tff(2007,plain,((~big_f(tptp_fun_X_2(Y!0), Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.71 tff(2008,plain,
% 2.17/1.71 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2007, 41, 30, 1672, 144, 45, 1663])).
% 2.17/1.71 tff(2009,plain,
% 2.17/1.71 (~(W1!8 = Y!0)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[524, 1456, 35, 45, 30])).
% 2.17/1.71 tff(2010,plain,
% 2.17/1.71 (W1!8 = X!1),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[19, 2009])).
% 2.17/1.71 tff(2011,plain,
% 2.17/1.71 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[803, 2009, 154])).
% 2.17/1.71 tff(2012,plain,
% 2.17/1.71 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8),
% 2.17/1.71 inference(transitivity,[status(thm)],[1765, 1672, 1469])).
% 2.17/1.71 tff(2013,plain,
% 2.17/1.71 (tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = tptp_fun_Z1_9(W1!8)),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2012])).
% 2.17/1.71 tff(2014,plain,
% 2.17/1.71 ((Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2013])).
% 2.17/1.71 tff(2015,plain,
% 2.17/1.71 ((Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.17/1.71 inference(transitivity,[status(thm)],[2014, 43])).
% 2.17/1.71 tff(2016,plain,
% 2.17/1.71 ((~(Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))) <=> (~(tptp_fun_Z1_9(W1!8) = Y!0))),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2015])).
% 2.17/1.71 tff(2017,plain,
% 2.17/1.71 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.17/1.71 inference(monotonicity,[status(thm)],[1766])).
% 2.17/1.71 tff(2018,plain,
% 2.17/1.71 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.17/1.71 inference(transitivity,[status(thm)],[2017, 24])).
% 2.17/1.71 tff(2019,plain,
% 2.17/1.71 ((W1!8 = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)),
% 2.17/1.71 inference(symmetry,[status(thm)],[2018])).
% 2.17/1.71 tff(2020,plain,
% 2.17/1.71 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[1289, 2019])).
% 2.17/1.71 tff(2021,plain,
% 2.17/1.71 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))))))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2022,plain,
% 2.17/1.71 ((~((~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))) | (~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))))) <=> (~((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1))))))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2023,plain,
% 2.17/1.71 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))) | (~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))))))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[2022])).
% 2.17/1.72 tff(2024,plain,
% 2.17/1.72 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))) | (~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))))))),
% 2.17/1.72 inference(transitivity,[status(thm)],[2023, 2021])).
% 2.17/1.72 tff(2025,plain,
% 2.17/1.72 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))) | (~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))))))),
% 2.17/1.72 inference(quant_inst,[status(thm)],[])).
% 2.17/1.72 tff(2026,plain,
% 2.17/1.72 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1))))))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 2.17/1.72 tff(2027,plain,
% 2.17/1.72 (~((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1)))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2026, 1268])).
% 2.17/1.72 tff(2028,plain,
% 2.17/1.72 (((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) = Z1))))) | ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))),
% 2.17/1.72 inference(tautology,[status(thm)],[])).
% 2.17/1.72 tff(2029,plain,
% 2.17/1.72 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2028, 2027])).
% 2.17/1.72 tff(2030,plain,
% 2.17/1.72 ((~((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))))) | (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))),
% 2.17/1.72 inference(tautology,[status(thm)],[])).
% 2.17/1.72 tff(2031,plain,
% 2.17/1.72 (![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2030, 2029, 2020])).
% 2.17/1.72 tff(2032,plain,
% 2.17/1.72 ((~![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))) | (big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))),
% 2.17/1.72 inference(quant_inst,[status(thm)],[])).
% 2.17/1.72 tff(2033,plain,
% 2.17/1.72 (big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2032, 2031])).
% 2.17/1.72 tff(2034,assumption,(~(tptp_fun_Y1_11(X!1) = W1!8)), introduced(assumption)).
% 2.17/1.72 tff(2035,plain,
% 2.17/1.72 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[794, 1279, 2034])).
% 2.17/1.72 tff(2036,plain,
% 2.17/1.72 ((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[788, 2035])).
% 2.17/1.72 tff(2037,plain,
% 2.17/1.72 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[786, 2036, 144, 45])).
% 2.17/1.72 tff(2038,plain,
% 2.17/1.72 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[191, 2037])).
% 2.17/1.72 tff(2039,plain,
% 2.17/1.72 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[88, 2038])).
% 2.17/1.72 tff(2040,plain,
% 2.17/1.72 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[82, 2039])).
% 2.17/1.72 tff(2041,plain,
% 2.17/1.72 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[56, 2040])).
% 2.17/1.72 tff(2042,plain,
% 2.17/1.72 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[54, 2041])).
% 2.17/1.72 tff(2043,plain,
% 2.17/1.72 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[52, 2042, 30])).
% 2.17/1.72 tff(2044,plain,
% 2.17/1.72 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[198, 2043])).
% 2.17/1.72 tff(2045,plain,
% 2.17/1.72 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[675, 2044, 35])).
% 2.17/1.72 tff(2046,plain,
% 2.17/1.72 (X!1 = tptp_fun_Y_4(X!1, Y!0)),
% 2.17/1.72 inference(symmetry,[status(thm)],[2045])).
% 2.17/1.72 tff(2047,plain,
% 2.17/1.72 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_Y_4(X!1, Y!0)),
% 2.17/1.72 inference(transitivity,[status(thm)],[1765, 1672, 2046])).
% 2.17/1.72 tff(2048,plain,
% 2.17/1.72 (big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[31, 2047])).
% 2.17/1.72 tff(2049,plain,
% 2.17/1.72 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.17/1.72 inference(symmetry,[status(thm)],[2048])).
% 2.17/1.72 tff(2050,plain,
% 2.17/1.72 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (~big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[2049])).
% 2.17/1.72 tff(2051,plain,
% 2.17/1.72 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[236, 2045, 2044])).
% 2.17/1.72 tff(2052,plain,
% 2.17/1.72 (~big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 2.17/1.72 tff(2053,plain,
% 2.17/1.72 ((~(big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))) | big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) | (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))),
% 2.17/1.72 inference(tautology,[status(thm)],[])).
% 2.17/1.72 tff(2054,plain,
% 2.17/1.72 (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2053, 2052, 2033])).
% 2.17/1.72 tff(2055,plain,
% 2.17/1.72 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2054, 2016])).
% 2.17/1.72 tff(2056,plain,
% 2.17/1.72 ((X!1 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.17/1.72 inference(commutativity,[status(thm)],[])).
% 2.17/1.72 tff(2057,plain,
% 2.17/1.72 ((X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[2013])).
% 2.17/1.72 tff(2058,plain,
% 2.17/1.72 ((X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.17/1.72 inference(transitivity,[status(thm)],[2057, 2056])).
% 2.17/1.72 tff(2059,plain,
% 2.17/1.72 ((~(X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[2058])).
% 2.17/1.72 tff(2060,plain,
% 2.17/1.72 ((~![X1: $i] : (big_f(X1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))) | (big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))),
% 2.17/1.72 inference(quant_inst,[status(thm)],[])).
% 2.17/1.72 tff(2061,plain,
% 2.17/1.72 (big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2060, 2031])).
% 2.17/1.72 tff(2062,plain,
% 2.17/1.72 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[220, 2040])).
% 2.17/1.72 tff(2063,plain,
% 2.17/1.72 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1713, 2062])).
% 2.17/1.72 tff(2064,plain,
% 2.17/1.72 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1711, 2063, 1663])).
% 2.17/1.72 tff(2065,plain,
% 2.17/1.72 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1709, 2064])).
% 2.17/1.72 tff(2066,plain,
% 2.17/1.72 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1692, 2065, 1663, 45])).
% 2.17/1.72 tff(2067,plain,
% 2.17/1.72 (tptp_fun_Y_4(X!1, X!1) = X!1),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1694, 2065, 2066])).
% 2.17/1.72 tff(2068,plain,
% 2.17/1.72 (X!1 = tptp_fun_Y_4(X!1, X!1)),
% 2.17/1.72 inference(symmetry,[status(thm)],[2067])).
% 2.17/1.72 tff(2069,plain,
% 2.17/1.72 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_Y_4(X!1, X!1)),
% 2.17/1.72 inference(transitivity,[status(thm)],[1765, 1672, 2068])).
% 2.17/1.72 tff(2070,plain,
% 2.17/1.72 (big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[1664, 2069])).
% 2.17/1.72 tff(2071,plain,
% 2.17/1.72 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.17/1.72 inference(symmetry,[status(thm)],[2070])).
% 2.17/1.72 tff(2072,plain,
% 2.17/1.72 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (~big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[2071])).
% 2.17/1.72 tff(2073,plain,
% 2.17/1.72 (~big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2066, 2072])).
% 2.17/1.72 tff(2074,plain,
% 2.17/1.72 ((~(big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))) | big_f(X!1, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) | (~(X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))))),
% 2.17/1.72 inference(tautology,[status(thm)],[])).
% 2.17/1.72 tff(2075,plain,
% 2.17/1.72 (~(X!1 = tptp_fun_Z1_9(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2074, 2073, 2061])).
% 2.17/1.72 tff(2076,plain,
% 2.17/1.72 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2075, 2059])).
% 2.17/1.72 tff(2077,plain,
% 2.17/1.72 ($false),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[522, 2076, 2055])).
% 2.17/1.72 tff(2078,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~(W1!8 = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0) | (tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(X!1) = W1!8)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.72 tff(2079,plain,
% 2.17/1.72 ($false),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2078, 2011, 2010, 1672, 30, 1663, 45, 35, 144, 1268])).
% 2.17/1.72 tff(2080,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.72 tff(2081,plain,
% 2.17/1.72 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2080, 2008, 30, 1663, 45, 1672, 144])).
% 2.17/1.72 tff(2082,plain,
% 2.17/1.72 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[462, 2081])).
% 2.17/1.72 tff(2083,plain,
% 2.17/1.72 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1746, 2082, 144, 45, 41, 1663, 30])).
% 2.17/1.72 tff(2084,plain,
% 2.17/1.72 (big_f(Y!0, Y!0) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1748, 2083])).
% 2.17/1.72 tff(2085,plain,
% 2.17/1.72 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, Y!0))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[1751])).
% 2.17/1.72 tff(2086,plain,
% 2.17/1.72 (~big_f(Y!0, Y!0)),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2008, 2085])).
% 2.17/1.72 tff(2087,plain,
% 2.17/1.72 ((~(big_f(Y!0, Y!0) <=> (Y!0 = tptp_fun_W_6(Y!0)))) | big_f(Y!0, Y!0) | (~(Y!0 = tptp_fun_W_6(Y!0)))),
% 2.17/1.72 inference(tautology,[status(thm)],[])).
% 2.17/1.72 tff(2088,plain,
% 2.17/1.72 (~(Y!0 = tptp_fun_W_6(Y!0))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2087, 2086, 2084])).
% 2.17/1.72 tff(2089,plain,
% 2.17/1.72 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2088, 1673])).
% 2.17/1.73 tff(2090,plain,
% 2.17/1.73 (tptp_fun_W_6(Y!0) = X!1),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[403, 2089])).
% 2.17/1.73 tff(2091,plain,
% 2.17/1.73 (X!1 = tptp_fun_W_6(Y!0)),
% 2.17/1.73 inference(symmetry,[status(thm)],[2090])).
% 2.17/1.73 tff(2092,plain,
% 2.17/1.73 ((tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0)) <=> (tptp_fun_Y1_11(Y!0) = X!1)),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2090])).
% 2.17/1.73 tff(2093,plain,
% 2.17/1.73 ((~(tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0))) <=> (~(tptp_fun_Y1_11(Y!0) = X!1))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2092])).
% 2.17/1.73 tff(2094,plain,
% 2.17/1.73 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1758, 2083])).
% 2.17/1.73 tff(2095,plain,
% 2.17/1.73 (~(tptp_fun_Y1_11(Y!0) = tptp_fun_W_6(Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1761, 2094])).
% 2.17/1.73 tff(2096,plain,
% 2.17/1.73 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2095, 2093])).
% 2.17/1.73 tff(2097,plain,
% 2.17/1.73 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[39, 2096])).
% 2.17/1.73 tff(2098,plain,
% 2.17/1.73 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[189, 2097, 144, 45, 41])).
% 2.17/1.73 tff(2099,plain,
% 2.17/1.73 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[191, 2098])).
% 2.17/1.73 tff(2100,plain,
% 2.17/1.73 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[88, 2099])).
% 2.17/1.73 tff(2101,plain,
% 2.17/1.73 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[82, 2100])).
% 2.17/1.73 tff(2102,plain,
% 2.17/1.73 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[56, 2101])).
% 2.17/1.73 tff(2103,plain,
% 2.17/1.73 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[54, 2102])).
% 2.17/1.73 tff(2104,plain,
% 2.17/1.73 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[52, 2103, 30])).
% 2.17/1.73 tff(2105,plain,
% 2.17/1.73 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[198, 2104])).
% 2.17/1.73 tff(2106,plain,
% 2.17/1.73 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[675, 2105, 2008])).
% 2.17/1.73 tff(2107,plain,
% 2.17/1.73 (tptp_fun_Y_4(X!1, Y!0) = tptp_fun_W_6(Y!0)),
% 2.17/1.73 inference(transitivity,[status(thm)],[2106, 2091])).
% 2.17/1.73 tff(2108,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[30, 2107])).
% 2.17/1.73 tff(2109,plain,
% 2.17/1.73 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.73 inference(symmetry,[status(thm)],[2108])).
% 2.17/1.73 tff(2110,plain,
% 2.17/1.73 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[451, 2083])).
% 2.17/1.73 tff(2111,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 2.17/1.73 tff(2112,plain,
% 2.17/1.73 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[236, 2106, 2105])).
% 2.17/1.73 tff(2113,plain,
% 2.17/1.73 ($false),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2112, 2111])).
% 2.17/1.73 tff(2114,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.73 tff(2115,plain,
% 2.17/1.73 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2114, 1663, 144, 45, 30, 1672])).
% 2.17/1.73 tff(2116,plain,
% 2.17/1.73 (tptp_fun_Y_4(X!1, Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.17/1.73 inference(transitivity,[status(thm)],[859, 599])).
% 2.17/1.73 tff(2117,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[30, 2116])).
% 2.17/1.73 tff(2118,plain,
% 2.17/1.73 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.73 inference(symmetry,[status(thm)],[2117])).
% 2.17/1.73 tff(2119,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[135, 2118])).
% 2.17/1.73 tff(2120,plain,
% 2.17/1.73 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[236, 859, 214])).
% 2.17/1.73 tff(2121,plain,
% 2.17/1.73 ($false),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2120, 2119])).
% 2.17/1.73 tff(2122,plain,((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.73 tff(2123,plain,
% 2.17/1.73 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2122, 669, 135, 30, 35])).
% 2.17/1.73 tff(2124,plain,
% 2.17/1.73 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[39, 2123])).
% 2.17/1.73 tff(2125,plain,
% 2.17/1.73 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.73 inference(monotonicity,[status(thm)],[31, 2124])).
% 2.17/1.73 tff(2126,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.73 inference(symmetry,[status(thm)],[2125])).
% 2.17/1.73 tff(2127,plain,
% 2.17/1.73 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2126])).
% 2.17/1.73 tff(2128,plain,
% 2.17/1.73 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[35, 2127])).
% 2.17/1.73 tff(2129,plain,
% 2.17/1.73 ($false),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[135, 2128])).
% 2.17/1.73 tff(2130,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.73 tff(2131,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2130, 2115, 30, 144, 45])).
% 2.17/1.73 tff(2132,plain,
% 2.17/1.73 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1329, 2131, 154, 30, 45])).
% 2.17/1.73 tff(2133,plain,
% 2.17/1.73 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[788, 2132])).
% 2.17/1.73 tff(2134,plain,
% 2.17/1.73 (~((~big_f(tptp_fun_X1_13(Y!0, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Y!0, Y!0) = Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[140, 109, 135, 45])).
% 2.17/1.73 tff(2135,plain,
% 2.17/1.73 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[115, 2134])).
% 2.17/1.73 tff(2136,plain,
% 2.17/1.73 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[113, 2135, 109])).
% 2.17/1.73 tff(2137,plain,
% 2.17/1.73 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[86, 2136])).
% 2.17/1.73 tff(2138,plain,
% 2.17/1.73 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[84, 2137])).
% 2.17/1.73 tff(2139,plain,
% 2.17/1.73 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[82, 2138])).
% 2.17/1.73 tff(2140,plain,
% 2.17/1.73 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[56, 2139])).
% 2.17/1.73 tff(2141,plain,
% 2.17/1.73 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[54, 2140])).
% 2.17/1.73 tff(2142,plain,
% 2.17/1.73 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[52, 2141, 30])).
% 2.17/1.73 tff(2143,plain,
% 2.17/1.73 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[50, 2142])).
% 2.17/1.73 tff(2144,plain,
% 2.17/1.73 (tptp_fun_Y_4(Y!0, Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.17/1.73 inference(transitivity,[status(thm)],[1334, 146])).
% 2.17/1.73 tff(2145,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[30, 2144])).
% 2.17/1.73 tff(2146,plain,
% 2.17/1.73 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.17/1.73 inference(symmetry,[status(thm)],[2145])).
% 2.17/1.73 tff(2147,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[135, 2146])).
% 2.17/1.73 tff(2148,plain,
% 2.17/1.73 ($false),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[107, 2147])).
% 2.17/1.73 tff(2149,plain,(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.73 tff(2150,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2149, 2143, 135, 30, 109])).
% 2.17/1.73 tff(2151,plain,
% 2.17/1.73 (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1129, 2150, 2143])).
% 2.17/1.73 tff(2152,plain,
% 2.17/1.73 (tptp_fun_Y_4(Y!0, Y!0) = X!1),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[95, 2151])).
% 2.17/1.73 tff(2153,plain,
% 2.17/1.73 (X!1 = tptp_fun_Y_4(Y!0, Y!0)),
% 2.17/1.73 inference(symmetry,[status(thm)],[2152])).
% 2.17/1.73 tff(2154,plain,
% 2.17/1.73 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[220, 2139])).
% 2.17/1.73 tff(2155,plain,
% 2.17/1.73 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1713, 2154])).
% 2.17/1.73 tff(2156,plain,
% 2.17/1.73 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1711, 2155, 1663])).
% 2.17/1.73 tff(2157,plain,
% 2.17/1.73 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1709, 2156])).
% 2.17/1.73 tff(2158,plain,
% 2.17/1.73 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1707, 2157, 1663, 45])).
% 2.17/1.73 tff(2159,plain,
% 2.17/1.73 (X!1 = tptp_fun_Y_4(Y!0, Y!0)),
% 2.17/1.73 inference(symmetry,[status(thm)],[108])).
% 2.17/1.73 tff(2160,plain,
% 2.17/1.73 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[389, 2159])).
% 2.17/1.73 tff(2161,plain,
% 2.17/1.73 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(Z!5, X!1)),
% 2.17/1.73 inference(symmetry,[status(thm)],[2160])).
% 2.17/1.73 tff(2162,assumption,(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))), introduced(assumption)).
% 2.17/1.73 tff(2163,plain,
% 2.17/1.73 (big_f(Z!5, X!1)),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 2.17/1.73 tff(2164,plain,
% 2.17/1.73 (X!1 = tptp_fun_W_6(Z!5)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[989, 2163, 1212])).
% 2.17/1.73 tff(2165,plain,
% 2.17/1.73 (X!1 = Y!0),
% 2.17/1.73 inference(transitivity,[status(thm)],[2164, 1211])).
% 2.17/1.73 tff(2166,plain,
% 2.17/1.73 ($false),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[741, 2165])).
% 2.17/1.73 tff(2167,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) | (~(tptp_fun_Y_4(Y!0, Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.73 tff(2168,plain,
% 2.17/1.73 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2167, 2152, 2150, 30, 692, 2158])).
% 2.17/1.73 tff(2169,plain,
% 2.17/1.73 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[462, 2168])).
% 2.17/1.73 tff(2170,plain,
% 2.17/1.73 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1269, 2169])).
% 2.17/1.73 tff(2171,plain,
% 2.17/1.73 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1271, 2170])).
% 2.17/1.73 tff(2172,plain,
% 2.17/1.73 ((W1!8 = X!1) <=> (X!1 = W1!8)),
% 2.17/1.73 inference(symmetry,[status(thm)],[24])).
% 2.17/1.73 tff(2173,plain,
% 2.17/1.73 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1329, 692, 796, 30, 45])).
% 2.17/1.73 tff(2174,plain,
% 2.17/1.73 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[788, 2173])).
% 2.17/1.73 tff(2175,plain,
% 2.17/1.73 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[790, 2169])).
% 2.17/1.73 tff(2176,plain,
% 2.17/1.73 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[792, 2175])).
% 2.17/1.73 tff(2177,plain,
% 2.17/1.73 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[794, 2176, 2174])).
% 2.17/1.73 tff(2178,plain,
% 2.17/1.73 (W1!8 = Y!0),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[803, 2177, 796])).
% 2.17/1.73 tff(2179,plain,
% 2.17/1.73 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2178])).
% 2.17/1.73 tff(2180,plain,
% 2.17/1.73 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.17/1.73 inference(transitivity,[status(thm)],[2179, 46])).
% 2.17/1.73 tff(2181,plain,
% 2.17/1.73 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.17/1.73 inference(symmetry,[status(thm)],[2180])).
% 2.17/1.73 tff(2182,plain,
% 2.17/1.73 ((X!1 = Y!0) <=> (X!1 = W1!8)),
% 2.17/1.73 inference(transitivity,[status(thm)],[2181, 2172])).
% 2.17/1.73 tff(2183,plain,
% 2.17/1.73 ((~(X!1 = Y!0)) <=> (~(X!1 = W1!8))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2182])).
% 2.23/1.74 tff(2184,plain,
% 2.23/1.74 (~(X!1 = W1!8)),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[741, 2183])).
% 2.23/1.74 tff(2185,plain,
% 2.23/1.74 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1273, 2184, 2171])).
% 2.23/1.74 tff(2186,plain,
% 2.23/1.74 ((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1256, 2185])).
% 2.23/1.74 tff(2187,plain,
% 2.23/1.74 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1692, 2157, 1663, 45])).
% 2.23/1.74 tff(2188,plain,
% 2.23/1.74 (tptp_fun_Y_4(X!1, X!1) = X!1),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1694, 1702, 1675])).
% 2.23/1.74 tff(2189,assumption,(tptp_fun_X1_10(Y!0, X!1) = X!1), introduced(assumption)).
% 2.23/1.74 tff(2190,plain,
% 2.23/1.74 (X!1 = tptp_fun_X1_10(Y!0, X!1)),
% 2.23/1.74 inference(symmetry,[status(thm)],[2189])).
% 2.23/1.74 tff(2191,plain,
% 2.23/1.74 (tptp_fun_X_2(X!1) = tptp_fun_X1_10(Y!0, X!1)),
% 2.23/1.74 inference(transitivity,[status(thm)],[1663, 2190])).
% 2.23/1.74 tff(2192,plain,
% 2.23/1.74 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.23/1.74 inference(monotonicity,[status(thm)],[2191, 2188])).
% 2.23/1.74 tff(2193,plain,
% 2.23/1.74 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.23/1.74 inference(symmetry,[status(thm)],[2192])).
% 2.23/1.74 tff(2194,assumption,(big_f(tptp_fun_X1_10(Y!0, X!1), X!1)), introduced(assumption)).
% 2.23/1.74 tff(2195,plain,
% 2.23/1.74 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 2.23/1.74 tff(2196,plain,
% 2.23/1.74 ($false),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1702, 2195])).
% 2.23/1.74 tff(2197,plain,(big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) | (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) | (~(tptp_fun_X1_10(Y!0, X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/1.74 tff(2198,plain,
% 2.23/1.74 ($false),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2197, 1250, 1244, 1663, 1702, 1675])).
% 2.23/1.74 tff(2199,plain,((tptp_fun_X1_10(Y!0, X!1) = Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.23/1.74 tff(2200,plain,
% 2.23/1.74 (tptp_fun_X1_10(Y!0, X!1) = Y!0),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2199, 2187, 1663, 2157, 2186])).
% 2.23/1.74 tff(2201,plain,
% 2.23/1.74 (tptp_fun_X1_10(Y!0, X!1) = tptp_fun_X_2(Y!0)),
% 2.23/1.74 inference(transitivity,[status(thm)],[2200, 31])).
% 2.23/1.74 tff(2202,plain,
% 2.23/1.74 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.23/1.74 inference(monotonicity,[status(thm)],[2201, 2153])).
% 2.23/1.74 tff(2203,plain,
% 2.23/1.74 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.23/1.74 inference(symmetry,[status(thm)],[2202])).
% 2.23/1.74 tff(2204,plain,
% 2.23/1.74 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[2150, 2203])).
% 2.23/1.74 tff(2205,plain,
% 2.23/1.74 (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1230, 2200, 2186])).
% 2.23/1.74 tff(2206,plain,
% 2.23/1.74 ($false),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2205, 2204])).
% 2.23/1.74 tff(2207,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | big_f(X!1, Y!0) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.23/1.74 tff(2208,plain,
% 2.23/1.74 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2207, 1663, 30, 154, 2131, 45, 2115])).
% 2.23/1.74 tff(2209,plain,
% 2.23/1.74 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[39, 2208])).
% 2.23/1.74 tff(2210,plain,
% 2.23/1.74 (tptp_fun_Y_4(X!1, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.23/1.74 inference(transitivity,[status(thm)],[1695, 599])).
% 2.23/1.74 tff(2211,plain,
% 2.23/1.74 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.23/1.74 inference(monotonicity,[status(thm)],[1663, 2210])).
% 2.23/1.74 tff(2212,plain,
% 2.23/1.74 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.23/1.74 inference(symmetry,[status(thm)],[2211])).
% 2.23/1.74 tff(2213,plain,
% 2.23/1.74 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[622, 2212])).
% 2.23/1.74 tff(2214,plain,
% 2.23/1.74 ($false),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1693, 2213])).
% 2.23/1.74 tff(2215,plain,((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.23/1.74 tff(2216,plain,
% 2.23/1.74 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2215, 622, 40, 1663, 45])).
% 2.23/1.74 tff(2217,plain,
% 2.23/1.74 (~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1709, 2216])).
% 2.23/1.74 tff(2218,plain,
% 2.23/1.74 (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1711, 2217, 1663])).
% 2.23/1.74 tff(2219,plain,
% 2.23/1.74 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1713, 2218])).
% 2.23/1.74 tff(2220,plain,
% 2.23/1.74 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[220, 2219])).
% 2.23/1.74 tff(2221,plain,
% 2.23/1.74 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[82, 2220])).
% 2.23/1.74 tff(2222,plain,
% 2.23/1.74 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[84, 2221])).
% 2.23/1.74 tff(2223,plain,
% 2.23/1.74 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[561, 2222])).
% 2.23/1.74 tff(2224,plain,
% 2.23/1.74 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[563, 2223, 34])).
% 2.23/1.74 tff(2225,plain,
% 2.23/1.74 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[583, 2224])).
% 2.23/1.74 tff(2226,plain,
% 2.23/1.74 (Y!0 = tptp_fun_Z1_12(Y!0)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1181, 2225, 135])).
% 2.23/1.74 tff(2227,plain,
% 2.23/1.74 (tptp_fun_Z1_12(Y!0) = Y!0),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[2226, 581])).
% 2.23/1.74 tff(2228,plain,
% 2.23/1.74 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[576, 2224])).
% 2.23/1.74 tff(2229,plain,
% 2.23/1.74 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[751, 2228, 622])).
% 2.23/1.74 tff(2230,plain,
% 2.23/1.74 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1191, 2229])).
% 2.23/1.74 tff(2231,plain,
% 2.23/1.74 ($false),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2230, 2227])).
% 2.23/1.74 tff(2232,plain,((~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (tptp_fun_Y1_11(Y!0) = Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.23/1.74 tff(2233,plain,
% 2.23/1.74 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2232, 2115, 2208, 1663, 45])).
% 2.23/1.74 tff(2234,plain,
% 2.23/1.74 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1206, 2233, 2209, 45])).
% 2.23/1.74 tff(2235,plain,
% 2.23/1.74 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1219, 2115, 2209, 2131, 30, 2234])).
% 2.23/1.74 tff(2236,plain,
% 2.23/1.74 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[462, 2235])).
% 2.23/1.74 tff(2237,plain,
% 2.23/1.74 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[790, 2236])).
% 2.23/1.74 tff(2238,plain,
% 2.23/1.74 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[792, 2237])).
% 2.23/1.74 tff(2239,plain,
% 2.23/1.74 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[794, 2238, 2133])).
% 2.23/1.74 tff(2240,plain,
% 2.23/1.74 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.23/1.74 inference(symmetry,[status(thm)],[2239])).
% 2.23/1.74 tff(2241,plain,
% 2.23/1.74 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1254, 2209, 2233, 2115])).
% 2.23/1.74 tff(2242,plain,
% 2.23/1.74 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1256, 2241])).
% 2.23/1.74 tff(2243,plain,
% 2.23/1.74 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1269, 2236])).
% 2.23/1.74 tff(2244,plain,
% 2.23/1.74 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1271, 2243])).
% 2.23/1.74 tff(2245,plain,
% 2.23/1.74 (X!1 = W1!8),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[1273, 2244, 2242])).
% 2.23/1.74 tff(2246,plain,
% 2.23/1.74 (W1!8 = X!1),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[28, 2245])).
% 2.23/1.74 tff(2247,plain,
% 2.23/1.74 (X!1 = W1!8),
% 2.23/1.74 inference(symmetry,[status(thm)],[2246])).
% 2.23/1.74 tff(2248,plain,
% 2.23/1.74 (X!1 = Y!0),
% 2.23/1.74 inference(transitivity,[status(thm)],[2247, 2240, 154])).
% 2.23/1.74 tff(2249,plain,
% 2.23/1.74 ($false),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[741, 2248])).
% 2.23/1.74 tff(2250,plain,((~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | (tptp_fun_Y1_11(X!1) = X!1) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/1.74 tff(2251,plain,
% 2.23/1.74 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2250, 45, 1663, 30, 144])).
% 2.23/1.74 tff(2252,plain,
% 2.23/1.74 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0))),
% 2.23/1.74 inference(rewrite,[status(thm)],[])).
% 2.23/1.74 tff(2253,plain,
% 2.23/1.74 (((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) <=> ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0))),
% 2.23/1.74 inference(rewrite,[status(thm)],[])).
% 2.23/1.74 tff(2254,plain,
% 2.23/1.74 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)))),
% 2.23/1.74 inference(monotonicity,[status(thm)],[2253])).
% 2.23/1.74 tff(2255,plain,
% 2.23/1.74 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0))),
% 2.23/1.74 inference(transitivity,[status(thm)],[2254, 2252])).
% 2.23/1.74 tff(2256,plain,
% 2.23/1.74 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.23/1.74 inference(quant_inst,[status(thm)],[])).
% 2.23/1.74 tff(2257,plain,
% 2.23/1.74 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 2.23/1.74 tff(2258,plain,
% 2.23/1.74 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2257, 12])).
% 2.23/1.74 tff(2259,plain,
% 2.23/1.74 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.23/1.74 inference(unit_resolution,[status(thm)],[2258, 2251])).
% 2.23/1.74 tff(2260,plain,
% 2.23/1.74 (Y!0 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.23/1.74 inference(symmetry,[status(thm)],[2259])).
% 2.23/1.74 tff(2261,plain,
% 2.23/1.74 (tptp_fun_X_2(Y!0) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.23/1.74 inference(transitivity,[status(thm)],[30, 2260, 1671])).
% 2.23/1.74 tff(2262,plain,
% 2.23/1.74 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.23/1.74 inference(monotonicity,[status(thm)],[2261])).
% 2.23/1.74 tff(2263,plain,
% 2.23/1.74 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.23/1.74 inference(transitivity,[status(thm)],[2262, 1670, 1667])).
% 2.23/1.74 tff(2264,plain,
% 2.23/1.74 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)))),
% 2.23/1.74 inference(monotonicity,[status(thm)],[2263])).
% 2.23/1.74 tff(2265,plain,
% 2.23/1.74 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[35, 2264])).
% 2.23/1.74 tff(2266,plain,
% 2.23/1.74 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.23/1.74 inference(monotonicity,[status(thm)],[1665, 1663])).
% 2.23/1.74 tff(2267,plain,
% 2.23/1.74 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1))),
% 2.23/1.74 inference(symmetry,[status(thm)],[2266])).
% 2.23/1.74 tff(2268,plain,
% 2.23/1.74 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.23/1.74 inference(monotonicity,[status(thm)],[1668])).
% 2.23/1.74 tff(2269,plain,
% 2.23/1.74 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.23/1.74 inference(symmetry,[status(thm)],[2268])).
% 2.23/1.74 tff(2270,plain,
% 2.23/1.74 ((X!1 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.23/1.74 inference(commutativity,[status(thm)],[])).
% 2.23/1.74 tff(2271,plain,
% 2.23/1.74 (Y!0 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.23/1.74 inference(transitivity,[status(thm)],[2260, 1671])).
% 2.23/1.74 tff(2272,plain,
% 2.23/1.74 ((X!1 = Y!0) <=> (X!1 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.23/1.74 inference(monotonicity,[status(thm)],[2271])).
% 2.23/1.74 tff(2273,plain,
% 2.23/1.74 ((X!1 = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.23/1.74 inference(transitivity,[status(thm)],[2272, 2270])).
% 2.23/1.74 tff(2274,plain,
% 2.23/1.74 ((X!1 = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1))),
% 2.23/1.74 inference(transitivity,[status(thm)],[2273, 2269, 2267])).
% 2.23/1.74 tff(2275,plain,
% 2.23/1.74 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1)))),
% 2.23/1.74 inference(monotonicity,[status(thm)],[2274])).
% 2.23/1.74 tff(2276,plain,
% 2.23/1.74 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1))),
% 2.23/1.74 inference(modus_ponens,[status(thm)],[741, 2275])).
% 2.23/1.74 tff(2277,plain,
% 2.23/1.74 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1)))) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1))),
% 2.23/1.75 inference(tautology,[status(thm)],[])).
% 2.23/1.75 tff(2278,plain,
% 2.23/1.75 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1)))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[2277, 2276, 2265])).
% 2.23/1.75 tff(2279,plain,
% 2.23/1.75 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))) | ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y1_11(X!1)) = tptp_fun_X_2(X!1)))),
% 2.23/1.75 inference(quant_inst,[status(thm)],[])).
% 2.23/1.75 tff(2280,plain,
% 2.23/1.75 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[2279, 2278])).
% 2.23/1.75 tff(2281,plain,
% 2.23/1.75 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[661, 45, 30, 35, 144])).
% 2.23/1.75 tff(2282,plain,
% 2.23/1.75 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[191, 2281])).
% 2.23/1.75 tff(2283,plain,
% 2.23/1.75 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[88, 2282])).
% 2.23/1.75 tff(2284,plain,
% 2.23/1.75 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[82, 2283])).
% 2.23/1.75 tff(2285,plain,
% 2.23/1.75 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[220, 2284])).
% 2.23/1.75 tff(2286,plain,
% 2.23/1.75 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1713, 2285])).
% 2.23/1.75 tff(2287,plain,
% 2.23/1.75 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1711, 2286, 1663])).
% 2.23/1.75 tff(2288,plain,
% 2.23/1.75 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1709, 2287])).
% 2.23/1.75 tff(2289,plain,
% 2.23/1.75 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1707, 2288, 1663, 45])).
% 2.23/1.75 tff(2290,plain,
% 2.23/1.75 (~(X!1 = Z!5)),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[346, 345, 2289])).
% 2.23/1.75 tff(2291,plain,
% 2.23/1.75 (~(Z!5 = X!1)),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[353, 2290])).
% 2.23/1.75 tff(2292,plain,
% 2.23/1.75 (Z!5 = Y!0),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[361, 2291])).
% 2.23/1.75 tff(2293,plain,
% 2.23/1.75 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.23/1.75 inference(monotonicity,[status(thm)],[2292])).
% 2.23/1.75 tff(2294,plain,
% 2.23/1.75 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.23/1.75 inference(monotonicity,[status(thm)],[2293])).
% 2.23/1.75 tff(2295,plain,
% 2.23/1.75 ((X!1 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.23/1.75 inference(transitivity,[status(thm)],[2294, 1537])).
% 2.23/1.75 tff(2296,plain,
% 2.23/1.75 ((~(X!1 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.23/1.75 inference(monotonicity,[status(thm)],[2295])).
% 2.23/1.75 tff(2297,plain,
% 2.23/1.75 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[56, 2284])).
% 2.23/1.75 tff(2298,plain,
% 2.23/1.75 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[54, 2297])).
% 2.23/1.75 tff(2299,plain,
% 2.23/1.75 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[52, 2298, 30])).
% 2.23/1.75 tff(2300,plain,
% 2.23/1.75 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[198, 2299])).
% 2.23/1.75 tff(2301,plain,
% 2.23/1.75 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[675, 2300, 35])).
% 2.23/1.75 tff(2302,plain,
% 2.23/1.75 (X!1 = tptp_fun_Y_4(X!1, Y!0)),
% 2.23/1.75 inference(symmetry,[status(thm)],[2301])).
% 2.23/1.75 tff(2303,plain,
% 2.23/1.75 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.23/1.75 inference(transitivity,[status(thm)],[2292, 31])).
% 2.23/1.75 tff(2304,plain,
% 2.23/1.75 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.23/1.75 inference(monotonicity,[status(thm)],[2303, 2302])).
% 2.23/1.75 tff(2305,plain,
% 2.23/1.75 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Z!5, X!1)),
% 2.23/1.75 inference(symmetry,[status(thm)],[2304])).
% 2.23/1.75 tff(2306,plain,
% 2.23/1.75 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (~big_f(Z!5, X!1))),
% 2.23/1.75 inference(monotonicity,[status(thm)],[2305])).
% 2.23/1.75 tff(2307,plain,
% 2.23/1.75 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[236, 2301, 2300])).
% 2.23/1.75 tff(2308,plain,
% 2.23/1.75 (~big_f(Z!5, X!1)),
% 2.23/1.75 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 2.23/1.75 tff(2309,plain,
% 2.23/1.75 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1547, 2308, 1212])).
% 2.23/1.75 tff(2310,plain,
% 2.23/1.75 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.23/1.75 inference(modus_ponens,[status(thm)],[2309, 2296])).
% 2.23/1.75 tff(2311,plain,
% 2.23/1.75 (tptp_fun_W_6(Y!0) = Y!0),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[403, 2310])).
% 2.23/1.75 tff(2312,plain,
% 2.23/1.75 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.23/1.75 inference(monotonicity,[status(thm)],[31, 2311])).
% 2.23/1.75 tff(2313,plain,
% 2.23/1.75 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.23/1.75 inference(symmetry,[status(thm)],[2312])).
% 2.23/1.75 tff(2314,plain,
% 2.23/1.75 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.23/1.75 inference(monotonicity,[status(thm)],[2313])).
% 2.23/1.75 tff(2315,plain,
% 2.23/1.75 (~big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.23/1.75 inference(modus_ponens,[status(thm)],[35, 2314])).
% 2.23/1.75 tff(2316,plain,
% 2.23/1.75 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[2130, 45, 30, 35, 144])).
% 2.23/1.75 tff(2317,plain,
% 2.23/1.75 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1746, 341, 1663, 144, 45, 2316, 30])).
% 2.23/1.75 tff(2318,plain,
% 2.23/1.75 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[451, 2317])).
% 2.23/1.75 tff(2319,plain,
% 2.23/1.75 ($false),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[2318, 2315])).
% 2.23/1.75 tff(2320,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.23/1.75 tff(2321,plain,
% 2.23/1.75 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[2320, 45, 30, 1663, 144, 35])).
% 2.23/1.75 tff(2322,plain,
% 2.23/1.75 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[462, 2321])).
% 2.23/1.75 tff(2323,plain,
% 2.23/1.75 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[790, 2322])).
% 2.23/1.75 tff(2324,plain,
% 2.23/1.75 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[792, 2323])).
% 2.23/1.75 tff(2325,plain,
% 2.23/1.75 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[481, 2322])).
% 2.23/1.75 tff(2326,plain,
% 2.23/1.75 (~(W1!8 = Y!0)),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[524, 2325, 30, 35, 45])).
% 2.23/1.75 tff(2327,plain,
% 2.23/1.75 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[803, 2326, 154])).
% 2.23/1.75 tff(2328,plain,
% 2.23/1.75 ($false),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[794, 2327, 2324, 2280])).
% 2.23/1.75 tff(2329,plain,(big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/1.75 tff(2330,plain,
% 2.23/1.75 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[2329, 45, 144, 1663, 30])).
% 2.23/1.75 tff(2331,plain,
% 2.23/1.75 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[2232, 135, 1663, 45, 34])).
% 2.23/1.75 tff(2332,plain,
% 2.23/1.75 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1254, 2331, 40, 135])).
% 2.23/1.75 tff(2333,plain,
% 2.23/1.75 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1256, 2332])).
% 2.23/1.75 tff(2334,plain,
% 2.23/1.75 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1206, 2331, 40, 45])).
% 2.23/1.75 tff(2335,plain,
% 2.23/1.75 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1219, 2334, 40, 692, 30, 135])).
% 2.23/1.75 tff(2336,plain,
% 2.23/1.75 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[462, 2335])).
% 2.23/1.75 tff(2337,plain,
% 2.23/1.75 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1269, 2336])).
% 2.23/1.75 tff(2338,plain,
% 2.23/1.75 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1271, 2337])).
% 2.23/1.75 tff(2339,plain,
% 2.23/1.75 (X!1 = W1!8),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[1273, 2338, 2333])).
% 2.23/1.75 tff(2340,plain,
% 2.23/1.75 (W1!8 = X!1),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[28, 2339])).
% 2.23/1.75 tff(2341,plain,
% 2.23/1.75 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[790, 2336])).
% 2.23/1.75 tff(2342,plain,
% 2.23/1.75 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.23/1.75 inference(unit_resolution,[status(thm)],[792, 2341])).
% 2.23/1.75 tff(2343,plain,
% 2.23/1.75 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[794, 2342, 2174])).
% 2.24/1.75 tff(2344,assumption,(~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)), introduced(assumption)).
% 2.24/1.75 tff(2345,plain,
% 2.24/1.75 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[2258, 2344])).
% 2.24/1.75 tff(2346,plain,
% 2.24/1.75 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1),
% 2.24/1.75 inference(transitivity,[status(thm)],[2345, 1786, 2343, 2340])).
% 2.24/1.75 tff(2347,plain,
% 2.24/1.75 ($false),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[2344, 2346])).
% 2.24/1.75 tff(2348,plain,((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.75 tff(2349,plain,
% 2.24/1.75 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[2348, 2251, 154, 2330, 30, 45, 1663, 34])).
% 2.24/1.75 tff(2350,plain,
% 2.24/1.75 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[1132, 2349, 40, 30, 2330])).
% 2.24/1.75 tff(2351,plain,
% 2.24/1.75 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[50, 2350])).
% 2.24/1.75 tff(2352,plain,
% 2.24/1.75 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[52, 2351, 30])).
% 2.24/1.75 tff(2353,plain,
% 2.24/1.75 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[54, 2352])).
% 2.24/1.75 tff(2354,plain,
% 2.24/1.75 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[56, 2353])).
% 2.24/1.75 tff(2355,plain,
% 2.24/1.75 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[82, 2354])).
% 2.24/1.75 tff(2356,plain,
% 2.24/1.75 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[84, 2355])).
% 2.24/1.75 tff(2357,plain,
% 2.24/1.75 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[561, 2356])).
% 2.24/1.75 tff(2358,plain,
% 2.24/1.75 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[563, 2357, 34])).
% 2.24/1.75 tff(2359,plain,
% 2.24/1.75 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[596, 2358, 2349])).
% 2.24/1.75 tff(2360,plain,
% 2.24/1.75 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[576, 2358])).
% 2.24/1.75 tff(2361,plain,
% 2.24/1.75 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[751, 2360, 2359])).
% 2.24/1.75 tff(2362,plain,
% 2.24/1.75 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[1191, 2361])).
% 2.24/1.75 tff(2363,plain,
% 2.24/1.75 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[594, 2362])).
% 2.24/1.75 tff(2364,plain,
% 2.24/1.75 (tptp_fun_Z1_12(Y!0) = tptp_fun_X_2(X!1)),
% 2.24/1.75 inference(transitivity,[status(thm)],[2363, 1664])).
% 2.24/1.75 tff(2365,plain,
% 2.24/1.75 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1))),
% 2.24/1.75 inference(monotonicity,[status(thm)],[2364])).
% 2.24/1.75 tff(2366,plain,
% 2.24/1.75 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[718, 2349, 40, 30, 2330])).
% 2.24/1.75 tff(2367,plain,
% 2.24/1.75 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[720, 2366])).
% 2.24/1.75 tff(2368,plain,
% 2.24/1.75 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[627, 2359, 45, 40])).
% 2.24/1.75 tff(2369,plain,
% 2.24/1.75 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[629, 2368])).
% 2.24/1.75 tff(2370,plain,
% 2.24/1.75 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[743, 2369, 40, 2367])).
% 2.24/1.75 tff(2371,plain,
% 2.24/1.75 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[462, 2370])).
% 2.24/1.75 tff(2372,plain,
% 2.24/1.75 (~((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[746, 2371])).
% 2.24/1.75 tff(2373,plain,
% 2.24/1.75 ((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[748, 2372])).
% 2.24/1.75 tff(2374,plain,
% 2.24/1.75 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.24/1.75 inference(monotonicity,[status(thm)],[2363])).
% 2.24/1.75 tff(2375,plain,
% 2.24/1.75 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.24/1.75 inference(transitivity,[status(thm)],[2374, 24])).
% 2.24/1.75 tff(2376,plain,
% 2.24/1.75 ((W1!8 = X!1) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.24/1.75 inference(symmetry,[status(thm)],[2375])).
% 2.24/1.75 tff(2377,plain,
% 2.24/1.75 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[1329, 2330, 154, 30, 45])).
% 2.24/1.75 tff(2378,plain,
% 2.24/1.75 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[788, 2377])).
% 2.24/1.75 tff(2379,plain,
% 2.24/1.75 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[790, 2371])).
% 2.24/1.75 tff(2380,plain,
% 2.24/1.75 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[792, 2379])).
% 2.24/1.75 tff(2381,plain,
% 2.24/1.75 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[794, 2380, 2378])).
% 2.24/1.75 tff(2382,plain,
% 2.24/1.75 (W1!8 = Y!0),
% 2.24/1.75 inference(unit_resolution,[status(thm)],[803, 2381, 154])).
% 2.24/1.75 tff(2383,plain,
% 2.24/1.75 (W1!8 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.24/1.75 inference(transitivity,[status(thm)],[2382, 2260])).
% 2.24/1.75 tff(2384,plain,
% 2.24/1.75 ((W1!8 = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.24/1.75 inference(monotonicity,[status(thm)],[2383])).
% 2.24/1.75 tff(2385,plain,
% 2.24/1.75 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) <=> (W1!8 = X!1)),
% 2.24/1.75 inference(symmetry,[status(thm)],[2384])).
% 2.24/1.76 tff(2386,plain,
% 2.24/1.76 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.24/1.76 inference(transitivity,[status(thm)],[2385, 2376])).
% 2.24/1.76 tff(2387,plain,
% 2.24/1.76 ((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) <=> (~(tptp_fun_Z1_12(Y!0) = W1!8))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2386])).
% 2.24/1.76 tff(2388,plain,
% 2.24/1.76 (~(tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.24/1.76 inference(modus_ponens,[status(thm)],[2251, 2387])).
% 2.24/1.76 tff(2389,plain,
% 2.24/1.76 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[811, 2388, 2373])).
% 2.24/1.76 tff(2390,plain,
% 2.24/1.76 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))) | ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))))),
% 2.24/1.76 inference(quant_inst,[status(thm)],[])).
% 2.24/1.76 tff(2391,plain,
% 2.24/1.76 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2390, 2389])).
% 2.24/1.76 tff(2392,plain,
% 2.24/1.76 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))) | (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(quant_inst,[status(thm)],[])).
% 2.24/1.76 tff(2393,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2392, 2358])).
% 2.24/1.76 tff(2394,plain,
% 2.24/1.76 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))) | (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(quant_inst,[status(thm)],[])).
% 2.24/1.76 tff(2395,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2394, 2358])).
% 2.24/1.76 tff(2396,plain,
% 2.24/1.76 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[813, 2389])).
% 2.24/1.76 tff(2397,plain,
% 2.24/1.76 (tptp_fun_Z1_12(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.24/1.76 inference(transitivity,[status(thm)],[1260, 599])).
% 2.24/1.76 tff(2398,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2397])).
% 2.24/1.76 tff(2399,plain,
% 2.24/1.76 ((X!1 = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.76 inference(commutativity,[status(thm)],[])).
% 2.24/1.76 tff(2400,assumption,(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))), introduced(assumption)).
% 2.24/1.76 tff(2401,plain,
% 2.24/1.76 (tptp_fun_Y1_11(Y!0) = tptp_fun_X_2(X!1)),
% 2.24/1.76 inference(transitivity,[status(thm)],[598, 1664])).
% 2.24/1.76 tff(2402,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2401])).
% 2.24/1.76 tff(2403,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(symmetry,[status(thm)],[2402])).
% 2.24/1.76 tff(2404,plain,
% 2.24/1.76 (tptp_fun_Z1_12(Y!0) = tptp_fun_X_2(X!1)),
% 2.24/1.76 inference(transitivity,[status(thm)],[1260, 1664])).
% 2.24/1.76 tff(2405,plain,
% 2.24/1.76 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2404])).
% 2.24/1.76 tff(2406,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2405, 2404])).
% 2.24/1.76 tff(2407,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(transitivity,[status(thm)],[2406, 2403])).
% 2.24/1.76 tff(2408,assumption,(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))), introduced(assumption)).
% 2.24/1.76 tff(2409,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 2.24/1.76 tff(2410,plain,
% 2.24/1.76 ((~(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)))) | (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(tautology,[status(thm)],[])).
% 2.24/1.76 tff(2411,plain,
% 2.24/1.76 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2410, 2409, 2400])).
% 2.24/1.76 tff(2412,plain,
% 2.24/1.76 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1),
% 2.24/1.76 inference(transitivity,[status(thm)],[2411, 1260])).
% 2.24/1.76 tff(2413,plain,
% 2.24/1.76 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))) <=> (X!1 = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2412])).
% 2.24/1.76 tff(2414,plain,
% 2.24/1.76 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.76 inference(transitivity,[status(thm)],[2413, 2399])).
% 2.24/1.76 tff(2415,plain,
% 2.24/1.76 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))) <=> (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2414])).
% 2.24/1.76 tff(2416,plain,
% 2.24/1.76 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2405])).
% 2.24/1.76 tff(2417,plain,
% 2.24/1.76 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))) <=> (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2416])).
% 2.24/1.76 tff(2418,assumption,((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))), introduced(assumption)).
% 2.24/1.76 tff(2419,plain,
% 2.24/1.76 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))))) | (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) | (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))))),
% 2.24/1.76 inference(tautology,[status(thm)],[])).
% 2.24/1.76 tff(2420,plain,
% 2.24/1.76 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2419, 2408, 2418])).
% 2.24/1.76 tff(2421,plain,
% 2.24/1.76 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(modus_ponens,[status(thm)],[2420, 2417])).
% 2.24/1.76 tff(2422,plain,
% 2.24/1.76 (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.76 inference(modus_ponens,[status(thm)],[2421, 2415])).
% 2.24/1.76 tff(2423,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[835, 2422, 834])).
% 2.24/1.76 tff(2424,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(modus_ponens,[status(thm)],[2423, 2398])).
% 2.24/1.76 tff(2425,assumption,(big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0))), introduced(assumption)).
% 2.24/1.76 tff(2426,plain,
% 2.24/1.76 ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.76 inference(monotonicity,[status(thm)],[1260])).
% 2.24/1.76 tff(2427,plain,
% 2.24/1.76 ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(symmetry,[status(thm)],[2426])).
% 2.24/1.76 tff(2428,plain,
% 2.24/1.76 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(transitivity,[status(thm)],[2414, 2427])).
% 2.24/1.76 tff(2429,plain,
% 2.24/1.76 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))) <=> (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2428])).
% 2.24/1.76 tff(2430,plain,
% 2.24/1.76 (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(modus_ponens,[status(thm)],[2421, 2429])).
% 2.24/1.76 tff(2431,plain,
% 2.24/1.76 ((~(big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0)))) | (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))) | (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(tautology,[status(thm)],[])).
% 2.24/1.76 tff(2432,plain,
% 2.24/1.76 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2431, 2430, 2425])).
% 2.24/1.76 tff(2433,plain,
% 2.24/1.76 ($false),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2432, 2424])).
% 2.24/1.76 tff(2434,plain,((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0)))) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))) | (~(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)))) | (~(tptp_fun_X_2(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.76 tff(2435,plain,
% 2.24/1.76 (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2434, 2396, 40, 2395, 2363, 2393, 1663, 2391])).
% 2.24/1.76 tff(2436,plain,
% 2.24/1.76 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))))) | big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.24/1.76 inference(tautology,[status(thm)],[])).
% 2.24/1.76 tff(2437,plain,
% 2.24/1.76 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(unit_resolution,[status(thm)],[2436, 2435, 2391])).
% 2.24/1.76 tff(2438,plain,
% 2.24/1.76 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.24/1.76 inference(symmetry,[status(thm)],[2437])).
% 2.24/1.76 tff(2439,plain,
% 2.24/1.76 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1))),
% 2.24/1.76 inference(transitivity,[status(thm)],[2438, 2365])).
% 2.24/1.76 tff(2440,plain,
% 2.24/1.76 ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1)),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2439])).
% 2.24/1.76 tff(2441,plain,
% 2.24/1.76 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.76 inference(symmetry,[status(thm)],[2440])).
% 2.24/1.76 tff(2442,plain,
% 2.24/1.76 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1)),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2363])).
% 2.24/1.76 tff(2443,plain,
% 2.24/1.76 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.76 inference(transitivity,[status(thm)],[2442, 2441])).
% 2.24/1.76 tff(2444,plain,
% 2.24/1.76 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))) <=> (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2443])).
% 2.24/1.76 tff(2445,plain,
% 2.24/1.76 (tptp_fun_Y1_11(Y!0) = tptp_fun_X_2(X!1)),
% 2.24/1.76 inference(transitivity,[status(thm)],[40, 1664])).
% 2.24/1.76 tff(2446,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2445])).
% 2.24/1.76 tff(2447,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(symmetry,[status(thm)],[2446])).
% 2.24/1.76 tff(2448,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2365, 2364])).
% 2.24/1.76 tff(2449,plain,
% 2.24/1.76 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.76 inference(transitivity,[status(thm)],[2448, 2447])).
% 2.24/1.76 tff(2450,plain,
% 2.24/1.76 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)))),
% 2.24/1.76 inference(monotonicity,[status(thm)],[2449])).
% 2.24/1.76 tff(2451,plain,
% 2.24/1.77 (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2435, 2450])).
% 2.24/1.77 tff(2452,plain,
% 2.24/1.77 ((~(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)))) | big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)))),
% 2.24/1.77 inference(tautology,[status(thm)],[])).
% 2.24/1.77 tff(2453,plain,
% 2.24/1.77 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2452, 2451, 2393])).
% 2.24/1.77 tff(2454,plain,
% 2.24/1.77 (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2453, 2444])).
% 2.24/1.77 tff(2455,plain,
% 2.24/1.77 (X!1 = tptp_fun_Y1_11(Y!0)),
% 2.24/1.77 inference(symmetry,[status(thm)],[40])).
% 2.24/1.77 tff(2456,plain,
% 2.24/1.77 (tptp_fun_Z1_12(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.24/1.77 inference(transitivity,[status(thm)],[2363, 2455])).
% 2.24/1.77 tff(2457,plain,
% 2.24/1.77 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2456])).
% 2.24/1.77 tff(2458,plain,
% 2.24/1.77 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.24/1.77 inference(symmetry,[status(thm)],[2457])).
% 2.24/1.77 tff(2459,plain,
% 2.24/1.77 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2439, 2445])).
% 2.24/1.77 tff(2460,plain,
% 2.24/1.77 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.24/1.77 inference(symmetry,[status(thm)],[2459])).
% 2.24/1.77 tff(2461,plain,
% 2.24/1.77 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.24/1.77 inference(transitivity,[status(thm)],[2460, 2458])).
% 2.24/1.77 tff(2462,plain,
% 2.24/1.77 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2461])).
% 2.24/1.77 tff(2463,plain,
% 2.24/1.77 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1)))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2448])).
% 2.24/1.77 tff(2464,plain,
% 2.24/1.77 (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_X_2(X!1))),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2435, 2463])).
% 2.24/1.77 tff(2465,plain,
% 2.24/1.77 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2464, 2462])).
% 2.24/1.77 tff(2466,plain,
% 2.24/1.77 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[835, 2465, 2396])).
% 2.24/1.77 tff(2467,plain,
% 2.24/1.77 ($false),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2466, 2454])).
% 2.24/1.77 tff(2468,plain,(big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | (tptp_fun_Y1_11(Y!0) = Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.77 tff(2469,plain,
% 2.24/1.77 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2468, 144, 45, 30, 1662])).
% 2.24/1.77 tff(2470,plain,
% 2.24/1.77 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2329, 144, 45, 1662, 30])).
% 2.24/1.77 tff(2471,plain,
% 2.24/1.77 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2207, 2470, 1662, 30, 154, 45, 2469])).
% 2.24/1.77 tff(2472,plain,
% 2.24/1.77 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[1139, 2470, 30, 2471])).
% 2.24/1.77 tff(2473,plain,
% 2.24/1.77 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[50, 2472])).
% 2.24/1.77 tff(2474,plain,
% 2.24/1.77 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[52, 2473, 30])).
% 2.24/1.77 tff(2475,plain,
% 2.24/1.77 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[54, 2474])).
% 2.24/1.77 tff(2476,plain,
% 2.24/1.77 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[189, 2471, 144, 45, 2469])).
% 2.24/1.77 tff(2477,plain,
% 2.24/1.77 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[191, 2476])).
% 2.24/1.77 tff(2478,plain,
% 2.24/1.77 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[88, 2477])).
% 2.24/1.77 tff(2479,plain,
% 2.24/1.77 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[82, 2478])).
% 2.24/1.77 tff(2480,plain,
% 2.24/1.77 ($false),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[56, 2479, 2475])).
% 2.24/1.77 tff(2481,plain,((tptp_fun_Y1_11(X!1) = X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.77 tff(2482,plain,
% 2.24/1.77 (tptp_fun_Y1_11(X!1) = X!1),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2481, 45, 30])).
% 2.24/1.77 tff(2483,plain,
% 2.24/1.77 (X!1 = tptp_fun_X_2(X!1)),
% 2.24/1.77 inference(symmetry,[status(thm)],[1662])).
% 2.24/1.77 tff(2484,plain,
% 2.24/1.77 ((~(X!1 = tptp_fun_Z1_9(W1!8))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2056])).
% 2.24/1.77 tff(2485,plain,
% 2.24/1.77 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[1713, 1436])).
% 2.24/1.77 tff(2486,plain,
% 2.24/1.77 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[1711, 2485, 1662])).
% 2.24/1.77 tff(2487,plain,
% 2.24/1.77 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[1709, 2486])).
% 2.24/1.77 tff(2488,plain,
% 2.24/1.77 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[1707, 2487, 1662, 45])).
% 2.24/1.77 tff(2489,plain,
% 2.24/1.77 (X!1 = tptp_fun_Y1_11(X!1)),
% 2.24/1.77 inference(symmetry,[status(thm)],[2482])).
% 2.24/1.77 tff(2490,plain,
% 2.24/1.77 (tptp_fun_Y_4(X!1, Y!0) = tptp_fun_Y1_11(X!1)),
% 2.24/1.77 inference(transitivity,[status(thm)],[1445, 2489])).
% 2.24/1.77 tff(2491,plain,
% 2.24/1.77 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[30, 2490])).
% 2.24/1.77 tff(2492,plain,
% 2.24/1.77 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (~big_f(Y!0, tptp_fun_Y1_11(X!1)))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2491])).
% 2.24/1.77 tff(2493,plain,
% 2.24/1.77 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[236, 1445, 1444])).
% 2.24/1.77 tff(2494,plain,
% 2.24/1.77 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 2.24/1.77 tff(2495,plain,
% 2.24/1.77 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[363])).
% 2.24/1.77 tff(2496,plain,
% 2.24/1.77 ((X!1 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.24/1.77 inference(transitivity,[status(thm)],[2495, 1537])).
% 2.24/1.77 tff(2497,plain,
% 2.24/1.77 ((~(X!1 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2496])).
% 2.24/1.77 tff(2498,plain,
% 2.24/1.77 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[362, 889])).
% 2.24/1.77 tff(2499,plain,
% 2.24/1.77 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Z!5, X!1)),
% 2.24/1.77 inference(symmetry,[status(thm)],[2498])).
% 2.24/1.77 tff(2500,plain,
% 2.24/1.77 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Z!5, X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2499])).
% 2.24/1.77 tff(2501,assumption,(~big_f(Y!0, tptp_fun_Y1_11(X!1))), introduced(assumption)).
% 2.24/1.77 tff(2502,plain,
% 2.24/1.77 (~big_f(Z!5, X!1)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2501, 2500])).
% 2.24/1.77 tff(2503,plain,
% 2.24/1.77 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[1547, 2502, 1212])).
% 2.24/1.77 tff(2504,plain,
% 2.24/1.77 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2503, 2497])).
% 2.24/1.77 tff(2505,plain,
% 2.24/1.77 ($false),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[403, 2504, 396])).
% 2.24/1.77 tff(2506,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.77 tff(2507,plain,
% 2.24/1.77 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2506, 2494, 2482, 35, 30, 2488])).
% 2.24/1.77 tff(2508,plain,
% 2.24/1.77 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[462, 2507])).
% 2.24/1.77 tff(2509,plain,
% 2.24/1.77 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[481, 2508])).
% 2.24/1.77 tff(2510,plain,
% 2.24/1.77 (big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[496, 2509])).
% 2.24/1.77 tff(2511,plain,
% 2.24/1.77 (~(W1!8 = Y!0)),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[524, 2509, 30, 45, 35])).
% 2.24/1.77 tff(2512,plain,
% 2.24/1.77 (W1!8 = X!1),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[19, 2511])).
% 2.24/1.77 tff(2513,plain,
% 2.24/1.77 (big_f(X!1, W1!8) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2483, 2512])).
% 2.24/1.77 tff(2514,plain,
% 2.24/1.77 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(X!1, W1!8)),
% 2.24/1.77 inference(symmetry,[status(thm)],[2513])).
% 2.24/1.77 tff(2515,plain,
% 2.24/1.77 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(X!1, W1!8))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2514])).
% 2.24/1.77 tff(2516,plain,
% 2.24/1.77 (~big_f(X!1, W1!8)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[828, 2515])).
% 2.24/1.77 tff(2517,plain,
% 2.24/1.77 (~(X!1 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[502, 2516, 2510])).
% 2.24/1.77 tff(2518,plain,
% 2.24/1.77 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2517, 2484])).
% 2.24/1.77 tff(2519,plain,
% 2.24/1.77 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[483, 2509])).
% 2.24/1.77 tff(2520,plain,
% 2.24/1.77 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.24/1.77 inference(transitivity,[status(thm)],[2512, 2489])).
% 2.24/1.77 tff(2521,plain,
% 2.24/1.77 (big_f(Y!0, W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2520])).
% 2.24/1.77 tff(2522,plain,
% 2.24/1.77 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, W1!8)),
% 2.24/1.77 inference(symmetry,[status(thm)],[2521])).
% 2.24/1.77 tff(2523,plain,
% 2.24/1.77 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, W1!8))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2522])).
% 2.24/1.77 tff(2524,plain,
% 2.24/1.77 (~big_f(Y!0, W1!8)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2494, 2523])).
% 2.24/1.77 tff(2525,plain,
% 2.24/1.77 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[516, 2524, 2519])).
% 2.24/1.77 tff(2526,plain,
% 2.24/1.77 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2525, 44])).
% 2.24/1.77 tff(2527,plain,
% 2.24/1.77 ($false),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[522, 2526, 2518])).
% 2.24/1.77 tff(2528,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.77 tff(2529,plain,
% 2.24/1.77 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[2528, 35, 30, 45, 828])).
% 2.24/1.77 tff(2530,plain,
% 2.24/1.77 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[82, 2529])).
% 2.24/1.77 tff(2531,plain,
% 2.24/1.77 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[88, 2530])).
% 2.24/1.77 tff(2532,plain,
% 2.24/1.77 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[90, 2531])).
% 2.24/1.77 tff(2533,plain,
% 2.24/1.77 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[269, 2532, 2482])).
% 2.24/1.77 tff(2534,plain,
% 2.24/1.77 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[879, 2533])).
% 2.24/1.77 tff(2535,plain,
% 2.24/1.77 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[271, 2533])).
% 2.24/1.77 tff(2536,plain,
% 2.24/1.77 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[483, 1456])).
% 2.24/1.77 tff(2537,plain,
% 2.24/1.77 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.24/1.77 inference(transitivity,[status(thm)],[1458, 2489])).
% 2.24/1.77 tff(2538,plain,
% 2.24/1.77 (big_f(Y!0, W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2537])).
% 2.24/1.77 tff(2539,plain,
% 2.24/1.77 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, W1!8)),
% 2.24/1.77 inference(symmetry,[status(thm)],[2538])).
% 2.24/1.77 tff(2540,plain,
% 2.24/1.77 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, W1!8))),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2539])).
% 2.24/1.77 tff(2541,plain,
% 2.24/1.77 (~big_f(Y!0, W1!8)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2501, 2540])).
% 2.24/1.77 tff(2542,plain,
% 2.24/1.77 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.77 inference(unit_resolution,[status(thm)],[516, 2541, 2536])).
% 2.24/1.77 tff(2543,plain,
% 2.24/1.77 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[2542, 44])).
% 2.24/1.77 tff(2544,plain,
% 2.24/1.77 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (X!1 = W1!8)),
% 2.24/1.77 inference(monotonicity,[status(thm)],[2482])).
% 2.24/1.77 tff(2545,plain,
% 2.24/1.77 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (W1!8 = X!1)),
% 2.24/1.77 inference(transitivity,[status(thm)],[2544, 24])).
% 2.24/1.77 tff(2546,plain,
% 2.24/1.77 ((W1!8 = X!1) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.24/1.77 inference(symmetry,[status(thm)],[2545])).
% 2.24/1.77 tff(2547,plain,
% 2.24/1.77 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.24/1.77 inference(modus_ponens,[status(thm)],[1458, 2546])).
% 2.24/1.77 tff(2548,plain,
% 2.24/1.77 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1465, 2547, 1460])).
% 2.24/1.78 tff(2549,plain,
% 2.24/1.78 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1467, 2548])).
% 2.24/1.78 tff(2550,plain,
% 2.24/1.78 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1490, 2549, 2482, 1458, 290])).
% 2.24/1.78 tff(2551,plain,
% 2.24/1.78 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[522, 2550])).
% 2.24/1.78 tff(2552,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2551, 2543])).
% 2.24/1.78 tff(2553,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(2554,plain,
% 2.24/1.78 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2553, 2501, 290, 30, 45, 35])).
% 2.24/1.78 tff(2555,plain,
% 2.24/1.78 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[462, 2554])).
% 2.24/1.78 tff(2556,plain,
% 2.24/1.78 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2506, 2555, 2482, 35, 30, 2501])).
% 2.24/1.78 tff(2557,plain,
% 2.24/1.78 (~(tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[337, 2556, 2482, 290, 45])).
% 2.24/1.78 tff(2558,plain,
% 2.24/1.78 (tptp_fun_X1_13(X!1, X!1) = Y!0),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[285, 2557])).
% 2.24/1.78 tff(2559,plain,
% 2.24/1.78 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2558])).
% 2.24/1.78 tff(2560,plain,
% 2.24/1.78 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(symmetry,[status(thm)],[2559])).
% 2.24/1.78 tff(2561,plain,
% 2.24/1.78 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2560])).
% 2.24/1.78 tff(2562,plain,
% 2.24/1.78 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[2501, 2561])).
% 2.24/1.78 tff(2563,plain,
% 2.24/1.78 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[291, 2557, 290])).
% 2.24/1.78 tff(2564,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2563, 2562])).
% 2.24/1.78 tff(2565,plain,(big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(2566,plain,
% 2.24/1.78 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2565, 2535, 45, 35, 30])).
% 2.24/1.78 tff(2567,plain,
% 2.24/1.78 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[901])).
% 2.24/1.78 tff(2568,plain,
% 2.24/1.78 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(symmetry,[status(thm)],[2567])).
% 2.24/1.78 tff(2569,assumption,(big_f(Y!0, tptp_fun_Y1_11(X!1))), introduced(assumption)).
% 2.24/1.78 tff(2570,plain,
% 2.24/1.78 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 2.24/1.78 tff(2571,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[908, 2570])).
% 2.24/1.78 tff(2572,plain,((~(tptp_fun_X1_13(Y!0, X!1) = Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(2573,plain,
% 2.24/1.78 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2572, 2566, 2534])).
% 2.24/1.78 tff(2574,plain,
% 2.24/1.78 (tptp_fun_X1_13(Y!0, X!1) = X!1),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[915, 2573])).
% 2.24/1.78 tff(2575,plain,
% 2.24/1.78 (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_X_2(X!1)),
% 2.24/1.78 inference(transitivity,[status(thm)],[2574, 2483])).
% 2.24/1.78 tff(2576,plain,
% 2.24/1.78 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2575, 2482])).
% 2.24/1.78 tff(2577,plain,
% 2.24/1.78 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(symmetry,[status(thm)],[2576])).
% 2.24/1.78 tff(2578,plain,
% 2.24/1.78 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2577])).
% 2.24/1.78 tff(2579,plain,
% 2.24/1.78 (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[828, 2578])).
% 2.24/1.78 tff(2580,plain,
% 2.24/1.78 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[920, 2573, 2534])).
% 2.24/1.78 tff(2581,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2580, 2579])).
% 2.24/1.78 tff(2582,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | big_f(tptp_fun_X_2(X!1), X!1) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(2583,plain,
% 2.24/1.78 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2582, 35, 45, 30])).
% 2.24/1.78 tff(2584,plain,
% 2.24/1.78 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1692, 1675, 45, 1663])).
% 2.24/1.78 tff(2585,plain,
% 2.24/1.78 (tptp_fun_Y_4(X!1, X!1) = X!1),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1694, 2584, 1675])).
% 2.24/1.78 tff(2586,plain,
% 2.24/1.78 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2585])).
% 2.24/1.78 tff(2587,plain,
% 2.24/1.78 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.24/1.78 inference(symmetry,[status(thm)],[2586])).
% 2.24/1.78 tff(2588,plain,
% 2.24/1.78 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[862, 2587])).
% 2.24/1.78 tff(2589,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2584, 2588])).
% 2.24/1.78 tff(2590,plain,((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | (~big_f(tptp_fun_X_2(X!1), X!1)) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(2591,plain,
% 2.24/1.78 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2590, 2583, 45, 1662])).
% 2.24/1.78 tff(2592,plain,
% 2.24/1.78 (~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1709, 2591])).
% 2.24/1.78 tff(2593,plain,
% 2.24/1.78 (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1711, 2592, 1662])).
% 2.24/1.78 tff(2594,plain,
% 2.24/1.78 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1713, 2593])).
% 2.24/1.78 tff(2595,plain,
% 2.24/1.78 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[220, 2594])).
% 2.24/1.78 tff(2596,plain,
% 2.24/1.78 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[82, 2595])).
% 2.24/1.78 tff(2597,plain,
% 2.24/1.78 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[88, 2596])).
% 2.24/1.78 tff(2598,plain,
% 2.24/1.78 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[90, 2597])).
% 2.24/1.78 tff(2599,plain,
% 2.24/1.78 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[269, 2598, 2482])).
% 2.24/1.78 tff(2600,plain,
% 2.24/1.78 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[879, 2599])).
% 2.24/1.78 tff(2601,plain,
% 2.24/1.78 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[271, 2599])).
% 2.24/1.78 tff(2602,plain,
% 2.24/1.78 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2565, 2601, 45, 35, 30])).
% 2.24/1.78 tff(2603,plain,
% 2.24/1.78 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1139, 692, 30, 41])).
% 2.24/1.78 tff(2604,plain,
% 2.24/1.78 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[50, 2603])).
% 2.24/1.78 tff(2605,plain,
% 2.24/1.78 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[52, 2604, 30])).
% 2.24/1.78 tff(2606,plain,
% 2.24/1.78 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[54, 2605])).
% 2.24/1.78 tff(2607,plain,
% 2.24/1.78 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[56, 2606])).
% 2.24/1.78 tff(2608,plain,
% 2.24/1.78 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[82, 2607])).
% 2.24/1.78 tff(2609,plain,
% 2.24/1.78 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1562, 2608, 41, 277])).
% 2.24/1.78 tff(2610,plain,
% 2.24/1.78 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.24/1.78 inference(monotonicity,[status(thm)],[31, 2609])).
% 2.24/1.78 tff(2611,plain,
% 2.24/1.78 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.78 inference(symmetry,[status(thm)],[2610])).
% 2.24/1.78 tff(2612,plain,
% 2.24/1.78 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[692, 2611])).
% 2.24/1.78 tff(2613,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[41, 2612])).
% 2.24/1.78 tff(2614,plain,((~big_f(tptp_fun_X_2(Y!0), Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(2615,plain,
% 2.24/1.78 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2614, 41, 30, 2482])).
% 2.24/1.78 tff(2616,plain,
% 2.24/1.78 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1562, 34, 41, 2482])).
% 2.24/1.78 tff(2617,plain,
% 2.24/1.78 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[82, 2616])).
% 2.24/1.78 tff(2618,plain,
% 2.24/1.78 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[220, 2617])).
% 2.24/1.78 tff(2619,plain,
% 2.24/1.78 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1713, 2618])).
% 2.24/1.78 tff(2620,assumption,((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))), introduced(assumption)).
% 2.24/1.78 tff(2621,plain,
% 2.24/1.78 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1711, 1663, 2620])).
% 2.24/1.78 tff(2622,plain,
% 2.24/1.78 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2215, 1663, 598, 622, 45])).
% 2.24/1.78 tff(2623,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1709, 2622, 2621])).
% 2.24/1.78 tff(2624,plain,((~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | big_f(X!1, Y!0) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(2625,plain,
% 2.24/1.78 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[2624, 2619, 45, 1662, 40])).
% 2.24/1.78 tff(2626,plain,
% 2.24/1.78 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1206, 2625, 40, 45])).
% 2.24/1.78 tff(2627,plain,
% 2.24/1.78 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1822, 2625, 40, 45])).
% 2.24/1.78 tff(2628,plain,
% 2.24/1.78 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[56, 2617])).
% 2.24/1.78 tff(2629,plain,
% 2.24/1.78 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[54, 2628])).
% 2.24/1.78 tff(2630,plain,
% 2.24/1.78 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1206, 42, 40, 45])).
% 2.24/1.78 tff(2631,plain,
% 2.24/1.78 (W1!8 = tptp_fun_Y1_11(Y!0)),
% 2.24/1.78 inference(transitivity,[status(thm)],[1289, 599])).
% 2.24/1.78 tff(2632,plain,
% 2.24/1.78 (big_f(X!1, W1!8) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2631])).
% 2.24/1.78 tff(2633,plain,
% 2.24/1.78 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, W1!8)),
% 2.24/1.78 inference(symmetry,[status(thm)],[2632])).
% 2.24/1.78 tff(2634,plain,
% 2.24/1.78 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(X!1, W1!8))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2633])).
% 2.24/1.78 tff(2635,plain,
% 2.24/1.78 (~big_f(X!1, W1!8)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[42, 2634])).
% 2.24/1.78 tff(2636,plain,
% 2.24/1.78 (~(X!1 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[502, 2635, 497])).
% 2.24/1.78 tff(2637,plain,
% 2.24/1.78 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[2636, 2484])).
% 2.24/1.78 tff(2638,plain,
% 2.24/1.78 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[522, 2637])).
% 2.24/1.78 tff(2639,plain,
% 2.24/1.78 (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[2638, 2631])).
% 2.24/1.78 tff(2640,plain,
% 2.24/1.78 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.24/1.78 inference(symmetry,[status(thm)],[2639])).
% 2.24/1.78 tff(2641,plain,
% 2.24/1.79 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2640])).
% 2.24/1.79 tff(2642,plain,
% 2.24/1.79 (~big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[41, 2641])).
% 2.24/1.79 tff(2643,plain,
% 2.24/1.79 (big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1506, 495])).
% 2.24/1.79 tff(2644,plain,
% 2.24/1.79 ($false),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2643, 2642])).
% 2.24/1.79 tff(2645,plain,((~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(W1!8 = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.79 tff(2646,plain,
% 2.24/1.79 (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2645, 42, 1289, 40, 41])).
% 2.24/1.79 tff(2647,plain,
% 2.24/1.79 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[481, 2646])).
% 2.24/1.79 tff(2648,plain,
% 2.24/1.79 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[462, 2647])).
% 2.24/1.79 tff(2649,plain,
% 2.24/1.79 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[342, 2648])).
% 2.24/1.79 tff(2650,plain,
% 2.24/1.79 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[344, 2649])).
% 2.24/1.79 tff(2651,plain,
% 2.24/1.79 (~(X!1 = Z!5)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[346, 2650, 2630])).
% 2.24/1.79 tff(2652,plain,
% 2.24/1.79 (~(Z!5 = X!1)),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[2651, 1848])).
% 2.24/1.79 tff(2653,plain,
% 2.24/1.79 (Z!5 = Y!0),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[361, 2652])).
% 2.24/1.79 tff(2654,plain,
% 2.24/1.79 (Y!0 = Z!5),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[2653, 434])).
% 2.24/1.79 tff(2655,plain,
% 2.24/1.79 (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[428, 2648])).
% 2.24/1.79 tff(2656,plain,
% 2.24/1.79 ((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[430, 2655])).
% 2.24/1.79 tff(2657,plain,
% 2.24/1.79 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[596, 42, 41])).
% 2.24/1.79 tff(2658,plain,
% 2.24/1.79 (~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[563, 2657, 34])).
% 2.24/1.79 tff(2659,plain,
% 2.24/1.79 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[561, 2658])).
% 2.24/1.79 tff(2660,plain,
% 2.24/1.79 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[84, 2659])).
% 2.24/1.79 tff(2661,plain,
% 2.24/1.79 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[82, 2660])).
% 2.24/1.79 tff(2662,plain,
% 2.24/1.79 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[56, 2661])).
% 2.24/1.79 tff(2663,plain,
% 2.24/1.79 (((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))) | ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.24/1.79 inference(tautology,[status(thm)],[])).
% 2.24/1.79 tff(2664,plain,
% 2.24/1.79 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2663, 2662])).
% 2.24/1.79 tff(2665,plain,
% 2.24/1.79 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1822, 42, 45, 40])).
% 2.24/1.79 tff(2666,plain,
% 2.24/1.79 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[54, 2662])).
% 2.24/1.79 tff(2667,plain,
% 2.24/1.79 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1925, 2648, 40, 41, 2666, 2665, 42, 2664, 2630])).
% 2.24/1.79 tff(2668,plain,
% 2.24/1.79 (tptp_fun_W_6(Y!0) = X!1),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[403, 2667])).
% 2.24/1.79 tff(2669,plain,
% 2.24/1.79 (tptp_fun_W_6(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.24/1.79 inference(transitivity,[status(thm)],[2668, 2455])).
% 2.24/1.79 tff(2670,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2669])).
% 2.24/1.79 tff(2671,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.24/1.79 inference(symmetry,[status(thm)],[2670])).
% 2.24/1.79 tff(2672,plain,
% 2.24/1.79 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2671])).
% 2.24/1.79 tff(2673,plain,
% 2.24/1.79 (~big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[41, 2672])).
% 2.24/1.79 tff(2674,plain,
% 2.24/1.79 (~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[451, 2673])).
% 2.24/1.79 tff(2675,plain,
% 2.24/1.79 (~(Y!0 = Z!5)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[432, 2674, 2656])).
% 2.24/1.79 tff(2676,plain,
% 2.24/1.79 ($false),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2675, 2654])).
% 2.24/1.79 tff(2677,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(W1!8 = X!1)) | (tptp_fun_Y1_11(Y!0) = Y!0) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.79 tff(2678,plain,
% 2.24/1.79 (~(W1!8 = X!1)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2677, 2625, 41, 45, 34])).
% 2.24/1.79 tff(2679,plain,
% 2.24/1.79 (W1!8 = Y!0),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[19, 2678])).
% 2.24/1.79 tff(2680,plain,
% 2.24/1.79 (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[524, 2679, 30, 45, 35])).
% 2.24/1.79 tff(2681,plain,
% 2.24/1.79 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[481, 2680])).
% 2.24/1.79 tff(2682,plain,
% 2.24/1.79 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[462, 2681])).
% 2.24/1.79 tff(2683,plain,
% 2.24/1.79 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1925, 2682, 41, 40, 2625, 2629, 1825, 2627, 2626])).
% 2.24/1.79 tff(2684,plain,
% 2.24/1.79 (tptp_fun_W_6(Y!0) = X!1),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[403, 2683])).
% 2.24/1.79 tff(2685,plain,
% 2.24/1.79 (tptp_fun_W_6(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.24/1.79 inference(transitivity,[status(thm)],[2684, 2489])).
% 2.24/1.79 tff(2686,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2685])).
% 2.24/1.79 tff(2687,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.24/1.79 inference(symmetry,[status(thm)],[2686])).
% 2.24/1.79 tff(2688,plain,
% 2.24/1.79 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2687])).
% 2.24/1.79 tff(2689,plain,
% 2.24/1.79 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.24/1.79 inference(transitivity,[status(thm)],[40, 2489])).
% 2.24/1.79 tff(2690,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2689])).
% 2.24/1.79 tff(2691,plain,
% 2.24/1.79 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_Y1_11(X!1)))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2690])).
% 2.24/1.79 tff(2692,plain,
% 2.24/1.79 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[41, 2691])).
% 2.24/1.79 tff(2693,plain,
% 2.24/1.79 (~big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[2692, 2688])).
% 2.24/1.79 tff(2694,plain,
% 2.24/1.79 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[441, 2682, 2626])).
% 2.24/1.79 tff(2695,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[451, 2694])).
% 2.24/1.79 tff(2696,plain,
% 2.24/1.79 ($false),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2695, 2693])).
% 2.24/1.79 tff(2697,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.79 tff(2698,plain,
% 2.24/1.79 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2697, 2615, 30, 45, 41])).
% 2.24/1.79 tff(2699,plain,
% 2.24/1.79 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2582, 2615, 45, 30])).
% 2.24/1.79 tff(2700,plain,
% 2.24/1.79 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2590, 2699, 45, 1662])).
% 2.24/1.79 tff(2701,plain,
% 2.24/1.79 (~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1709, 2700])).
% 2.24/1.79 tff(2702,plain,
% 2.24/1.79 (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1711, 2701, 1662])).
% 2.24/1.79 tff(2703,plain,
% 2.24/1.79 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1713, 2702])).
% 2.24/1.79 tff(2704,plain,
% 2.24/1.79 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[220, 2703])).
% 2.24/1.79 tff(2705,plain,
% 2.24/1.79 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[82, 2704])).
% 2.24/1.79 tff(2706,plain,
% 2.24/1.79 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[88, 2705])).
% 2.24/1.79 tff(2707,plain,
% 2.24/1.79 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[90, 2706])).
% 2.24/1.79 tff(2708,plain,
% 2.24/1.79 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[269, 2707, 2482])).
% 2.24/1.79 tff(2709,plain,
% 2.24/1.79 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[271, 2708])).
% 2.24/1.79 tff(2710,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2565, 2709, 45, 2615, 30])).
% 2.24/1.79 tff(2711,plain,
% 2.24/1.79 (tptp_fun_Y_7(X!1, Y!0) = tptp_fun_Y1_11(X!1)),
% 2.24/1.79 inference(transitivity,[status(thm)],[936, 947, 889])).
% 2.24/1.79 tff(2712,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2711])).
% 2.24/1.79 tff(2713,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.24/1.79 inference(symmetry,[status(thm)],[2712])).
% 2.24/1.79 tff(2714,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[2569, 2713])).
% 2.24/1.79 tff(2715,plain,
% 2.24/1.79 ($false),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[954, 2714])).
% 2.24/1.79 tff(2716,plain,((~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.79 tff(2717,plain,
% 2.24/1.79 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2716, 2710, 2482, 2698, 41])).
% 2.24/1.79 tff(2718,plain,
% 2.24/1.79 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[629, 2717])).
% 2.24/1.79 tff(2719,plain,
% 2.24/1.79 ((tptp_fun_Y1_11(Y!0) = X!1) <=> (Y!0 = X!1)),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2698])).
% 2.24/1.79 tff(2720,plain,
% 2.24/1.79 ((tptp_fun_Y1_11(Y!0) = X!1) <=> (X!1 = Y!0)),
% 2.24/1.79 inference(transitivity,[status(thm)],[2719, 46])).
% 2.24/1.79 tff(2721,plain,
% 2.24/1.79 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(Y!0) = X!1)),
% 2.24/1.79 inference(symmetry,[status(thm)],[2720])).
% 2.24/1.79 tff(2722,plain,
% 2.24/1.79 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(Y!0) = X!1))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2721])).
% 2.24/1.79 tff(2723,plain,
% 2.24/1.79 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[741, 2722])).
% 2.24/1.79 tff(2724,plain,
% 2.24/1.79 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[84, 2705])).
% 2.24/1.79 tff(2725,plain,
% 2.24/1.79 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[86, 2724])).
% 2.24/1.79 tff(2726,plain,
% 2.24/1.79 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[113, 2725, 2698])).
% 2.24/1.79 tff(2727,plain,
% 2.24/1.79 ((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[958, 2726])).
% 2.24/1.79 tff(2728,plain,
% 2.24/1.79 (tptp_fun_X1_13(X!1, Y!0) = X!1),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[977, 2727, 41])).
% 2.24/1.79 tff(2729,plain,
% 2.24/1.79 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[879, 2708])).
% 2.24/1.79 tff(2730,plain,
% 2.24/1.79 (~(Z!5 = X!1)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1062, 739, 931])).
% 2.24/1.79 tff(2731,plain,
% 2.24/1.79 (Z!5 = Y!0),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[361, 2730])).
% 2.24/1.79 tff(2732,plain,
% 2.24/1.79 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[2731, 889])).
% 2.24/1.79 tff(2733,plain,
% 2.24/1.79 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Z!5, X!1)),
% 2.24/1.79 inference(symmetry,[status(thm)],[2732])).
% 2.24/1.79 tff(2734,plain,
% 2.24/1.79 (big_f(Z!5, X!1)),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[2569, 2733])).
% 2.24/1.79 tff(2735,plain,
% 2.24/1.79 (X!1 = tptp_fun_W_6(Z!5)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[989, 2734, 1212])).
% 2.24/1.79 tff(2736,plain,
% 2.24/1.79 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2572, 2569, 906])).
% 2.24/1.79 tff(2737,plain,
% 2.24/1.79 (Y!0 = Z!5),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[438, 2731])).
% 2.24/1.80 tff(2738,plain,
% 2.24/1.80 (~(tptp_fun_X1_13(X!1, Y!0) = Z!5)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1005, 2731, 999])).
% 2.24/1.80 tff(2739,plain,
% 2.24/1.80 (~(X!1 = Z!5)),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[2738, 995])).
% 2.24/1.80 tff(2740,plain,
% 2.24/1.80 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1008, 2739, 981])).
% 2.24/1.80 tff(2741,plain,
% 2.24/1.80 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1010, 2740])).
% 2.24/1.80 tff(2742,plain,
% 2.24/1.80 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1034, 2735, 2741, 2737, 45])).
% 2.24/1.80 tff(2743,plain,
% 2.24/1.80 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1036, 2742, 2741])).
% 2.24/1.80 tff(2744,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1053, 2743, 2742, 277, 2736, 2735, 2731, 906])).
% 2.24/1.80 tff(2745,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | big_f(X!1, Y!0) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_X1_13(X!1, Y!0) = X!1)) | (tptp_fun_Y1_11(Y!0) = X!1) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2746,plain,
% 2.24/1.80 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2745, 2729, 2482, 45, 2710, 2728, 2723, 2718])).
% 2.24/1.80 tff(2747,plain,
% 2.24/1.80 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[462, 2746])).
% 2.24/1.80 tff(2748,plain,
% 2.24/1.80 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[481, 2747])).
% 2.24/1.80 tff(2749,plain,
% 2.24/1.80 (~(W1!8 = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[524, 2748, 30, 45, 2615])).
% 2.24/1.80 tff(2750,plain,
% 2.24/1.80 (W1!8 = X!1),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[19, 2749])).
% 2.24/1.80 tff(2751,plain,
% 2.24/1.80 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.24/1.80 inference(transitivity,[status(thm)],[2750, 2489])).
% 2.24/1.80 tff(2752,plain,
% 2.24/1.80 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2751])).
% 2.24/1.80 tff(2753,plain,
% 2.24/1.80 (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_9(W1!8)),
% 2.24/1.80 inference(symmetry,[status(thm)],[2752])).
% 2.24/1.80 tff(2754,plain,
% 2.24/1.80 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2572, 2710, 2729])).
% 2.24/1.80 tff(2755,plain,
% 2.24/1.80 (tptp_fun_X1_13(Y!0, X!1) = X!1),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[915, 2754])).
% 2.24/1.80 tff(2756,plain,
% 2.24/1.80 ((tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2755, 2753])).
% 2.24/1.80 tff(2757,plain,
% 2.24/1.80 ((tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.24/1.80 inference(transitivity,[status(thm)],[2756, 2056])).
% 2.24/1.80 tff(2758,plain,
% 2.24/1.80 (X!1 = tptp_fun_X1_13(Y!0, X!1)),
% 2.24/1.80 inference(symmetry,[status(thm)],[2755])).
% 2.24/1.80 tff(2759,plain,
% 2.24/1.80 ((X!1 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2758, 2752])).
% 2.24/1.80 tff(2760,plain,
% 2.24/1.80 ((X!1 = tptp_fun_Z1_9(W1!8)) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.24/1.80 inference(transitivity,[status(thm)],[2759, 2757])).
% 2.24/1.80 tff(2761,plain,
% 2.24/1.80 (big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[496, 2748])).
% 2.24/1.80 tff(2762,plain,
% 2.24/1.80 (big_f(X!1, W1!8) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2483, 2750])).
% 2.24/1.80 tff(2763,plain,
% 2.24/1.80 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(X!1, W1!8)),
% 2.24/1.80 inference(symmetry,[status(thm)],[2762])).
% 2.24/1.80 tff(2764,plain,
% 2.24/1.80 (big_f(X!1, W1!8)),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[2699, 2763])).
% 2.24/1.80 tff(2765,plain,
% 2.24/1.80 (X!1 = tptp_fun_Z1_9(W1!8)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[923, 2764, 2761])).
% 2.24/1.80 tff(2766,plain,
% 2.24/1.80 (tptp_fun_Z1_9(W1!8) = X!1),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[2765, 2760])).
% 2.24/1.80 tff(2767,plain,
% 2.24/1.80 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[790, 2747])).
% 2.24/1.80 tff(2768,plain,
% 2.24/1.80 ((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1459, 2767])).
% 2.24/1.80 tff(2769,plain,
% 2.24/1.80 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[2750, 2546])).
% 2.24/1.80 tff(2770,plain,
% 2.24/1.80 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1465, 2769, 2768])).
% 2.24/1.80 tff(2771,plain,
% 2.24/1.80 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1467, 2770])).
% 2.24/1.80 tff(2772,plain,
% 2.24/1.80 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1490, 2771, 2482, 2750, 2709])).
% 2.24/1.80 tff(2773,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2772, 2766])).
% 2.24/1.80 tff(2774,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2775,plain,
% 2.24/1.80 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2774, 45, 30])).
% 2.24/1.80 tff(2776,plain,
% 2.24/1.80 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[84, 2596])).
% 2.24/1.80 tff(2777,plain,
% 2.24/1.80 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[86, 2776])).
% 2.24/1.80 tff(2778,plain,
% 2.24/1.80 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1168, 2777, 45, 2775])).
% 2.24/1.80 tff(2779,plain,
% 2.24/1.80 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2232, 2778, 1662, 45, 2775])).
% 2.24/1.80 tff(2780,plain,
% 2.24/1.80 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[39, 2778])).
% 2.24/1.80 tff(2781,plain,
% 2.24/1.80 (tptp_fun_X1_13(Y!0, X!1) = Y!0),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1118, 2780, 2482, 2600, 2779])).
% 2.24/1.80 tff(2782,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2572, 2781, 2602, 2600])).
% 2.24/1.80 tff(2783,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2784,plain,
% 2.24/1.80 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2783, 45, 30])).
% 2.24/1.80 tff(2785,plain,
% 2.24/1.80 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.24/1.80 inference(transitivity,[status(thm)],[598, 889])).
% 2.24/1.80 tff(2786,plain,
% 2.24/1.80 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2785])).
% 2.24/1.80 tff(2787,plain,
% 2.24/1.80 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.80 inference(symmetry,[status(thm)],[2786])).
% 2.24/1.80 tff(2788,plain,
% 2.24/1.80 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2787])).
% 2.24/1.80 tff(2789,plain,
% 2.24/1.80 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[2501, 2788])).
% 2.24/1.80 tff(2790,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[135, 2789])).
% 2.24/1.80 tff(2791,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2792,plain,
% 2.24/1.80 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2791, 2501, 2775, 2482])).
% 2.24/1.80 tff(2793,plain,
% 2.24/1.80 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[39, 2792])).
% 2.24/1.80 tff(2794,plain,
% 2.24/1.80 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1168, 2793, 45, 2775])).
% 2.24/1.80 tff(2795,plain,
% 2.24/1.80 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[86, 2794])).
% 2.24/1.80 tff(2796,plain,
% 2.24/1.80 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[84, 2795])).
% 2.24/1.80 tff(2797,plain,
% 2.24/1.80 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[82, 2796])).
% 2.24/1.80 tff(2798,plain,
% 2.24/1.80 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[56, 2797])).
% 2.24/1.80 tff(2799,plain,
% 2.24/1.80 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[54, 2798])).
% 2.24/1.80 tff(2800,plain,
% 2.24/1.80 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[52, 2799, 30])).
% 2.24/1.80 tff(2801,plain,
% 2.24/1.80 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[50, 2800])).
% 2.24/1.80 tff(2802,plain,
% 2.24/1.80 (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1341, 2801, 2784])).
% 2.24/1.80 tff(2803,plain,
% 2.24/1.80 (tptp_fun_Y_4(Y!0, Y!0) = tptp_fun_Y1_11(X!1)),
% 2.24/1.80 inference(transitivity,[status(thm)],[96, 889])).
% 2.24/1.80 tff(2804,plain,
% 2.24/1.80 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[30, 2803])).
% 2.24/1.80 tff(2805,plain,
% 2.24/1.80 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.24/1.80 inference(symmetry,[status(thm)],[2804])).
% 2.24/1.80 tff(2806,plain,
% 2.24/1.80 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2805])).
% 2.24/1.80 tff(2807,plain,
% 2.24/1.80 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[2501, 2806])).
% 2.24/1.80 tff(2808,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1075, 2807])).
% 2.24/1.80 tff(2809,plain,((tptp_fun_Y_4(Y!0, Y!0) = Y!0) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2810,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2809, 2802, 2801, 2482, 30, 2501])).
% 2.24/1.80 tff(2811,plain,(big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2812,plain,
% 2.24/1.80 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2811, 45, 30])).
% 2.24/1.80 tff(2813,plain,
% 2.24/1.80 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2232, 1642, 1663, 45, 135])).
% 2.24/1.80 tff(2814,plain,
% 2.24/1.80 (tptp_fun_X1_13(Y!0, X!1) = Y!0),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1118, 1645, 277, 1647, 2813])).
% 2.24/1.80 tff(2815,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2572, 2814, 1645, 2569])).
% 2.24/1.80 tff(2816,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2817,plain,
% 2.24/1.80 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2816, 2812, 2482, 1662, 45, 2775])).
% 2.24/1.80 tff(2818,plain,
% 2.24/1.80 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[82, 2817])).
% 2.24/1.80 tff(2819,plain,
% 2.24/1.80 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[56, 2818])).
% 2.24/1.80 tff(2820,plain,
% 2.24/1.80 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[54, 2819])).
% 2.24/1.80 tff(2821,plain,
% 2.24/1.80 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[52, 2820, 30])).
% 2.24/1.80 tff(2822,plain,
% 2.24/1.80 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[50, 2821])).
% 2.24/1.80 tff(2823,plain,
% 2.24/1.80 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1339, 2822, 2784])).
% 2.24/1.80 tff(2824,plain,
% 2.24/1.80 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[220, 2818])).
% 2.24/1.80 tff(2825,plain,
% 2.24/1.80 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1713, 2824])).
% 2.24/1.80 tff(2826,plain,
% 2.24/1.80 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1711, 2825, 1662])).
% 2.24/1.80 tff(2827,plain,
% 2.24/1.80 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1709, 2826])).
% 2.24/1.80 tff(2828,plain,
% 2.24/1.80 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1707, 2827, 45, 1662])).
% 2.24/1.80 tff(2829,plain,
% 2.24/1.80 (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1341, 2822, 2784])).
% 2.24/1.80 tff(2830,plain,
% 2.24/1.80 (tptp_fun_Y_4(Y!0, Y!0) = X!1),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[95, 2829])).
% 2.24/1.80 tff(2831,plain,
% 2.24/1.80 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2167, 2830, 30, 2784, 2828, 2823])).
% 2.24/1.80 tff(2832,plain,
% 2.24/1.80 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[462, 2831])).
% 2.24/1.80 tff(2833,plain,
% 2.24/1.80 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[481, 2832])).
% 2.24/1.80 tff(2834,plain,
% 2.24/1.80 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[483, 2833])).
% 2.24/1.80 tff(2835,assumption,(~(X!1 = W1!8)), introduced(assumption)).
% 2.24/1.80 tff(2836,plain,
% 2.24/1.80 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1692, 2487, 45, 1662])).
% 2.24/1.80 tff(2837,plain,
% 2.24/1.80 (tptp_fun_X1_10(Y!0, X!1) = Y!0),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2199, 1224, 1663, 1675, 1702])).
% 2.24/1.80 tff(2838,plain,
% 2.24/1.80 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[2837, 889])).
% 2.24/1.80 tff(2839,plain,
% 2.24/1.80 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.24/1.80 inference(symmetry,[status(thm)],[2838])).
% 2.24/1.80 tff(2840,plain,
% 2.24/1.80 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[2569, 2839])).
% 2.24/1.80 tff(2841,plain,
% 2.24/1.80 (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1230, 2837, 1224])).
% 2.24/1.80 tff(2842,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2841, 2840])).
% 2.24/1.80 tff(2843,plain,((~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(2844,plain,
% 2.24/1.80 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[2843, 2836, 2482, 1662, 2812, 2487])).
% 2.24/1.80 tff(2845,plain,
% 2.24/1.80 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1256, 2844])).
% 2.24/1.80 tff(2846,plain,
% 2.24/1.80 (~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1273, 2845, 2835])).
% 2.24/1.80 tff(2847,plain,
% 2.24/1.80 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[50, 1443])).
% 2.24/1.80 tff(2848,plain,
% 2.24/1.80 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1339, 2847, 2784])).
% 2.24/1.80 tff(2849,plain,
% 2.24/1.80 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1707, 2487, 45, 1662])).
% 2.24/1.81 tff(2850,plain,
% 2.24/1.81 (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[1341, 2847, 2784])).
% 2.24/1.81 tff(2851,plain,
% 2.24/1.81 (tptp_fun_Y_4(Y!0, Y!0) = X!1),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[95, 2850])).
% 2.24/1.81 tff(2852,plain,
% 2.24/1.81 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2167, 2851, 30, 2784, 2849, 2848])).
% 2.24/1.81 tff(2853,plain,
% 2.24/1.81 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[462, 2852])).
% 2.24/1.81 tff(2854,plain,
% 2.24/1.81 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[1269, 2853])).
% 2.24/1.81 tff(2855,plain,
% 2.24/1.81 ($false),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[1271, 2854, 2846])).
% 2.24/1.81 tff(2856,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (X!1 = W1!8) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.81 tff(2857,plain,
% 2.24/1.81 (X!1 = W1!8),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2856, 2818, 30, 45])).
% 2.24/1.81 tff(2858,plain,
% 2.24/1.81 (W1!8 = X!1),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[28, 2857])).
% 2.24/1.81 tff(2859,plain,
% 2.24/1.81 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.24/1.81 inference(transitivity,[status(thm)],[2858, 2489])).
% 2.24/1.81 tff(2860,plain,
% 2.24/1.81 (big_f(Y!0, W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[2859])).
% 2.24/1.81 tff(2861,plain,
% 2.24/1.81 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, W1!8)),
% 2.24/1.81 inference(symmetry,[status(thm)],[2860])).
% 2.24/1.81 tff(2862,plain,
% 2.24/1.81 (big_f(Y!0, W1!8)),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[2812, 2861])).
% 2.24/1.81 tff(2863,plain,
% 2.24/1.81 (Y!0 = tptp_fun_Z1_9(W1!8)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[886, 2862, 2834])).
% 2.24/1.81 tff(2864,plain,
% 2.24/1.81 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.24/1.81 inference(symmetry,[status(thm)],[2863])).
% 2.24/1.81 tff(2865,plain,
% 2.24/1.81 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))))))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(2866,plain,
% 2.24/1.81 ((~((~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))) | (~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))))) <=> (~((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))))))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(2867,plain,
% 2.24/1.81 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))) | (~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8))))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[2866])).
% 2.24/1.81 tff(2868,plain,
% 2.24/1.81 (((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))) | (~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8))))))))) <=> ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))))))),
% 2.24/1.81 inference(transitivity,[status(thm)],[2867, 2865])).
% 2.24/1.81 tff(2869,plain,
% 2.24/1.81 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))) | (~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8))))))))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(2870,plain,
% 2.24/1.81 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))))))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 2.24/1.81 tff(2871,plain,
% 2.24/1.81 (~((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2870, 2832])).
% 2.24/1.81 tff(2872,plain,
% 2.24/1.81 (((~((~(tptp_fun_Z1_9(W1!8) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_9(W1!8)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_9(W1!8)))))) | (~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))))) | ((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))),
% 2.24/1.81 inference(tautology,[status(thm)],[])).
% 2.24/1.81 tff(2873,plain,
% 2.24/1.81 ((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2872, 2871])).
% 2.24/1.81 tff(2874,plain,
% 2.24/1.81 ((tptp_fun_Z1_9(W1!8) = W1!8) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.24/1.81 inference(monotonicity,[status(thm)],[2858])).
% 2.24/1.81 tff(2875,plain,
% 2.24/1.81 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_Z1_9(W1!8) = W1!8)),
% 2.24/1.81 inference(symmetry,[status(thm)],[2874])).
% 2.24/1.81 tff(2876,plain,
% 2.24/1.81 ((~(tptp_fun_Z1_9(W1!8) = X!1)) <=> (~(tptp_fun_Z1_9(W1!8) = W1!8))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[2875])).
% 2.24/1.81 tff(2877,plain,
% 2.30/1.81 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[2590, 2827, 45, 1662])).
% 2.30/1.81 tff(2878,assumption,(~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))), introduced(assumption)).
% 2.30/1.81 tff(2879,plain,
% 2.30/1.81 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.30/1.81 inference(monotonicity,[status(thm)],[286])).
% 2.30/1.81 tff(2880,plain,
% 2.30/1.81 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.30/1.81 inference(symmetry,[status(thm)],[2879])).
% 2.30/1.81 tff(2881,plain,
% 2.30/1.81 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.30/1.81 inference(modus_ponens,[status(thm)],[2569, 2880])).
% 2.30/1.81 tff(2882,plain,
% 2.30/1.81 (((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)) | (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) | (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.30/1.81 inference(tautology,[status(thm)],[])).
% 2.30/1.81 tff(2883,plain,
% 2.30/1.81 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[2882, 278, 2878])).
% 2.30/1.81 tff(2884,plain,
% 2.30/1.81 ($false),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[2883, 2881])).
% 2.30/1.81 tff(2885,plain,((tptp_fun_X1_13(X!1, X!1) = X!1) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.81 tff(2886,plain,
% 2.30/1.81 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[2885, 2878, 2569])).
% 2.30/1.81 tff(2887,plain,
% 2.30/1.81 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_X_2(X!1)),
% 2.30/1.81 inference(transitivity,[status(thm)],[2886, 1664])).
% 2.30/1.81 tff(2888,plain,
% 2.30/1.81 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.30/1.81 inference(monotonicity,[status(thm)],[2887, 277])).
% 2.30/1.81 tff(2889,plain,
% 2.30/1.81 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.30/1.81 inference(symmetry,[status(thm)],[2888])).
% 2.30/1.81 tff(2890,plain,
% 2.30/1.81 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)))),
% 2.30/1.81 inference(monotonicity,[status(thm)],[2889])).
% 2.30/1.81 tff(2891,plain,
% 2.30/1.81 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.30/1.81 inference(modus_ponens,[status(thm)],[828, 2890])).
% 2.30/1.81 tff(2892,plain,
% 2.30/1.81 (((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)) | big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) | (~(tptp_fun_X1_13(X!1, X!1) = X!1))),
% 2.30/1.81 inference(tautology,[status(thm)],[])).
% 2.30/1.81 tff(2893,plain,
% 2.30/1.81 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[2892, 2886, 2878])).
% 2.30/1.81 tff(2894,plain,
% 2.30/1.81 ($false),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[2893, 2891])).
% 2.30/1.81 tff(2895,plain,(((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)) | big_f(tptp_fun_X_2(X!1), X!1) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(Y!0, tptp_fun_Y1_11(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.81 tff(2896,plain,
% 2.30/1.81 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[2895, 2877, 2482, 1662, 2812])).
% 2.30/1.81 tff(2897,plain,
% 2.30/1.81 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[790, 2832])).
% 2.30/1.81 tff(2898,plain,
% 2.30/1.81 ((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[1459, 2897])).
% 2.30/1.81 tff(2899,plain,
% 2.30/1.81 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.30/1.81 inference(modus_ponens,[status(thm)],[2858, 2546])).
% 2.30/1.81 tff(2900,plain,
% 2.30/1.81 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.30/1.81 inference(unit_resolution,[status(thm)],[1465, 2899, 2898])).
% 2.30/1.82 tff(2901,plain,
% 2.30/1.82 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[1467, 2900])).
% 2.30/1.82 tff(2902,plain,
% 2.30/1.82 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[1490, 2901, 2482, 2858, 2896])).
% 2.30/1.82 tff(2903,plain,
% 2.30/1.82 (~(tptp_fun_Z1_9(W1!8) = W1!8)),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[2902, 2876])).
% 2.30/1.82 tff(2904,plain,
% 2.30/1.82 ((~((tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1)))) | (tptp_fun_Z1_9(W1!8) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))),
% 2.30/1.82 inference(tautology,[status(thm)],[])).
% 2.30/1.82 tff(2905,plain,
% 2.30/1.82 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2904, 2903, 2873])).
% 2.30/1.82 tff(2906,plain,
% 2.30/1.82 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_9(W1!8)) = Z1))) | ((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0))),
% 2.30/1.82 inference(quant_inst,[status(thm)],[])).
% 2.30/1.82 tff(2907,plain,
% 2.30/1.82 ((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0)),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2906, 2905])).
% 2.30/1.82 tff(2908,assumption,(Y!0 = tptp_fun_Z1_9(W1!8)), introduced(assumption)).
% 2.30/1.82 tff(2909,plain,
% 2.30/1.82 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.30/1.82 inference(symmetry,[status(thm)],[2908])).
% 2.30/1.82 tff(2910,assumption,(~(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0)), introduced(assumption)).
% 2.30/1.82 tff(2911,plain,
% 2.30/1.82 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = X!1))),
% 2.30/1.82 inference(rewrite,[status(thm)],[])).
% 2.30/1.82 tff(2912,plain,
% 2.30/1.82 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = X!1))),
% 2.30/1.82 inference(quant_inst,[status(thm)],[])).
% 2.30/1.82 tff(2913,plain,
% 2.30/1.82 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = X!1)),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[2912, 2911])).
% 2.30/1.82 tff(2914,plain,
% 2.30/1.82 ((tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = X!1)),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2913, 12])).
% 2.30/1.82 tff(2915,plain,
% 2.30/1.82 (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = X!1),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2914, 2910])).
% 2.30/1.82 tff(2916,plain,
% 2.30/1.82 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8)) <=> big_f(X!1, Y!0)),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2915, 2909])).
% 2.30/1.82 tff(2917,plain,
% 2.30/1.82 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))),
% 2.30/1.82 inference(symmetry,[status(thm)],[2916])).
% 2.30/1.82 tff(2918,plain,
% 2.30/1.82 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8)))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2917])).
% 2.30/1.82 tff(2919,plain,
% 2.30/1.82 (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[45, 2918])).
% 2.30/1.82 tff(2920,assumption,((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0)), introduced(assumption)).
% 2.30/1.82 tff(2921,plain,
% 2.30/1.82 ((~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0))) | big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8)) | (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0)),
% 2.30/1.82 inference(tautology,[status(thm)],[])).
% 2.30/1.82 tff(2922,plain,
% 2.30/1.82 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2921, 2910, 2920])).
% 2.30/1.82 tff(2923,plain,
% 2.30/1.82 ($false),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2922, 2919])).
% 2.30/1.82 tff(2924,plain,((tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0) | big_f(X!1, Y!0) | (~(Y!0 = tptp_fun_Z1_9(W1!8))) | (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.82 tff(2925,plain,
% 2.30/1.82 (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2924, 45, 2863, 2907])).
% 2.30/1.82 tff(2926,plain,
% 2.30/1.82 (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = tptp_fun_X_2(Y!0)),
% 2.30/1.82 inference(transitivity,[status(thm)],[2925, 31])).
% 2.30/1.82 tff(2927,plain,
% 2.30/1.82 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2926, 2864])).
% 2.30/1.82 tff(2928,plain,
% 2.30/1.82 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))),
% 2.30/1.82 inference(symmetry,[status(thm)],[2927])).
% 2.30/1.82 tff(2929,plain,
% 2.30/1.82 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[2784, 2928])).
% 2.30/1.82 tff(2930,plain,
% 2.30/1.82 ((~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0))) | (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))) | (~(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)) = Y!0))),
% 2.30/1.82 inference(tautology,[status(thm)],[])).
% 2.30/1.82 tff(2931,plain,
% 2.30/1.82 (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Z1_9(W1!8)), tptp_fun_Z1_9(W1!8))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2930, 2925, 2907])).
% 2.30/1.82 tff(2932,plain,
% 2.30/1.82 ($false),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2931, 2929])).
% 2.30/1.82 tff(2933,plain,(big_f(X!1, Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.82 tff(2934,plain,
% 2.30/1.82 (~(tptp_fun_X_2(Y!0) = Y!0)),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2933, 45])).
% 2.30/1.82 tff(2935,plain,
% 2.30/1.82 (tptp_fun_X_2(Y!0) = X!1),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[1877, 2934])).
% 2.30/1.82 tff(2936,plain,
% 2.30/1.82 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2935])).
% 2.30/1.82 tff(2937,plain,
% 2.30/1.82 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.30/1.82 inference(symmetry,[status(thm)],[2936])).
% 2.30/1.82 tff(2938,plain,
% 2.30/1.82 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X_2(Y!0), Y!0))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2937])).
% 2.30/1.82 tff(2939,plain,
% 2.30/1.82 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[45, 2938])).
% 2.30/1.82 tff(2940,plain,
% 2.30/1.82 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[1894, 42, 40, 1857, 35])).
% 2.30/1.82 tff(2941,plain,
% 2.30/1.82 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2663, 2940])).
% 2.30/1.82 tff(2942,plain,
% 2.30/1.82 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[56, 2941])).
% 2.30/1.82 tff(2943,plain,
% 2.30/1.82 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[82, 2942])).
% 2.30/1.82 tff(2944,plain,
% 2.30/1.82 ($false),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[84, 2943, 2659])).
% 2.30/1.82 tff(2945,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | (tptp_fun_Y1_11(Y!0) = Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_X_2(Y!0) = Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.82 tff(2946,plain,
% 2.30/1.82 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2945, 41, 34, 2934, 2939])).
% 2.30/1.82 tff(2947,plain,
% 2.30/1.82 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[627, 2946, 45, 40])).
% 2.30/1.82 tff(2948,plain,
% 2.30/1.82 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[629, 2947])).
% 2.30/1.82 tff(2949,assumption,(~(tptp_fun_Y1_11(X!1) = Y!0)), introduced(assumption)).
% 2.30/1.82 tff(2950,plain,
% 2.30/1.82 (tptp_fun_Y1_11(X!1) = X!1),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[153, 2949])).
% 2.30/1.82 tff(2951,plain,
% 2.30/1.82 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2945, 41, 1857, 34, 35])).
% 2.30/1.82 tff(2952,plain,
% 2.30/1.82 (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[650, 2951, 2950, 41, 40])).
% 2.30/1.82 tff(2953,plain,
% 2.30/1.82 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[90, 2952])).
% 2.30/1.82 tff(2954,plain,
% 2.30/1.82 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[88, 2953])).
% 2.30/1.82 tff(2955,plain,
% 2.30/1.82 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[82, 2954])).
% 2.30/1.82 tff(2956,plain,
% 2.30/1.82 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[220, 2955])).
% 2.30/1.82 tff(2957,plain,
% 2.30/1.82 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[1713, 2956])).
% 2.30/1.82 tff(2958,plain,
% 2.30/1.82 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2624, 2951, 40, 45, 2957])).
% 2.30/1.82 tff(2959,plain,
% 2.30/1.82 (tptp_fun_X_2(X!1) = Y!0),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[105, 2958])).
% 2.30/1.82 tff(2960,plain,
% 2.30/1.82 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2959])).
% 2.30/1.82 tff(2961,plain,
% 2.30/1.82 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))),
% 2.30/1.82 inference(symmetry,[status(thm)],[2960])).
% 2.30/1.82 tff(2962,plain,
% 2.30/1.82 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[222, 2956])).
% 2.30/1.82 tff(2963,plain,
% 2.30/1.82 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[224, 2958, 2962])).
% 2.30/1.82 tff(2964,plain,
% 2.30/1.82 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[234, 2963])).
% 2.30/1.82 tff(2965,plain,
% 2.30/1.82 (~(tptp_fun_W_3(X!1) = X!1)),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[1578, 2964, 41, 40, 2959])).
% 2.30/1.82 tff(2966,plain,
% 2.30/1.82 (tptp_fun_W_3(X!1) = Y!0),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[252, 2965])).
% 2.30/1.82 tff(2967,plain,
% 2.30/1.82 (X!1 = tptp_fun_X_2(Y!0)),
% 2.30/1.82 inference(symmetry,[status(thm)],[1878])).
% 2.30/1.82 tff(2968,plain,
% 2.30/1.82 (tptp_fun_Y1_11(Y!0) = tptp_fun_X_2(Y!0)),
% 2.30/1.82 inference(transitivity,[status(thm)],[40, 2967])).
% 2.30/1.82 tff(2969,plain,
% 2.30/1.82 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2968])).
% 2.30/1.82 tff(2970,plain,
% 2.30/1.82 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2969])).
% 2.30/1.82 tff(2971,plain,
% 2.30/1.82 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[41, 2970])).
% 2.30/1.82 tff(2972,plain,
% 2.30/1.82 (X!1 = tptp_fun_X_2(Y!0)),
% 2.30/1.82 inference(symmetry,[status(thm)],[1906])).
% 2.30/1.82 tff(2973,plain,
% 2.30/1.82 (tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0) = tptp_fun_Y_7(Y!0, Y!0)),
% 2.30/1.82 inference(monotonicity,[status(thm)],[238])).
% 2.30/1.82 tff(2974,plain,
% 2.30/1.82 (tptp_fun_Y_7(Y!0, Y!0) = tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0)),
% 2.30/1.82 inference(symmetry,[status(thm)],[2973])).
% 2.30/1.82 tff(2975,plain,
% 2.30/1.82 (tptp_fun_W_3(X!1) = tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0)),
% 2.30/1.82 inference(transitivity,[status(thm)],[238, 695, 2974])).
% 2.30/1.82 tff(2976,plain,
% 2.30/1.82 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[240, 2975])).
% 2.30/1.82 tff(2977,plain,
% 2.30/1.82 (big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.30/1.82 inference(symmetry,[status(thm)],[2976])).
% 2.30/1.82 tff(2978,plain,
% 2.30/1.82 ((~big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2977])).
% 2.30/1.82 tff(2979,plain,
% 2.30/1.82 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2974])).
% 2.30/1.82 tff(2980,plain,
% 2.30/1.82 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (~big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0)))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2979])).
% 2.30/1.82 tff(2981,plain,
% 2.30/1.82 (~big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0))),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[700, 2980])).
% 2.30/1.82 tff(2982,plain,
% 2.30/1.82 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[2981, 2978])).
% 2.30/1.82 tff(2983,plain,
% 2.30/1.82 ($false),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[245, 2982])).
% 2.30/1.82 tff(2984,plain,((~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | (~(tptp_fun_W_3(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.82 tff(2985,plain,
% 2.30/1.82 (~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2984, 693, 238, 240, 245])).
% 2.30/1.82 tff(2986,plain,
% 2.30/1.82 (tptp_fun_Y_7(Y!0, Y!0) = X!1),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[708, 2985])).
% 2.30/1.82 tff(2987,plain,
% 2.30/1.82 (tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0) = tptp_fun_X_2(Y!0)),
% 2.30/1.82 inference(transitivity,[status(thm)],[2973, 2986, 2972])).
% 2.30/1.82 tff(2988,plain,
% 2.30/1.82 (big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2987])).
% 2.30/1.82 tff(2989,plain,
% 2.30/1.82 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0))),
% 2.30/1.82 inference(symmetry,[status(thm)],[2988])).
% 2.30/1.82 tff(2990,plain,
% 2.30/1.82 ((~big_f(Y!0, tptp_fun_X_2(Y!0))) <=> (~big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0)))),
% 2.30/1.82 inference(monotonicity,[status(thm)],[2989])).
% 2.30/1.82 tff(2991,assumption,(~big_f(Y!0, tptp_fun_X_2(Y!0))), introduced(assumption)).
% 2.30/1.82 tff(2992,plain,
% 2.30/1.82 (~big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0))),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[2991, 2990])).
% 2.30/1.82 tff(2993,plain,
% 2.30/1.82 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[714, 2985, 693])).
% 2.30/1.82 tff(2994,plain,
% 2.30/1.82 (big_f(Y!0, tptp_fun_Y_7(tptp_fun_W_3(X!1), Y!0))),
% 2.30/1.82 inference(modus_ponens,[status(thm)],[2993, 2979])).
% 2.30/1.82 tff(2995,plain,
% 2.30/1.82 ($false),
% 2.30/1.82 inference(unit_resolution,[status(thm)],[2994, 2992])).
% 2.30/1.82 tff(2996,plain,((~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_W_3(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.83 tff(2997,plain,
% 2.30/1.83 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[2996, 2971, 1878, 2966, 2959, 2964])).
% 2.30/1.83 tff(2998,plain,
% 2.30/1.83 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[720, 2997])).
% 2.30/1.83 tff(2999,plain,
% 2.30/1.83 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[627, 2951, 40, 45])).
% 2.30/1.83 tff(3000,plain,
% 2.30/1.83 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[629, 2999])).
% 2.30/1.83 tff(3001,plain,
% 2.30/1.83 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[743, 3000, 40, 2998])).
% 2.30/1.83 tff(3002,plain,
% 2.30/1.83 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[462, 3001])).
% 2.30/1.83 tff(3003,plain,
% 2.30/1.83 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))))))),
% 2.30/1.83 inference(quant_inst,[status(thm)],[])).
% 2.30/1.83 tff(3004,plain,
% 2.30/1.83 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3003, 3002])).
% 2.30/1.83 tff(3005,plain,
% 2.30/1.83 (((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))))) | ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))),
% 2.30/1.83 inference(tautology,[status(thm)],[])).
% 2.30/1.83 tff(3006,plain,
% 2.30/1.83 ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3005, 3004])).
% 2.30/1.83 tff(3007,plain,
% 2.30/1.83 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[790, 3002])).
% 2.30/1.83 tff(3008,plain,
% 2.30/1.83 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[792, 3007])).
% 2.30/1.83 tff(3009,plain,
% 2.30/1.83 (tptp_fun_Y1_11(X!1) = tptp_fun_X_2(Y!0)),
% 2.30/1.83 inference(transitivity,[status(thm)],[2950, 2967])).
% 2.30/1.83 tff(3010,plain,
% 2.30/1.83 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3009])).
% 2.30/1.83 tff(3011,plain,
% 2.30/1.83 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3010])).
% 2.30/1.83 tff(3012,plain,
% 2.30/1.83 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.30/1.83 inference(symmetry,[status(thm)],[3011])).
% 2.30/1.83 tff(3013,plain,
% 2.30/1.83 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))))))))),
% 2.30/1.83 inference(quant_inst,[status(thm)],[])).
% 2.30/1.83 tff(3014,plain,
% 2.30/1.83 (~((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))))))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3013, 3002])).
% 2.30/1.83 tff(3015,plain,
% 2.30/1.83 (((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))))))) | ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))),
% 2.30/1.83 inference(tautology,[status(thm)],[])).
% 2.30/1.83 tff(3016,plain,
% 2.30/1.83 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3015, 3014])).
% 2.30/1.83 tff(3017,plain,
% 2.30/1.83 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))))))),
% 2.30/1.83 inference(quant_inst,[status(thm)],[])).
% 2.30/1.83 tff(3018,plain,
% 2.30/1.83 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3017, 3002])).
% 2.30/1.83 tff(3019,plain,
% 2.30/1.83 (((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))))) | ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))),
% 2.30/1.83 inference(tautology,[status(thm)],[])).
% 2.30/1.83 tff(3020,plain,
% 2.30/1.83 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3019, 3018])).
% 2.30/1.83 tff(3021,assumption,((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))), introduced(assumption)).
% 2.30/1.83 tff(3022,assumption,(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0), introduced(assumption)).
% 2.30/1.83 tff(3023,plain,
% 2.30/1.83 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3022])).
% 2.30/1.83 tff(3024,plain,
% 2.30/1.83 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3023, 240])).
% 2.30/1.83 tff(3025,plain,
% 2.30/1.83 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1))) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0))),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3024])).
% 2.30/1.83 tff(3026,assumption,((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1))), introduced(assumption)).
% 2.30/1.83 tff(3027,plain,
% 2.30/1.83 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3023, 3022])).
% 2.30/1.83 tff(3028,plain,
% 2.30/1.83 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.30/1.83 inference(symmetry,[status(thm)],[3027])).
% 2.30/1.83 tff(3029,plain,
% 2.30/1.83 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1))),
% 2.30/1.83 inference(symmetry,[status(thm)],[3024])).
% 2.30/1.83 tff(3030,plain,
% 2.30/1.83 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3029])).
% 2.30/1.83 tff(3031,assumption,(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0), introduced(assumption)).
% 2.30/1.83 tff(3032,plain,
% 2.30/1.83 (Y!0 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.30/1.83 inference(symmetry,[status(thm)],[3031])).
% 2.30/1.83 tff(3033,plain,
% 2.30/1.83 (tptp_fun_X_2(X!1) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.30/1.83 inference(transitivity,[status(thm)],[240, 3032])).
% 2.30/1.83 tff(3034,plain,
% 2.30/1.83 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3033, 238])).
% 2.30/1.83 tff(3035,plain,
% 2.30/1.83 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.30/1.83 inference(symmetry,[status(thm)],[3034])).
% 2.30/1.83 tff(3036,plain,
% 2.30/1.83 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 2.30/1.83 inference(monotonicity,[status(thm)],[3035])).
% 2.30/1.83 tff(3037,plain,
% 2.30/1.83 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.30/1.83 inference(modus_ponens,[status(thm)],[1784, 3036])).
% 2.30/1.83 tff(3038,plain,
% 2.30/1.83 ($false),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[245, 3037])).
% 2.30/1.83 tff(3039,plain,((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) | (~(tptp_fun_W_3(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.83 tff(3040,plain,
% 2.30/1.83 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3039, 1784, 245, 238, 240])).
% 2.30/1.83 tff(3041,plain,
% 2.30/1.83 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1))),
% 2.30/1.83 inference(modus_ponens,[status(thm)],[3040, 3030])).
% 2.30/1.83 tff(3042,assumption,(big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))), introduced(assumption)).
% 2.30/1.83 tff(3043,plain,
% 2.30/1.83 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.83 inference(modus_ponens,[status(thm)],[3042, 3027])).
% 2.30/1.83 tff(3044,plain,
% 2.30/1.83 ($false),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[1784, 3043])).
% 2.30/1.83 tff(3045,plain,((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.83 tff(3046,plain,
% 2.30/1.83 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3045, 1784, 3022])).
% 2.30/1.83 tff(3047,plain,
% 2.30/1.83 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1))),
% 2.30/1.83 inference(tautology,[status(thm)],[])).
% 2.30/1.83 tff(3048,plain,
% 2.30/1.83 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3047, 3046, 3026])).
% 2.30/1.83 tff(3049,plain,
% 2.30/1.83 ($false),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3048, 3041])).
% 2.30/1.83 tff(3050,plain,(big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)) | (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | (~(tptp_fun_W_3(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.83 tff(3051,plain,
% 2.30/1.83 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3050, 3026, 3022, 240, 245, 238])).
% 2.30/1.83 tff(3052,plain,
% 2.30/1.83 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.30/1.83 inference(modus_ponens,[status(thm)],[3051, 3028])).
% 2.30/1.83 tff(3053,plain,
% 2.30/1.83 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))) | (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) | (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))),
% 2.30/1.83 inference(tautology,[status(thm)],[])).
% 2.30/1.83 tff(3054,plain,
% 2.30/1.83 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1))),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3053, 3052, 3026])).
% 2.30/1.83 tff(3055,plain,
% 2.30/1.83 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.30/1.83 inference(modus_ponens,[status(thm)],[3054, 3025])).
% 2.30/1.83 tff(3056,plain,
% 2.30/1.83 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1))),
% 2.30/1.83 inference(rewrite,[status(thm)],[])).
% 2.30/1.83 tff(3057,plain,
% 2.30/1.83 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1))),
% 2.30/1.83 inference(quant_inst,[status(thm)],[])).
% 2.30/1.83 tff(3058,plain,
% 2.30/1.83 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.30/1.83 inference(modus_ponens,[status(thm)],[3057, 3056])).
% 2.30/1.83 tff(3059,plain,
% 2.30/1.83 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.30/1.83 inference(unit_resolution,[status(thm)],[3058, 12])).
% 2.30/1.83 tff(3060,plain,
% 2.30/1.83 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3059, 3055])).
% 2.30/1.84 tff(3061,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3060])).
% 2.30/1.84 tff(3062,plain,
% 2.30/1.84 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.84 inference(symmetry,[status(thm)],[3061])).
% 2.30/1.84 tff(3063,plain,
% 2.30/1.84 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0))),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3062])).
% 2.30/1.84 tff(3064,plain,
% 2.30/1.84 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[45, 3063])).
% 2.30/1.84 tff(3065,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3051, 3064])).
% 2.30/1.84 tff(3066,plain,((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | (~(tptp_fun_W_3(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3067,plain,
% 2.30/1.84 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3066, 2345, 240, 45, 245, 238])).
% 2.30/1.84 tff(3068,plain,
% 2.30/1.84 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))) | ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = tptp_fun_X_2(X!1)))),
% 2.30/1.84 inference(quant_inst,[status(thm)],[])).
% 2.30/1.84 tff(3069,plain,
% 2.30/1.84 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3068, 3067])).
% 2.30/1.84 tff(3070,plain,
% 2.30/1.84 ((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))),
% 2.30/1.84 inference(tautology,[status(thm)],[])).
% 2.30/1.84 tff(3071,plain,
% 2.30/1.84 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3070, 3069, 3021])).
% 2.30/1.84 tff(3072,plain,
% 2.30/1.84 (W1!8 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(symmetry,[status(thm)],[3071])).
% 2.30/1.84 tff(3073,assumption,((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))), introduced(assumption)).
% 2.30/1.84 tff(3074,plain,
% 2.30/1.84 (Y!0 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(symmetry,[status(thm)],[3022])).
% 2.30/1.84 tff(3075,plain,
% 2.30/1.84 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3074])).
% 2.30/1.84 tff(3076,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(symmetry,[status(thm)],[3075])).
% 2.30/1.84 tff(3077,assumption,(big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))), introduced(assumption)).
% 2.30/1.84 tff(3078,plain,
% 2.30/1.84 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[3077, 3076])).
% 2.30/1.84 tff(3079,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[2991, 3078])).
% 2.30/1.84 tff(3080,plain,(big_f(Y!0, tptp_fun_X_2(Y!0)) | (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3081,plain,
% 2.30/1.84 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3080, 2345, 2991])).
% 2.30/1.84 tff(3082,plain,
% 2.30/1.84 ((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))) | big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) | (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.30/1.84 inference(tautology,[status(thm)],[])).
% 2.30/1.84 tff(3083,plain,
% 2.30/1.84 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3082, 3081, 2344])).
% 2.30/1.84 tff(3084,plain,
% 2.30/1.84 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))) | ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.30/1.84 inference(quant_inst,[status(thm)],[])).
% 2.30/1.84 tff(3085,plain,
% 2.30/1.84 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3084, 3083])).
% 2.30/1.84 tff(3086,plain,
% 2.30/1.84 ((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.30/1.84 inference(tautology,[status(thm)],[])).
% 2.30/1.84 tff(3087,plain,
% 2.30/1.84 (tptp_fun_X_2(Y!0) = W1!8),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3086, 3085, 3073])).
% 2.30/1.84 tff(3088,plain,
% 2.30/1.84 (X!1 = Y!0),
% 2.30/1.84 inference(transitivity,[status(thm)],[2972, 3087, 3072, 2345])).
% 2.30/1.84 tff(3089,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[741, 3088])).
% 2.30/1.84 tff(3090,plain,((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(X!1, Y!0) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | (~(tptp_fun_W_3(X!1) = Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3091,plain,
% 2.30/1.84 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3090, 3020, 1878, 3016, 2959, 45, 2964, 2966, 2971])).
% 2.30/1.84 tff(3092,plain,
% 2.30/1.84 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[3091, 3012])).
% 2.30/1.84 tff(3093,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3010, 3009])).
% 2.30/1.84 tff(3094,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.30/1.84 inference(symmetry,[status(thm)],[3093])).
% 2.30/1.84 tff(3095,plain,
% 2.30/1.84 (X!1 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(symmetry,[status(thm)],[3091])).
% 2.30/1.84 tff(3096,plain,
% 2.30/1.84 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3095, 2968])).
% 2.30/1.84 tff(3097,plain,
% 2.30/1.84 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.30/1.84 inference(transitivity,[status(thm)],[3096, 3094])).
% 2.30/1.84 tff(3098,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[2951, 3097])).
% 2.30/1.84 tff(3099,plain,
% 2.30/1.84 ((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))) | (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) | (~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.30/1.84 inference(tautology,[status(thm)],[])).
% 2.30/1.84 tff(3100,plain,
% 2.30/1.84 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3099, 3098, 3092])).
% 2.30/1.84 tff(3101,plain,
% 2.30/1.84 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))) | ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.30/1.84 inference(quant_inst,[status(thm)],[])).
% 2.30/1.84 tff(3102,plain,
% 2.30/1.84 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3101, 3100])).
% 2.30/1.84 tff(3103,plain,
% 2.30/1.84 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[794, 3102, 3008])).
% 2.30/1.84 tff(3104,plain,
% 2.30/1.84 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (tptp_fun_Y1_11(X!1) = Y!0)),
% 2.30/1.84 inference(monotonicity,[status(thm)],[486])).
% 2.30/1.84 tff(3105,plain,
% 2.30/1.84 (tptp_fun_Y1_11(X!1) = Y!0),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[799, 3104])).
% 2.30/1.84 tff(3106,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[2949, 3105])).
% 2.30/1.84 tff(3107,plain,((~(tptp_fun_Y1_11(X!1) = W1!8)) | (tptp_fun_Y1_11(X!1) = Y!0) | (~(W1!8 = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3108,plain,
% 2.30/1.84 (~(W1!8 = Y!0)),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3107, 3103, 2949])).
% 2.30/1.84 tff(3109,assumption,(Y!0 = W1!8), introduced(assumption)).
% 2.30/1.84 tff(3110,plain,
% 2.30/1.84 (W1!8 = Y!0),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[3109, 1])).
% 2.30/1.84 tff(3111,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[801, 3110])).
% 2.30/1.84 tff(3112,plain,((~(Y!0 = W1!8)) | (W1!8 = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3113,plain,
% 2.30/1.84 (~(Y!0 = W1!8)),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3112, 3108])).
% 2.30/1.84 tff(3114,plain,
% 2.30/1.84 ((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.30/1.84 inference(tautology,[status(thm)],[])).
% 2.30/1.84 tff(3115,plain,
% 2.30/1.84 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3114, 3113, 3006])).
% 2.30/1.84 tff(3116,plain,
% 2.30/1.84 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))) | ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))),
% 2.30/1.84 inference(quant_inst,[status(thm)],[])).
% 2.30/1.84 tff(3117,plain,
% 2.30/1.84 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3116, 3115])).
% 2.30/1.84 tff(3118,assumption,(~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)), introduced(assumption)).
% 2.30/1.84 tff(3119,plain,
% 2.30/1.84 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3059, 3118])).
% 2.30/1.84 tff(3120,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3119])).
% 2.30/1.84 tff(3121,plain,
% 2.30/1.84 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.84 inference(symmetry,[status(thm)],[3120])).
% 2.30/1.84 tff(3122,plain,
% 2.30/1.84 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0))),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3121])).
% 2.30/1.84 tff(3123,plain,
% 2.30/1.84 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[45, 3122])).
% 2.30/1.84 tff(3124,assumption,((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))), introduced(assumption)).
% 2.30/1.84 tff(3125,plain,
% 2.30/1.84 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.30/1.84 inference(monotonicity,[status(thm)],[240])).
% 2.30/1.84 tff(3126,assumption,(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)), introduced(assumption)).
% 2.30/1.84 tff(3127,plain,
% 2.30/1.84 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 2.30/1.84 tff(3128,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3118, 3127])).
% 2.30/1.84 tff(3129,plain,((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3130,plain,
% 2.30/1.84 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3129, 3118, 240])).
% 2.30/1.84 tff(3131,plain,
% 2.30/1.84 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))),
% 2.30/1.84 inference(tautology,[status(thm)],[])).
% 2.30/1.84 tff(3132,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3131, 3130, 3124])).
% 2.30/1.84 tff(3133,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3132, 3123])).
% 2.30/1.84 tff(3134,plain,((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) | big_f(X!1, Y!0) | (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3135,plain,
% 2.30/1.84 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3134, 3117, 45, 2959])).
% 2.30/1.84 tff(3136,plain,
% 2.30/1.84 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[3135, 2961])).
% 2.30/1.84 tff(3137,plain,
% 2.30/1.84 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3039, 3135, 2964, 2966, 2959])).
% 2.30/1.84 tff(3138,plain,
% 2.30/1.84 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))) | (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) | (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))),
% 2.30/1.84 inference(tautology,[status(thm)],[])).
% 2.30/1.84 tff(3139,plain,
% 2.30/1.84 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3138, 3137, 3117])).
% 2.30/1.84 tff(3140,plain,
% 2.30/1.84 ($false),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3139, 3136])).
% 2.30/1.84 tff(3141,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(X!1, Y!0) | (tptp_fun_Y1_11(X!1) = Y!0) | (tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.84 tff(3142,plain,
% 2.30/1.84 (tptp_fun_Y1_11(X!1) = Y!0),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[3141, 41, 34, 45, 2934, 2939])).
% 2.30/1.84 tff(3143,plain,
% 2.30/1.84 ((tptp_fun_Y1_11(X!1) = X!1) <=> (Y!0 = X!1)),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3142])).
% 2.30/1.84 tff(3144,plain,
% 2.30/1.84 ((tptp_fun_Y1_11(X!1) = X!1) <=> (X!1 = Y!0)),
% 2.30/1.84 inference(transitivity,[status(thm)],[3143, 46])).
% 2.30/1.84 tff(3145,plain,
% 2.30/1.84 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = X!1)),
% 2.30/1.84 inference(symmetry,[status(thm)],[3144])).
% 2.30/1.84 tff(3146,plain,
% 2.30/1.84 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = X!1))),
% 2.30/1.84 inference(monotonicity,[status(thm)],[3145])).
% 2.30/1.84 tff(3147,plain,
% 2.30/1.84 (~(tptp_fun_Y1_11(X!1) = X!1)),
% 2.30/1.84 inference(modus_ponens,[status(thm)],[741, 3146])).
% 2.30/1.84 tff(3148,plain,
% 2.30/1.84 (X!1 = tptp_fun_X_2(Y!0)),
% 2.30/1.84 inference(symmetry,[status(thm)],[2935])).
% 2.30/1.84 tff(3149,plain,
% 2.30/1.84 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.30/1.84 inference(unit_resolution,[status(thm)],[627, 622, 45, 40])).
% 2.30/1.84 tff(3150,plain,
% 2.30/1.84 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[629, 3149])).
% 2.30/1.85 tff(3151,plain,
% 2.30/1.85 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[191, 1555])).
% 2.30/1.85 tff(3152,plain,
% 2.30/1.85 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[786, 3151, 45, 144])).
% 2.30/1.85 tff(3153,plain,
% 2.30/1.85 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[788, 3152])).
% 2.30/1.85 tff(3154,plain,
% 2.30/1.85 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1194, 1560, 622])).
% 2.30/1.85 tff(3155,plain,
% 2.30/1.85 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[576, 1560])).
% 2.30/1.85 tff(3156,plain,
% 2.30/1.85 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[751, 3155, 622])).
% 2.30/1.85 tff(3157,plain,
% 2.30/1.85 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1191, 3156])).
% 2.30/1.85 tff(3158,plain,
% 2.30/1.85 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[594, 3157])).
% 2.30/1.85 tff(3159,plain,
% 2.30/1.85 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3017, 1268])).
% 2.30/1.85 tff(3160,plain,
% 2.30/1.85 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3019, 3159])).
% 2.30/1.85 tff(3161,plain,
% 2.30/1.85 (tptp_fun_Y1_11(Y!0) = tptp_fun_X_2(Y!0)),
% 2.30/1.85 inference(transitivity,[status(thm)],[598, 2972])).
% 2.30/1.85 tff(3162,plain,
% 2.30/1.85 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3161])).
% 2.30/1.85 tff(3163,plain,
% 2.30/1.85 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3162])).
% 2.30/1.85 tff(3164,plain,
% 2.30/1.85 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.85 inference(modus_ponens,[status(thm)],[41, 3163])).
% 2.30/1.85 tff(3165,plain,
% 2.30/1.85 ((tptp_fun_X_2(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.30/1.85 inference(monotonicity,[status(thm)],[1906])).
% 2.30/1.85 tff(3166,plain,
% 2.30/1.85 ((tptp_fun_X_2(Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.30/1.85 inference(transitivity,[status(thm)],[3165, 24])).
% 2.30/1.85 tff(3167,plain,
% 2.30/1.85 ((tptp_fun_X_2(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.30/1.85 inference(transitivity,[status(thm)],[3166, 2172])).
% 2.30/1.85 tff(3168,plain,
% 2.30/1.85 ((~(tptp_fun_X_2(Y!0) = W1!8)) <=> (~(X!1 = W1!8))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3167])).
% 2.30/1.85 tff(3169,assumption,(~(tptp_fun_X_2(Y!0) = W1!8)), introduced(assumption)).
% 2.30/1.85 tff(3170,plain,
% 2.30/1.85 (~(X!1 = W1!8)),
% 2.30/1.85 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 2.30/1.85 tff(3171,plain,
% 2.30/1.85 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1273, 3170, 1954])).
% 2.30/1.85 tff(3172,plain,
% 2.30/1.85 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1996, 3171])).
% 2.30/1.85 tff(3173,plain,
% 2.30/1.85 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1994, 3172, 41, 622, 598, 1260])).
% 2.30/1.85 tff(3174,plain,
% 2.30/1.85 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[2258, 3173])).
% 2.30/1.85 tff(3175,plain,
% 2.30/1.85 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3086, 3169, 3073])).
% 2.30/1.85 tff(3176,plain,
% 2.30/1.85 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3084, 3175])).
% 2.30/1.85 tff(3177,plain,
% 2.30/1.85 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3082, 3173, 3176])).
% 2.30/1.85 tff(3178,plain,
% 2.30/1.85 ($false),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3080, 3177, 3174, 3164])).
% 2.30/1.85 tff(3179,plain,((tptp_fun_X_2(Y!0) = W1!8) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | (~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.85 tff(3180,plain,
% 2.30/1.85 (tptp_fun_X_2(Y!0) = W1!8),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3179, 1272, 1906, 598, 41, 1260, 622, 3160])).
% 2.30/1.85 tff(3181,plain,
% 2.30/1.85 (X!1 = Y!0),
% 2.30/1.85 inference(transitivity,[status(thm)],[2972, 3180, 1281])).
% 2.30/1.85 tff(3182,plain,
% 2.30/1.85 ($false),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[741, 3181])).
% 2.30/1.85 tff(3183,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.85 tff(3184,plain,
% 2.30/1.85 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3183, 3158, 2935, 40, 154, 3154, 622, 3153])).
% 2.30/1.85 tff(3185,plain,
% 2.30/1.85 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[462, 3184])).
% 2.30/1.85 tff(3186,plain,
% 2.30/1.85 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[743, 3185, 40, 3150])).
% 2.30/1.85 tff(3187,plain,
% 2.30/1.85 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[720, 3186])).
% 2.30/1.85 tff(3188,plain,
% 2.30/1.85 (~(tptp_fun_Z1_12(X!1) = X!1)),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[182, 3151, 45, 144])).
% 2.30/1.85 tff(3189,plain,
% 2.30/1.85 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[187, 3188])).
% 2.30/1.85 tff(3190,plain,
% 2.30/1.85 (tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1)) = tptp_fun_Y_7(Y!0, Y!0)),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3189])).
% 2.30/1.85 tff(3191,plain,
% 2.30/1.85 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1))) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3189, 3190])).
% 2.30/1.85 tff(3192,plain,
% 2.30/1.85 ((Y!0 = tptp_fun_Z1_12(X!1)) <=> (tptp_fun_Z1_12(X!1) = Y!0)),
% 2.30/1.85 inference(commutativity,[status(thm)],[])).
% 2.30/1.85 tff(3193,plain,
% 2.30/1.85 ((tptp_fun_Z1_12(X!1) = Y!0) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.30/1.85 inference(symmetry,[status(thm)],[3192])).
% 2.30/1.85 tff(3194,plain,
% 2.30/1.85 (Y!0 = tptp_fun_Z1_12(X!1)),
% 2.30/1.85 inference(modus_ponens,[status(thm)],[652, 3193])).
% 2.30/1.85 tff(3195,plain,
% 2.30/1.85 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1)))),
% 2.30/1.85 inference(quant_inst,[status(thm)],[])).
% 2.30/1.85 tff(3196,plain,
% 2.30/1.85 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3195, 658])).
% 2.30/1.85 tff(3197,plain,
% 2.30/1.85 ((~(big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1)))) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(Y!0 = tptp_fun_Z1_12(X!1)))),
% 2.30/1.85 inference(tautology,[status(thm)],[])).
% 2.30/1.85 tff(3198,plain,
% 2.30/1.85 (~(Y!0 = tptp_fun_Z1_12(X!1))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3197, 3196, 2501])).
% 2.30/1.85 tff(3199,plain,
% 2.30/1.85 ($false),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3198, 3194])).
% 2.30/1.85 tff(3200,plain,((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.85 tff(3201,plain,
% 2.30/1.85 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3200, 45, 144, 2501])).
% 2.30/1.85 tff(3202,plain,
% 2.30/1.85 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[191, 3201])).
% 2.30/1.85 tff(3203,plain,
% 2.30/1.85 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[88, 3202])).
% 2.30/1.85 tff(3204,plain,
% 2.30/1.85 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[82, 3203])).
% 2.30/1.85 tff(3205,plain,
% 2.30/1.85 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[56, 3204])).
% 2.30/1.85 tff(3206,plain,
% 2.30/1.85 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[2663, 3205])).
% 2.30/1.85 tff(3207,plain,
% 2.30/1.85 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[220, 3204])).
% 2.30/1.85 tff(3208,plain,
% 2.30/1.85 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[222, 3207])).
% 2.30/1.85 tff(3209,plain,
% 2.30/1.85 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1713, 3207])).
% 2.30/1.85 tff(3210,plain,
% 2.30/1.85 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.30/1.85 inference(monotonicity,[status(thm)],[1878])).
% 2.30/1.85 tff(3211,plain,
% 2.30/1.85 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.30/1.85 inference(symmetry,[status(thm)],[3210])).
% 2.30/1.85 tff(3212,plain,
% 2.30/1.85 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X_2(Y!0), Y!0))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3211])).
% 2.30/1.85 tff(3213,plain,
% 2.30/1.85 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.30/1.85 inference(modus_ponens,[status(thm)],[45, 3212])).
% 2.30/1.85 tff(3214,plain,
% 2.30/1.85 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1894, 598, 1857, 1846, 3213])).
% 2.30/1.85 tff(3215,plain,
% 2.30/1.85 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[2624, 598, 45, 2620, 3214])).
% 2.30/1.85 tff(3216,plain,
% 2.30/1.85 (tptp_fun_X_2(X!1) = Y!0),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[105, 3215])).
% 2.30/1.85 tff(3217,assumption,((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))), introduced(assumption)).
% 2.30/1.85 tff(3218,plain,
% 2.30/1.85 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[224, 3215, 3217])).
% 2.30/1.85 tff(3219,plain,
% 2.30/1.85 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3216, 1786])).
% 2.30/1.85 tff(3220,plain,
% 2.30/1.85 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.30/1.85 inference(symmetry,[status(thm)],[3219])).
% 2.30/1.85 tff(3221,plain,
% 2.30/1.85 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X_2(X!1), Y!0))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3220])).
% 2.30/1.85 tff(3222,plain,
% 2.30/1.85 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.30/1.85 inference(modus_ponens,[status(thm)],[2501, 3221])).
% 2.30/1.85 tff(3223,plain,
% 2.30/1.85 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1588, 3222, 3218, 3216, 598])).
% 2.30/1.85 tff(3224,plain,
% 2.30/1.85 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[627, 3214, 45, 598])).
% 2.30/1.85 tff(3225,plain,
% 2.30/1.85 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[629, 3224])).
% 2.30/1.85 tff(3226,plain,
% 2.30/1.85 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1858, 1846, 1857])).
% 2.30/1.85 tff(3227,plain,
% 2.30/1.85 (tptp_fun_Y1_11(Y!0) = tptp_fun_X_2(Y!0)),
% 2.30/1.85 inference(transitivity,[status(thm)],[598, 2967])).
% 2.30/1.85 tff(3228,plain,
% 2.30/1.85 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.85 inference(monotonicity,[status(thm)],[3227])).
% 2.30/1.85 tff(3229,plain,
% 2.30/1.85 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.30/1.85 inference(modus_ponens,[status(thm)],[3223, 3228])).
% 2.30/1.85 tff(3230,assumption,(big_f(Y!0, tptp_fun_X_2(Y!0))), introduced(assumption)).
% 2.30/1.85 tff(3231,assumption,(![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))), introduced(assumption)).
% 2.30/1.85 tff(3232,assumption,(~(big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))), introduced(assumption)).
% 2.30/1.85 tff(3233,plain,
% 2.30/1.85 ((~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.30/1.85 inference(quant_inst,[status(thm)],[])).
% 2.30/1.85 tff(3234,plain,
% 2.30/1.85 ($false),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3233, 3231, 3232])).
% 2.30/1.85 tff(3235,plain,((big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))) | (~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.30/1.85 tff(3236,plain,
% 2.30/1.85 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3235, 3231])).
% 2.30/1.85 tff(3237,plain,
% 2.30/1.85 ((~(big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | (~big_f(Y!0, tptp_fun_X_2(Y!0))) | (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.30/1.85 inference(tautology,[status(thm)],[])).
% 2.30/1.85 tff(3238,plain,
% 2.30/1.85 (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[3237, 3236, 3230])).
% 2.30/1.85 tff(3239,plain,
% 2.30/1.85 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = Y!0),
% 2.30/1.85 inference(symmetry,[status(thm)],[3238])).
% 2.30/1.85 tff(3240,assumption,(![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))), introduced(assumption)).
% 2.30/1.85 tff(3241,plain,
% 2.30/1.85 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1860, 3240])).
% 2.30/1.85 tff(3242,plain,
% 2.30/1.85 (~(Y!0 = tptp_fun_W_3(Y!0))),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1862, 3241, 35])).
% 2.30/1.85 tff(3243,plain,
% 2.30/1.85 (~(tptp_fun_W_3(Y!0) = Y!0)),
% 2.30/1.85 inference(modus_ponens,[status(thm)],[3242, 1856])).
% 2.30/1.85 tff(3244,plain,
% 2.30/1.85 (tptp_fun_W_3(Y!0) = X!1),
% 2.30/1.85 inference(unit_resolution,[status(thm)],[1871, 3243])).
% 2.30/1.85 tff(3245,plain,
% 2.30/1.85 (X!1 = tptp_fun_W_3(Y!0)),
% 2.30/1.85 inference(symmetry,[status(thm)],[3244])).
% 2.30/1.85 tff(3246,plain,
% 2.30/1.85 (tptp_fun_X_2(Y!0) = tptp_fun_W_3(Y!0)),
% 2.30/1.85 inference(transitivity,[status(thm)],[1906, 3245])).
% 2.30/1.85 tff(3247,plain,
% 2.30/1.85 (big_f(X!1, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[2972, 3246])).
% 2.35/1.86 tff(3248,plain,
% 2.35/1.86 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(X!1, tptp_fun_X_2(Y!0))),
% 2.35/1.86 inference(symmetry,[status(thm)],[3247])).
% 2.35/1.86 tff(3249,plain,
% 2.35/1.86 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1891, 3240])).
% 2.35/1.86 tff(3250,plain,
% 2.35/1.86 (big_f(X!1, tptp_fun_X_2(Y!0))),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 2.35/1.86 tff(3251,plain,
% 2.35/1.86 ((~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | (big_f(X!1, tptp_fun_X_2(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.86 inference(quant_inst,[status(thm)],[])).
% 2.35/1.86 tff(3252,plain,
% 2.35/1.86 (big_f(X!1, tptp_fun_X_2(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3251, 3231])).
% 2.35/1.86 tff(3253,assumption,(~(X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))), introduced(assumption)).
% 2.35/1.86 tff(3254,plain,
% 2.35/1.86 ((~(big_f(X!1, tptp_fun_X_2(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | (~big_f(X!1, tptp_fun_X_2(Y!0))) | (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.35/1.86 inference(tautology,[status(thm)],[])).
% 2.35/1.86 tff(3255,plain,
% 2.35/1.86 ((~(big_f(X!1, tptp_fun_X_2(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | (~big_f(X!1, tptp_fun_X_2(Y!0)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3254, 3253])).
% 2.35/1.86 tff(3256,plain,
% 2.35/1.86 (~big_f(X!1, tptp_fun_X_2(Y!0))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3255, 3252])).
% 2.35/1.86 tff(3257,plain,
% 2.35/1.86 ($false),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3256, 3250])).
% 2.35/1.86 tff(3258,plain,((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (~(tptp_fun_X_2(Y!0) = X!1)) | (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) | (~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.86 tff(3259,plain,
% 2.35/1.86 (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3258, 3231, 1906, 3240, 35])).
% 2.35/1.86 tff(3260,plain,
% 2.35/1.86 (X!1 = Y!0),
% 2.35/1.86 inference(transitivity,[status(thm)],[3259, 3239])).
% 2.35/1.86 tff(3261,plain,
% 2.35/1.86 ($false),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[741, 3260])).
% 2.35/1.86 tff(3262,plain,((~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | (~big_f(Y!0, tptp_fun_X_2(Y!0))) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.86 tff(3263,plain,
% 2.35/1.86 (~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3262, 3229, 1878, 3226, 3213])).
% 2.35/1.86 tff(3264,plain,
% 2.35/1.86 ((~(tptp_fun_X_2(Y!0) = W1!8)) <=> (~(W1!8 = X!1))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3166])).
% 2.35/1.86 tff(3265,assumption,(~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))), introduced(assumption)).
% 2.35/1.86 tff(3266,plain,
% 2.35/1.86 (((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))))) | ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))),
% 2.35/1.86 inference(tautology,[status(thm)],[])).
% 2.35/1.86 tff(3267,plain,
% 2.35/1.86 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3266, 3159])).
% 2.35/1.86 tff(3268,plain,
% 2.35/1.86 ((~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))) | (~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.86 inference(tautology,[status(thm)],[])).
% 2.35/1.86 tff(3269,plain,
% 2.35/1.86 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3268, 3267, 3265])).
% 2.35/1.86 tff(3270,plain,
% 2.35/1.86 (~(W1!8 = X!1)),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3269, 3264])).
% 2.35/1.86 tff(3271,plain,
% 2.35/1.86 (W1!8 = Y!0),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[19, 3270])).
% 2.35/1.86 tff(3272,plain,
% 2.35/1.86 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.35/1.86 inference(transitivity,[status(thm)],[3271, 1786])).
% 2.35/1.86 tff(3273,plain,
% 2.35/1.86 (big_f(Y!0, W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3272])).
% 2.35/1.86 tff(3274,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, W1!8)),
% 2.35/1.86 inference(symmetry,[status(thm)],[3273])).
% 2.35/1.86 tff(3275,plain,
% 2.35/1.86 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, W1!8))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3274])).
% 2.35/1.86 tff(3276,plain,
% 2.35/1.86 (~big_f(Y!0, W1!8)),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[2501, 3275])).
% 2.35/1.86 tff(3277,plain,
% 2.35/1.86 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[516, 3276, 2536])).
% 2.35/1.86 tff(3278,plain,
% 2.35/1.86 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3277, 44])).
% 2.35/1.86 tff(3279,plain,
% 2.35/1.86 ((tptp_fun_Z1_9(Y!0) = X!1) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.35/1.86 inference(commutativity,[status(thm)],[])).
% 2.35/1.86 tff(3280,plain,
% 2.35/1.86 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(Y!0)),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3271])).
% 2.35/1.86 tff(3281,plain,
% 2.35/1.86 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_Z1_9(Y!0) = X!1)),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3280])).
% 2.35/1.86 tff(3282,plain,
% 2.35/1.86 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.35/1.86 inference(transitivity,[status(thm)],[3281, 3279])).
% 2.35/1.86 tff(3283,plain,
% 2.35/1.86 ((X!1 = tptp_fun_Z1_9(Y!0)) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.35/1.86 inference(symmetry,[status(thm)],[3282])).
% 2.35/1.86 tff(3284,plain,
% 2.35/1.86 ((~(X!1 = tptp_fun_Z1_9(Y!0))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3283])).
% 2.35/1.86 tff(3285,plain,
% 2.35/1.86 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3003, 1268])).
% 2.35/1.86 tff(3286,plain,
% 2.35/1.86 (((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))))) | ((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))),
% 2.35/1.86 inference(tautology,[status(thm)],[])).
% 2.35/1.86 tff(3287,plain,
% 2.35/1.86 ((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3286, 3285])).
% 2.35/1.86 tff(3288,plain,
% 2.35/1.86 (Y!0 = W1!8),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3271, 2])).
% 2.35/1.86 tff(3289,plain,
% 2.35/1.86 ((~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))) | (~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.86 inference(tautology,[status(thm)],[])).
% 2.35/1.86 tff(3290,plain,
% 2.35/1.86 (![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3289, 3288, 3287])).
% 2.35/1.86 tff(3291,plain,
% 2.35/1.86 ((~![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))) | (big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.86 inference(quant_inst,[status(thm)],[])).
% 2.35/1.86 tff(3292,plain,
% 2.35/1.86 (big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3291, 3290])).
% 2.35/1.86 tff(3293,plain,
% 2.35/1.86 ((~(big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0)))) | big_f(X!1, Y!0) | (~(X!1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.86 inference(tautology,[status(thm)],[])).
% 2.35/1.86 tff(3294,plain,
% 2.35/1.86 ((~(big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0)))) | (~(X!1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3293, 45])).
% 2.35/1.86 tff(3295,plain,
% 2.35/1.86 (~(X!1 = tptp_fun_Z1_9(Y!0))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3294, 3292])).
% 2.35/1.86 tff(3296,plain,
% 2.35/1.86 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3295, 3284])).
% 2.35/1.86 tff(3297,plain,
% 2.35/1.86 ($false),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[522, 3296, 3278])).
% 2.35/1.86 tff(3298,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | big_f(X!1, Y!0) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.86 tff(3299,plain,
% 2.35/1.86 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3298, 3263, 2501, 796, 1878, 45])).
% 2.35/1.86 tff(3300,plain,
% 2.35/1.86 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[462, 3299])).
% 2.35/1.86 tff(3301,plain,
% 2.35/1.86 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[743, 3300, 598, 3225])).
% 2.35/1.86 tff(3302,plain,
% 2.35/1.86 ((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1110, 3301])).
% 2.35/1.86 tff(3303,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1091, 3302, 598, 3223])).
% 2.35/1.86 tff(3304,plain,
% 2.35/1.86 (~(tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1093, 3302, 3303])).
% 2.35/1.86 tff(3305,plain,
% 2.35/1.86 (tptp_fun_Y_7(X!1, Y!0) = Y!0),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1101, 3304])).
% 2.35/1.86 tff(3306,plain,
% 2.35/1.86 (tptp_fun_Y_7(X!1, Y!0) = tptp_fun_Y1_11(X!1)),
% 2.35/1.86 inference(transitivity,[status(thm)],[3305, 1786])).
% 2.35/1.86 tff(3307,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3306])).
% 2.35/1.86 tff(3308,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.86 inference(symmetry,[status(thm)],[3307])).
% 2.35/1.86 tff(3309,plain,
% 2.35/1.86 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3308])).
% 2.35/1.86 tff(3310,plain,
% 2.35/1.86 (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[2501, 3309])).
% 2.35/1.86 tff(3311,plain,
% 2.35/1.86 ($false),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3303, 3310])).
% 2.35/1.86 tff(3312,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(X!1, Y!0) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))) | (tptp_fun_X_2(Y!0) = Y!0) | (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.86 tff(3313,plain,
% 2.35/1.86 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3312, 45, 154, 2501, 3208, 3209, 1857, 3206])).
% 2.35/1.86 tff(3314,plain,
% 2.35/1.86 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[39, 3313])).
% 2.35/1.86 tff(3315,plain,
% 2.35/1.86 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1858, 3206, 1857])).
% 2.35/1.86 tff(3316,plain,
% 2.35/1.86 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.35/1.86 inference(monotonicity,[status(thm)],[1906])).
% 2.35/1.86 tff(3317,plain,
% 2.35/1.86 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.86 inference(symmetry,[status(thm)],[3316])).
% 2.35/1.86 tff(3318,plain,
% 2.35/1.86 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_X_2(Y!0), Y!0))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3317])).
% 2.35/1.86 tff(3319,plain,
% 2.35/1.86 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[45, 3318])).
% 2.35/1.86 tff(3320,plain,
% 2.35/1.86 (~(Y!0 = tptp_fun_W_3(Y!0))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1862, 3319, 3241])).
% 2.35/1.86 tff(3321,plain,
% 2.35/1.86 (~(tptp_fun_W_3(Y!0) = Y!0)),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3320, 1856])).
% 2.35/1.86 tff(3322,plain,
% 2.35/1.86 (tptp_fun_W_3(Y!0) = X!1),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1871, 3321])).
% 2.35/1.86 tff(3323,plain,
% 2.35/1.86 (X!1 = tptp_fun_W_3(Y!0)),
% 2.35/1.86 inference(symmetry,[status(thm)],[3322])).
% 2.35/1.86 tff(3324,plain,
% 2.35/1.86 (~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3262, 3230, 1906, 3240, 3319])).
% 2.35/1.86 tff(3325,plain,
% 2.35/1.86 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3298, 3324, 2501, 796, 1906, 45])).
% 2.35/1.86 tff(3326,plain,
% 2.35/1.86 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[462, 3325])).
% 2.35/1.86 tff(3327,plain,
% 2.35/1.86 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[385, 3326])).
% 2.35/1.86 tff(3328,plain,
% 2.35/1.86 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[983, 3327])).
% 2.35/1.86 tff(3329,plain,
% 2.35/1.86 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.35/1.86 inference(transitivity,[status(thm)],[109, 1786])).
% 2.35/1.86 tff(3330,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3329])).
% 2.35/1.86 tff(3331,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.86 inference(symmetry,[status(thm)],[3330])).
% 2.35/1.86 tff(3332,plain,
% 2.35/1.86 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3331])).
% 2.35/1.86 tff(3333,plain,
% 2.35/1.86 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[2501, 3332])).
% 2.35/1.86 tff(3334,plain,
% 2.35/1.86 ((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.35/1.86 inference(monotonicity,[status(thm)],[937])).
% 2.35/1.86 tff(3335,plain,
% 2.35/1.86 ((~(tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)) <=> (~(tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3334])).
% 2.35/1.86 tff(3336,plain,
% 2.35/1.86 (~(tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[601, 3335])).
% 2.35/1.86 tff(3337,plain,
% 2.35/1.86 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[946, 601, 109, 41])).
% 2.35/1.86 tff(3338,plain,
% 2.35/1.86 (((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)) | (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) | (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)),
% 2.35/1.86 inference(tautology,[status(thm)],[])).
% 2.35/1.86 tff(3339,plain,
% 2.35/1.86 (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3338, 3337, 601])).
% 2.35/1.86 tff(3340,plain,
% 2.35/1.86 (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3339, 952])).
% 2.35/1.86 tff(3341,plain,
% 2.35/1.86 ($false),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[1089, 3340, 3336, 1079])).
% 2.35/1.86 tff(3342,plain,((tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1) | (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.86 tff(3343,plain,
% 2.35/1.86 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1),
% 2.35/1.86 inference(unit_resolution,[status(thm)],[3342, 1079, 109, 41])).
% 2.35/1.86 tff(3344,plain,
% 2.35/1.86 (tptp_fun_Y_7(X!1, Y!0) = X!1),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3343, 3334])).
% 2.35/1.86 tff(3345,plain,
% 2.35/1.86 (X!1 = tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.86 inference(symmetry,[status(thm)],[3343])).
% 2.35/1.86 tff(3346,plain,
% 2.35/1.86 (tptp_fun_X_2(Y!0) = tptp_fun_Y_7(X!1, Y!0)),
% 2.35/1.86 inference(transitivity,[status(thm)],[1906, 3345, 937])).
% 2.35/1.86 tff(3347,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.86 inference(monotonicity,[status(thm)],[3346])).
% 2.35/1.86 tff(3348,plain,
% 2.35/1.86 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.86 inference(modus_ponens,[status(thm)],[3230, 3347])).
% 2.35/1.87 tff(3349,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1093, 3348, 3344, 1079])).
% 2.35/1.87 tff(3350,plain,((~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | (~big_f(Y!0, tptp_fun_X_2(Y!0))) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3351,plain,
% 2.35/1.87 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3350, 3230, 1906, 109, 3333])).
% 2.35/1.87 tff(3352,plain,
% 2.35/1.87 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1110, 3351])).
% 2.35/1.87 tff(3353,plain,
% 2.35/1.87 (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[428, 3326])).
% 2.35/1.87 tff(3354,plain,
% 2.35/1.87 ((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[723, 3353])).
% 2.35/1.87 tff(3355,plain,
% 2.35/1.87 (Y!0 = Z!5),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[725, 3354, 3352])).
% 2.35/1.87 tff(3356,plain,
% 2.35/1.87 (Z!5 = Y!0),
% 2.35/1.87 inference(symmetry,[status(thm)],[3355])).
% 2.35/1.87 tff(3357,plain,
% 2.35/1.87 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3356, 2972])).
% 2.35/1.87 tff(3358,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Z!5, X!1)),
% 2.35/1.87 inference(symmetry,[status(thm)],[3357])).
% 2.35/1.87 tff(3359,plain,
% 2.35/1.87 (big_f(Z!5, X!1)),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[3230, 3358])).
% 2.35/1.87 tff(3360,plain,
% 2.35/1.87 (X!1 = tptp_fun_W_6(Z!5)),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[989, 3359, 3328])).
% 2.35/1.87 tff(3361,plain,
% 2.35/1.87 (tptp_fun_W_6(Z!5) = X!1),
% 2.35/1.87 inference(symmetry,[status(thm)],[3360])).
% 2.35/1.87 tff(3362,plain,
% 2.35/1.87 (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Z!5)),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3355])).
% 2.35/1.87 tff(3363,plain,
% 2.35/1.87 (X!1 = Z!5),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1008, 981, 1836])).
% 2.35/1.87 tff(3364,plain,
% 2.35/1.87 (X!1 = Y!0),
% 2.35/1.87 inference(transitivity,[status(thm)],[3363, 727])).
% 2.35/1.87 tff(3365,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[741, 3364])).
% 2.35/1.87 tff(3366,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3367,plain,
% 2.35/1.87 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3366, 3326, 3352])).
% 2.35/1.87 tff(3368,plain,
% 2.35/1.87 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1010, 3367])).
% 2.35/1.87 tff(3369,plain,
% 2.35/1.87 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1034, 3360, 3368, 3355, 45])).
% 2.35/1.87 tff(3370,plain,
% 2.35/1.87 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1036, 3369, 3368])).
% 2.35/1.87 tff(3371,plain,
% 2.35/1.87 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_3(Y!0)),
% 2.35/1.87 inference(transitivity,[status(thm)],[3370, 3362, 3361, 3323])).
% 2.35/1.87 tff(3372,plain,
% 2.35/1.87 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[2972, 3371])).
% 2.35/1.87 tff(3373,plain,
% 2.35/1.87 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.35/1.87 inference(symmetry,[status(thm)],[3372])).
% 2.35/1.87 tff(3374,plain,
% 2.35/1.87 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[3249, 3373])).
% 2.35/1.87 tff(3375,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3369, 3374])).
% 2.35/1.87 tff(3376,plain,((~big_f(Y!0, tptp_fun_X_2(Y!0))) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(X!1, Y!0) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (~(tptp_fun_Y1_11(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3377,plain,
% 2.35/1.87 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3376, 45, 1878, 2501, 154, 3315, 3314])).
% 2.35/1.87 tff(3378,plain,
% 2.35/1.87 (Y!0 = tptp_fun_Y1_11(X!1)),
% 2.35/1.87 inference(symmetry,[status(thm)],[154])).
% 2.35/1.87 tff(3379,plain,
% 2.35/1.87 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.35/1.87 inference(transitivity,[status(thm)],[3314, 3378])).
% 2.35/1.87 tff(3380,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3379])).
% 2.35/1.87 tff(3381,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.87 inference(symmetry,[status(thm)],[3380])).
% 2.35/1.87 tff(3382,plain,
% 2.35/1.87 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3381])).
% 2.35/1.87 tff(3383,plain,
% 2.35/1.87 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[2501, 3382])).
% 2.35/1.87 tff(3384,plain,
% 2.35/1.87 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[224, 47, 3217])).
% 2.35/1.87 tff(3385,plain,
% 2.35/1.87 (~(tptp_fun_W_3(X!1) = Y!0)),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[247, 245, 240, 41, 109])).
% 2.35/1.87 tff(3386,plain,
% 2.35/1.87 (tptp_fun_W_3(X!1) = X!1),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[252, 3385])).
% 2.35/1.87 tff(3387,plain,
% 2.35/1.87 (tptp_fun_W_3(X!1) = tptp_fun_X_2(Y!0)),
% 2.35/1.87 inference(transitivity,[status(thm)],[3386, 2972])).
% 2.35/1.87 tff(3388,plain,
% 2.35/1.87 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[240, 3387])).
% 2.35/1.87 tff(3389,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.35/1.87 inference(symmetry,[status(thm)],[3388])).
% 2.35/1.87 tff(3390,plain,
% 2.35/1.87 ((~big_f(Y!0, tptp_fun_X_2(Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3389])).
% 2.35/1.87 tff(3391,plain,
% 2.35/1.87 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[2991, 3390])).
% 2.35/1.87 tff(3392,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[245, 3391])).
% 2.35/1.87 tff(3393,plain,((~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3394,plain,
% 2.35/1.87 (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3393, 106, 1906, 109, 41, 2991])).
% 2.35/1.87 tff(3395,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[234, 3394, 3384])).
% 2.35/1.87 tff(3396,plain,((tptp_fun_X_2(X!1) = X!1) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3397,plain,
% 2.35/1.87 (tptp_fun_X_2(X!1) = X!1),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3396, 3314, 1878, 3383, 3377, 3208])).
% 2.35/1.87 tff(3398,plain,
% 2.35/1.87 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1711, 3397, 3209])).
% 2.35/1.87 tff(3399,plain,
% 2.35/1.87 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1709, 3398])).
% 2.35/1.87 tff(3400,plain,
% 2.35/1.87 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1692, 3399, 45, 3397])).
% 2.35/1.87 tff(3401,plain,
% 2.35/1.87 (tptp_fun_Y_4(X!1, X!1) = X!1),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1694, 3400, 3399])).
% 2.35/1.87 tff(3402,plain,
% 2.35/1.87 (~(Y!0 = tptp_fun_W_3(Y!0))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1862, 3213, 1861])).
% 2.35/1.87 tff(3403,plain,
% 2.35/1.87 (~(tptp_fun_W_3(Y!0) = Y!0)),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[3402, 1856])).
% 2.35/1.87 tff(3404,plain,
% 2.35/1.87 (tptp_fun_W_3(Y!0) = X!1),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1871, 3403])).
% 2.35/1.87 tff(3405,plain,
% 2.35/1.87 (tptp_fun_W_3(Y!0) = tptp_fun_Y_4(X!1, X!1)),
% 2.35/1.87 inference(transitivity,[status(thm)],[3404, 1697])).
% 2.35/1.87 tff(3406,plain,
% 2.35/1.87 (tptp_fun_X_2(Y!0) = tptp_fun_X_2(X!1)),
% 2.35/1.87 inference(transitivity,[status(thm)],[1878, 1664])).
% 2.35/1.87 tff(3407,plain,
% 2.35/1.87 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3406, 3405])).
% 2.35/1.87 tff(3408,plain,
% 2.35/1.87 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.35/1.87 inference(symmetry,[status(thm)],[3407])).
% 2.35/1.87 tff(3409,plain,
% 2.35/1.87 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (~big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3408])).
% 2.35/1.87 tff(3410,plain,
% 2.35/1.87 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[1702, 3409])).
% 2.35/1.87 tff(3411,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1892, 3410])).
% 2.35/1.87 tff(3412,plain,((tptp_fun_X_2(Y!0) = Y!0) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) | (~(tptp_fun_Y_4(X!1, X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0) | (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3413,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3412, 3401, 3400, 1857, 45, 3397, 3206])).
% 2.35/1.87 tff(3414,plain,(big_f(X!1, Y!0) | (tptp_fun_X_2(Y!0) = Y!0) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3415,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3414, 144, 45, 2934])).
% 2.35/1.87 tff(3416,plain,
% 2.35/1.87 (tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1)) = tptp_fun_Y_7(Y!0, Y!0)),
% 2.35/1.87 inference(monotonicity,[status(thm)],[156])).
% 2.35/1.87 tff(3417,plain,
% 2.35/1.87 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1))) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[156, 3416])).
% 2.35/1.87 tff(3418,plain,
% 2.35/1.87 ((~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1)))) <=> (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3417])).
% 2.35/1.87 tff(3419,assumption,(~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1)))), introduced(assumption)).
% 2.35/1.87 tff(3420,plain,
% 2.35/1.87 (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[3419, 3418])).
% 2.35/1.87 tff(3421,plain,
% 2.35/1.87 (tptp_fun_Y_7(Y!0, Y!0) = Y!0),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[714, 3420, 693])).
% 2.35/1.87 tff(3422,plain,
% 2.35/1.87 (tptp_fun_Y_7(Y!0, Y!0) = tptp_fun_Y1_11(X!1)),
% 2.35/1.87 inference(transitivity,[status(thm)],[3421, 1786])).
% 2.35/1.87 tff(3423,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3422])).
% 2.35/1.87 tff(3424,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.35/1.87 inference(symmetry,[status(thm)],[3423])).
% 2.35/1.87 tff(3425,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[2569, 3424])).
% 2.35/1.87 tff(3426,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3420, 3425])).
% 2.35/1.87 tff(3427,plain,((~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1))) | (~(tptp_fun_Z1_12(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3428,plain,
% 2.35/1.87 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1)))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3427, 3187, 154, 3415, 3189])).
% 2.35/1.87 tff(3429,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[3428, 3191])).
% 2.35/1.87 tff(3430,plain,
% 2.35/1.87 (~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[699, 3429, 3187])).
% 2.35/1.87 tff(3431,plain,
% 2.35/1.87 (tptp_fun_Y_7(Y!0, Y!0) = X!1),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[708, 3430])).
% 2.35/1.87 tff(3432,plain,
% 2.35/1.87 (tptp_fun_Y_7(Y!0, Y!0) = tptp_fun_X_2(Y!0)),
% 2.35/1.87 inference(transitivity,[status(thm)],[3431, 3148])).
% 2.35/1.87 tff(3433,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3432])).
% 2.35/1.87 tff(3434,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.35/1.87 inference(symmetry,[status(thm)],[3433])).
% 2.35/1.87 tff(3435,plain,
% 2.35/1.87 ((~big_f(Y!0, tptp_fun_X_2(Y!0))) <=> (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3434])).
% 2.35/1.87 tff(3436,plain,
% 2.35/1.87 (tptp_fun_Y1_11(Y!0) = tptp_fun_X_2(Y!0)),
% 2.35/1.87 inference(transitivity,[status(thm)],[40, 3148])).
% 2.35/1.87 tff(3437,plain,
% 2.35/1.87 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3436])).
% 2.35/1.87 tff(3438,plain,
% 2.35/1.87 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.35/1.87 inference(monotonicity,[status(thm)],[3437])).
% 2.35/1.87 tff(3439,plain,
% 2.35/1.87 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[3154, 3438])).
% 2.35/1.87 tff(3440,plain,
% 2.35/1.87 (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.35/1.87 inference(modus_ponens,[status(thm)],[3439, 3435])).
% 2.35/1.87 tff(3441,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3429, 3440])).
% 2.35/1.87 tff(3442,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (tptp_fun_Y1_11(Y!0) = Y!0) | big_f(X!1, Y!0) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3443,plain,
% 2.35/1.87 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3442, 3147, 34, 45, 2946])).
% 2.35/1.87 tff(3444,plain,
% 2.35/1.87 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[82, 3443])).
% 2.35/1.87 tff(3445,plain,
% 2.35/1.87 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[2663, 1441])).
% 2.35/1.87 tff(3446,plain,
% 2.35/1.87 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1711, 2485, 1663])).
% 2.35/1.87 tff(3447,plain,
% 2.35/1.87 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1709, 3446])).
% 2.35/1.87 tff(3448,plain,
% 2.35/1.87 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1692, 3447, 45, 1663])).
% 2.35/1.87 tff(3449,plain,
% 2.35/1.87 (tptp_fun_Y_4(X!1, X!1) = X!1),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[1694, 3448, 3447])).
% 2.35/1.87 tff(3450,plain,
% 2.35/1.87 ($false),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3412, 3449, 3448, 2934, 45, 1663, 3445])).
% 2.35/1.87 tff(3451,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.87 tff(3452,plain,
% 2.35/1.87 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[3451, 3444, 45])).
% 2.35/1.87 tff(3453,plain,
% 2.35/1.87 (tptp_fun_X_2(X!1) = Y!0),
% 2.35/1.87 inference(unit_resolution,[status(thm)],[105, 3452])).
% 2.35/1.87 tff(3454,plain,
% 2.35/1.87 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[220, 3444])).
% 2.35/1.88 tff(3455,plain,
% 2.35/1.88 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[222, 3454])).
% 2.35/1.88 tff(3456,plain,
% 2.35/1.88 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[224, 3455, 3452])).
% 2.35/1.88 tff(3457,plain,
% 2.35/1.88 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[234, 3456])).
% 2.35/1.88 tff(3458,plain,
% 2.35/1.88 (~(tptp_fun_W_3(X!1) = X!1)),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1578, 3457, 40, 41, 3453])).
% 2.35/1.88 tff(3459,plain,
% 2.35/1.88 (tptp_fun_W_3(X!1) = Y!0),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[252, 3458])).
% 2.35/1.88 tff(3460,plain,
% 2.35/1.88 (tptp_fun_X_2(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.35/1.88 inference(transitivity,[status(thm)],[2935, 2455])).
% 2.35/1.88 tff(3461,plain,
% 2.35/1.88 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.88 inference(monotonicity,[status(thm)],[3460])).
% 2.35/1.88 tff(3462,plain,
% 2.35/1.88 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.88 inference(symmetry,[status(thm)],[3461])).
% 2.35/1.88 tff(3463,plain,
% 2.35/1.88 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.35/1.88 inference(monotonicity,[status(thm)],[3462])).
% 2.35/1.88 tff(3464,plain,
% 2.35/1.88 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.88 inference(modus_ponens,[status(thm)],[41, 3463])).
% 2.35/1.88 tff(3465,plain,
% 2.35/1.88 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[2996, 3464, 3453, 3457, 2935, 3459])).
% 2.35/1.88 tff(3466,plain,
% 2.35/1.88 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[720, 3465])).
% 2.35/1.88 tff(3467,plain,
% 2.35/1.88 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[743, 3466, 40, 2948])).
% 2.35/1.88 tff(3468,plain,
% 2.35/1.88 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[462, 3467])).
% 2.35/1.88 tff(3469,plain,
% 2.35/1.88 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3017, 3468])).
% 2.35/1.88 tff(3470,plain,
% 2.35/1.88 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3019, 3469])).
% 2.35/1.88 tff(3471,plain,
% 2.35/1.88 (~((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3013, 3468])).
% 2.35/1.88 tff(3472,plain,
% 2.35/1.88 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3015, 3471])).
% 2.35/1.88 tff(3473,plain,
% 2.35/1.88 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3090, 3472, 45, 3453, 2935, 3464, 3459, 3457, 3470])).
% 2.35/1.88 tff(3474,plain,
% 2.35/1.88 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.35/1.88 inference(monotonicity,[status(thm)],[3460])).
% 2.35/1.88 tff(3475,plain,
% 2.35/1.88 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.35/1.88 inference(symmetry,[status(thm)],[3474])).
% 2.35/1.88 tff(3476,plain,
% 2.35/1.88 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.88 inference(monotonicity,[status(thm)],[3473])).
% 2.35/1.88 tff(3477,plain,
% 2.35/1.88 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.35/1.88 inference(symmetry,[status(thm)],[3476])).
% 2.35/1.88 tff(3478,plain,
% 2.35/1.88 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.35/1.88 inference(transitivity,[status(thm)],[3477, 3475])).
% 2.35/1.88 tff(3479,plain,
% 2.35/1.88 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.35/1.88 inference(modus_ponens,[status(thm)],[2946, 3478])).
% 2.35/1.88 tff(3480,plain,
% 2.35/1.88 ((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))) | (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.35/1.88 inference(tautology,[status(thm)],[])).
% 2.35/1.88 tff(3481,plain,
% 2.35/1.88 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3480, 3479, 3473])).
% 2.35/1.88 tff(3482,plain,
% 2.35/1.88 ((tptp_fun_X_2(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.35/1.88 inference(monotonicity,[status(thm)],[2935])).
% 2.35/1.88 tff(3483,plain,
% 2.35/1.88 ((tptp_fun_X_2(Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.35/1.88 inference(transitivity,[status(thm)],[3482, 24])).
% 2.35/1.88 tff(3484,plain,
% 2.35/1.88 ((W1!8 = X!1) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.35/1.88 inference(symmetry,[status(thm)],[3483])).
% 2.35/1.88 tff(3485,plain,
% 2.35/1.88 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))),
% 2.35/1.88 inference(symmetry,[status(thm)],[3125])).
% 2.35/1.88 tff(3486,plain,
% 2.35/1.88 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3134, 3124, 45, 240])).
% 2.35/1.88 tff(3487,plain,
% 2.35/1.88 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)),
% 2.35/1.88 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 2.35/1.88 tff(3488,plain,
% 2.35/1.88 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3039, 3486, 240, 245, 238])).
% 2.35/1.88 tff(3489,plain,
% 2.35/1.88 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3138, 3488, 3124])).
% 2.35/1.88 tff(3490,plain,
% 2.35/1.88 ($false),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3489, 3487])).
% 2.35/1.88 tff(3491,plain,((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | (~(tptp_fun_W_3(X!1) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.88 tff(3492,plain,
% 2.35/1.88 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3491, 3459, 45, 3453, 3457])).
% 2.35/1.88 tff(3493,plain,
% 2.35/1.88 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3116, 3492])).
% 2.35/1.88 tff(3494,plain,
% 2.35/1.88 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3003, 3468])).
% 2.35/1.88 tff(3495,plain,
% 2.35/1.88 ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3005, 3494])).
% 2.35/1.88 tff(3496,plain,
% 2.35/1.88 (Y!0 = W1!8),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3114, 3495, 3493])).
% 2.35/1.88 tff(3497,plain,
% 2.35/1.88 (W1!8 = Y!0),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3112, 3496])).
% 2.35/1.88 tff(3498,plain,
% 2.35/1.88 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.35/1.88 inference(monotonicity,[status(thm)],[3497])).
% 2.35/1.88 tff(3499,plain,
% 2.35/1.88 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.35/1.88 inference(transitivity,[status(thm)],[3498, 46])).
% 2.35/1.88 tff(3500,plain,
% 2.35/1.88 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.35/1.88 inference(symmetry,[status(thm)],[3499])).
% 2.35/1.88 tff(3501,plain,
% 2.35/1.88 ((X!1 = Y!0) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.35/1.88 inference(transitivity,[status(thm)],[3500, 3484])).
% 2.35/1.88 tff(3502,plain,
% 2.35/1.88 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X_2(Y!0) = W1!8))),
% 2.35/1.88 inference(monotonicity,[status(thm)],[3501])).
% 2.35/1.88 tff(3503,plain,
% 2.35/1.88 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.35/1.88 inference(modus_ponens,[status(thm)],[741, 3502])).
% 2.35/1.88 tff(3504,plain,
% 2.35/1.88 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3086, 3503, 3470])).
% 2.35/1.88 tff(3505,plain,
% 2.35/1.88 ($false),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3084, 3504, 3481])).
% 2.35/1.88 tff(3506,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(X!1, Y!0) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.88 tff(3507,plain,
% 2.35/1.88 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3506, 45, 34])).
% 2.35/1.88 tff(3508,plain,
% 2.35/1.88 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1254, 42, 40, 3507])).
% 2.35/1.88 tff(3509,plain,
% 2.35/1.88 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1256, 3508])).
% 2.35/1.88 tff(3510,plain,
% 2.35/1.88 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.88 inference(modus_ponens,[status(thm)],[3507, 3462])).
% 2.35/1.88 tff(3511,plain,
% 2.35/1.88 (tptp_fun_Y1_11(X!1) = tptp_fun_X_2(Y!0)),
% 2.35/1.88 inference(transitivity,[status(thm)],[277, 2967])).
% 2.35/1.88 tff(3512,plain,
% 2.35/1.88 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1894, 42, 1857, 598, 35])).
% 2.35/1.88 tff(3513,plain,
% 2.35/1.88 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[2663, 3512])).
% 2.35/1.88 tff(3514,plain,
% 2.35/1.88 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[56, 3513])).
% 2.35/1.88 tff(3515,plain,
% 2.35/1.88 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[82, 3514])).
% 2.35/1.88 tff(3516,plain,
% 2.35/1.88 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[88, 3515])).
% 2.35/1.88 tff(3517,plain,
% 2.35/1.88 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[90, 3516])).
% 2.35/1.88 tff(3518,plain,
% 2.35/1.88 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[269, 3517, 277])).
% 2.35/1.88 tff(3519,plain,
% 2.35/1.88 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[879, 3518])).
% 2.35/1.88 tff(3520,plain,
% 2.35/1.88 (tptp_fun_X1_13(Y!0, X!1) = Y!0),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1118, 42, 277, 598, 3519])).
% 2.35/1.88 tff(3521,plain,
% 2.35/1.88 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.35/1.88 inference(monotonicity,[status(thm)],[3520, 3511])).
% 2.35/1.88 tff(3522,plain,
% 2.35/1.88 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.35/1.88 inference(symmetry,[status(thm)],[3521])).
% 2.35/1.88 tff(3523,plain,
% 2.35/1.88 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.35/1.88 inference(modus_ponens,[status(thm)],[3230, 3522])).
% 2.35/1.88 tff(3524,plain,
% 2.35/1.88 (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[907, 3520, 3519])).
% 2.35/1.88 tff(3525,plain,
% 2.35/1.88 ($false),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3524, 3523])).
% 2.35/1.88 tff(3526,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~big_f(Y!0, tptp_fun_X_2(Y!0))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (tptp_fun_X_2(Y!0) = Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.88 tff(3527,plain,
% 2.35/1.88 (~(tptp_fun_Y1_11(X!1) = X!1)),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[3526, 42, 40, 2934, 3510, 2939])).
% 2.35/1.88 tff(3528,plain,
% 2.35/1.88 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1894, 42, 40, 2934, 2939])).
% 2.35/1.88 tff(3529,plain,
% 2.35/1.88 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[2663, 3528])).
% 2.35/1.88 tff(3530,plain,
% 2.35/1.88 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[56, 3529])).
% 2.35/1.88 tff(3531,plain,
% 2.35/1.88 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[82, 3530])).
% 2.35/1.88 tff(3532,plain,
% 2.35/1.88 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[88, 3531])).
% 2.35/1.88 tff(3533,plain,
% 2.35/1.88 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[191, 3532])).
% 2.35/1.88 tff(3534,plain,
% 2.35/1.88 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[786, 3533, 45, 3527])).
% 2.35/1.88 tff(3535,plain,
% 2.35/1.88 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[788, 3534])).
% 2.35/1.88 tff(3536,plain,
% 2.35/1.88 (tptp_fun_Y1_11(X!1) = Y!0),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[153, 3527])).
% 2.35/1.88 tff(3537,plain,
% 2.35/1.88 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[84, 3531])).
% 2.35/1.88 tff(3538,plain,
% 2.35/1.88 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[561, 3537])).
% 2.35/1.88 tff(3539,plain,
% 2.35/1.88 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[563, 3538, 34])).
% 2.35/1.88 tff(3540,plain,
% 2.35/1.88 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[576, 3539])).
% 2.35/1.88 tff(3541,plain,
% 2.35/1.88 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[578, 3540, 42])).
% 2.35/1.88 tff(3542,plain,
% 2.35/1.88 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1264, 3541])).
% 2.35/1.88 tff(3543,plain,
% 2.35/1.88 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1298, 3542, 3536, 3535, 3509])).
% 2.35/1.88 tff(3544,plain,
% 2.35/1.88 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[462, 3543])).
% 2.35/1.88 tff(3545,plain,
% 2.35/1.88 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[385, 3544])).
% 2.35/1.88 tff(3546,plain,
% 2.35/1.88 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[387, 3545])).
% 2.35/1.88 tff(3547,plain,
% 2.35/1.88 (Y!0 = tptp_fun_Y1_11(X!1)),
% 2.35/1.88 inference(symmetry,[status(thm)],[3536])).
% 2.35/1.88 tff(3548,assumption,(X!1 = Z!5), introduced(assumption)).
% 2.35/1.88 tff(3549,plain,
% 2.35/1.88 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1206, 42, 45, 40])).
% 2.35/1.88 tff(3550,plain,
% 2.35/1.88 (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[346, 3549, 3548])).
% 2.35/1.88 tff(3551,plain,
% 2.35/1.88 ((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[344, 3550])).
% 2.35/1.88 tff(3552,plain,
% 2.35/1.88 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[342, 3551])).
% 2.35/1.88 tff(3553,plain,
% 2.35/1.88 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[462, 3552])).
% 2.35/1.88 tff(3554,plain,
% 2.35/1.88 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[2945, 42, 2934, 2939, 34])).
% 2.35/1.88 tff(3555,plain,
% 2.35/1.88 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1254, 3554, 40, 42])).
% 2.35/1.88 tff(3556,plain,
% 2.35/1.88 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1256, 3555])).
% 2.35/1.88 tff(3557,plain,
% 2.35/1.88 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[1894, 42, 2934, 2939, 40])).
% 2.35/1.88 tff(3558,plain,
% 2.35/1.88 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[2663, 3557])).
% 2.35/1.88 tff(3559,plain,
% 2.35/1.88 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[56, 3558])).
% 2.35/1.88 tff(3560,plain,
% 2.35/1.88 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.88 inference(unit_resolution,[status(thm)],[82, 3559])).
% 2.35/1.88 tff(3561,plain,
% 2.35/1.88 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[88, 3560])).
% 2.35/1.89 tff(3562,plain,
% 2.35/1.89 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[191, 3561])).
% 2.35/1.89 tff(3563,plain,
% 2.35/1.89 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[786, 3562, 45, 144])).
% 2.35/1.89 tff(3564,plain,
% 2.35/1.89 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[788, 3563])).
% 2.35/1.89 tff(3565,plain,
% 2.35/1.89 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1298, 3564, 154, 3556, 3553])).
% 2.35/1.89 tff(3566,plain,
% 2.35/1.89 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[84, 3560])).
% 2.35/1.89 tff(3567,plain,
% 2.35/1.89 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[561, 3566])).
% 2.35/1.89 tff(3568,plain,
% 2.35/1.89 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[563, 3567, 34])).
% 2.35/1.89 tff(3569,plain,
% 2.35/1.89 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[576, 3568])).
% 2.35/1.89 tff(3570,plain,
% 2.35/1.89 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[578, 3569, 42])).
% 2.35/1.89 tff(3571,plain,
% 2.35/1.89 ($false),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1264, 3570, 3565])).
% 2.35/1.89 tff(3572,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | (tptp_fun_Y1_11(Y!0) = Y!0) | big_f(X!1, Y!0) | (tptp_fun_Y1_11(X!1) = X!1) | (~(X!1 = Z!5))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.89 tff(3573,plain,
% 2.35/1.89 (~(X!1 = Z!5)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3572, 3527, 34, 45, 42])).
% 2.35/1.89 tff(3574,plain,
% 2.35/1.89 (~(Z!5 = X!1)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[353, 3573])).
% 2.35/1.89 tff(3575,plain,
% 2.35/1.89 (Z!5 = Y!0),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[361, 3574])).
% 2.35/1.89 tff(3576,plain,
% 2.35/1.89 (big_f(Z!5, Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3575, 3547])).
% 2.35/1.89 tff(3577,plain,
% 2.35/1.89 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Z!5, Y!0)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3576])).
% 2.35/1.89 tff(3578,plain,
% 2.35/1.89 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3414, 3527, 45, 2934])).
% 2.35/1.89 tff(3579,plain,
% 2.35/1.89 (big_f(Z!5, Y!0)),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[3578, 3577])).
% 2.35/1.89 tff(3580,plain,
% 2.35/1.89 (Y!0 = tptp_fun_W_6(Z!5)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1209, 3579, 3546])).
% 2.35/1.89 tff(3581,plain,
% 2.35/1.89 (tptp_fun_W_6(Z!5) = Y!0),
% 2.35/1.89 inference(symmetry,[status(thm)],[3580])).
% 2.35/1.89 tff(3582,plain,
% 2.35/1.89 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3575])).
% 2.35/1.89 tff(3583,plain,
% 2.35/1.89 (tptp_fun_W_6(Y!0) = tptp_fun_W_6(Z!5)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3582])).
% 2.35/1.89 tff(3584,plain,
% 2.35/1.89 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1822, 42, 40, 45])).
% 2.35/1.89 tff(3585,plain,
% 2.35/1.89 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[342, 3544])).
% 2.35/1.89 tff(3586,plain,
% 2.35/1.89 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1840, 3585, 2630])).
% 2.35/1.89 tff(3587,plain,
% 2.35/1.89 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1010, 3586])).
% 2.35/1.89 tff(3588,plain,
% 2.35/1.89 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1036, 3587, 3584])).
% 2.35/1.89 tff(3589,plain,
% 2.35/1.89 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0),
% 2.35/1.89 inference(transitivity,[status(thm)],[3588, 3583, 3581])).
% 2.35/1.89 tff(3590,plain,
% 2.35/1.89 ((tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1) <=> (Y!0 = X!1)),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3589])).
% 2.35/1.89 tff(3591,plain,
% 2.35/1.89 ((tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1) <=> (X!1 = Y!0)),
% 2.35/1.89 inference(transitivity,[status(thm)],[3590, 46])).
% 2.35/1.89 tff(3592,plain,
% 2.35/1.89 ((X!1 = Y!0) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3591])).
% 2.35/1.89 tff(3593,plain,
% 2.35/1.89 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1))),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3592])).
% 2.35/1.89 tff(3594,plain,
% 2.35/1.89 (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[741, 3593])).
% 2.35/1.89 tff(3595,plain,
% 2.35/1.89 ((X!1 = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.35/1.89 inference(commutativity,[status(thm)],[])).
% 2.35/1.89 tff(3596,plain,
% 2.35/1.89 (tptp_fun_W_6(Y!0) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3588])).
% 2.35/1.89 tff(3597,plain,
% 2.35/1.89 (tptp_fun_W_6(Z!5) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.35/1.89 inference(transitivity,[status(thm)],[3582, 3596])).
% 2.35/1.89 tff(3598,plain,
% 2.35/1.89 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3597])).
% 2.35/1.89 tff(3599,plain,
% 2.35/1.89 ((X!1 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)),
% 2.35/1.89 inference(transitivity,[status(thm)],[3598, 3595])).
% 2.35/1.89 tff(3600,plain,
% 2.35/1.89 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[983, 3545])).
% 2.35/1.89 tff(3601,plain,
% 2.35/1.89 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3575, 2455])).
% 2.35/1.89 tff(3602,plain,
% 2.35/1.89 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, X!1)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3601])).
% 2.35/1.89 tff(3603,plain,
% 2.35/1.89 (big_f(Z!5, X!1)),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[3507, 3602])).
% 2.35/1.89 tff(3604,plain,
% 2.35/1.89 (X!1 = tptp_fun_W_6(Z!5)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[989, 3603, 3600])).
% 2.35/1.89 tff(3605,plain,
% 2.35/1.89 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[3604, 3599])).
% 2.35/1.89 tff(3606,plain,
% 2.35/1.89 ($false),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3605, 3594])).
% 2.35/1.89 tff(3607,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | (tptp_fun_Y1_11(Y!0) = Y!0) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.89 tff(3608,plain,
% 2.35/1.89 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3607, 45, 34])).
% 2.35/1.89 tff(3609,plain,
% 2.35/1.89 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[627, 3608, 45, 40])).
% 2.35/1.89 tff(3610,plain,
% 2.35/1.89 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[629, 3609])).
% 2.35/1.89 tff(3611,plain,
% 2.35/1.89 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[2232, 3608, 3507, 45, 34])).
% 2.35/1.89 tff(3612,plain,
% 2.35/1.89 (tptp_fun_X_2(X!1) = Y!0),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[105, 3611])).
% 2.35/1.89 tff(3613,plain,
% 2.35/1.89 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1413, 3612, 40, 3507])).
% 2.35/1.89 tff(3614,plain,
% 2.35/1.89 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1194, 3608, 3507])).
% 2.35/1.89 tff(3615,plain,
% 2.35/1.89 (~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[563, 3614, 34])).
% 2.35/1.89 tff(3616,plain,
% 2.35/1.89 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[561, 3615])).
% 2.35/1.89 tff(3617,plain,
% 2.35/1.89 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[84, 3616])).
% 2.35/1.89 tff(3618,plain,
% 2.35/1.89 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[82, 3617])).
% 2.35/1.89 tff(3619,plain,
% 2.35/1.89 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[220, 3618])).
% 2.35/1.89 tff(3620,plain,
% 2.35/1.89 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[222, 3619])).
% 2.35/1.89 tff(3621,plain,
% 2.35/1.89 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[224, 3620, 3611])).
% 2.35/1.89 tff(3622,plain,
% 2.35/1.89 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1157, 3621, 3613])).
% 2.35/1.89 tff(3623,plain,
% 2.35/1.89 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1091, 1079, 598, 135])).
% 2.35/1.89 tff(3624,plain,
% 2.35/1.89 (~(tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1093, 3623, 1079])).
% 2.35/1.89 tff(3625,plain,
% 2.35/1.89 (tptp_fun_Y_7(X!1, Y!0) = Y!0),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1101, 3624])).
% 2.35/1.89 tff(3626,plain,
% 2.35/1.89 (Y!0 = tptp_fun_Y_7(X!1, Y!0)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3625])).
% 2.35/1.89 tff(3627,plain,
% 2.35/1.89 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.35/1.89 inference(monotonicity,[status(thm)],[240, 3626])).
% 2.35/1.89 tff(3628,plain,
% 2.35/1.89 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3627])).
% 2.35/1.89 tff(3629,plain,
% 2.35/1.89 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[3623, 3628])).
% 2.35/1.89 tff(3630,plain,
% 2.35/1.89 ($false),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1568, 3629])).
% 2.35/1.89 tff(3631,plain,((~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | big_f(tptp_fun_X_2(X!1), Y!0) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.89 tff(3632,plain,
% 2.35/1.89 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3631, 3622, 40, 3507, 3612])).
% 2.35/1.89 tff(3633,plain,
% 2.35/1.89 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1110, 3632])).
% 2.35/1.89 tff(3634,plain,
% 2.35/1.89 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[743, 3633, 40, 3610])).
% 2.35/1.89 tff(3635,plain,
% 2.35/1.89 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[462, 3634])).
% 2.35/1.89 tff(3636,plain,
% 2.35/1.89 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[481, 3635])).
% 2.35/1.89 tff(3637,plain,
% 2.35/1.89 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[483, 3636])).
% 2.35/1.89 tff(3638,plain,
% 2.35/1.89 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[56, 3618])).
% 2.35/1.89 tff(3639,plain,
% 2.35/1.89 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[2663, 3638])).
% 2.35/1.89 tff(3640,plain,
% 2.35/1.89 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[1858, 3639, 2934])).
% 2.35/1.89 tff(3641,plain,
% 2.35/1.89 (~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3262, 3640, 2935, 2939, 3510])).
% 2.35/1.89 tff(3642,plain,
% 2.35/1.89 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3017, 3635])).
% 2.35/1.89 tff(3643,plain,
% 2.35/1.89 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3266, 3642])).
% 2.35/1.89 tff(3644,plain,
% 2.35/1.89 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3268, 3643, 3641])).
% 2.35/1.89 tff(3645,plain,
% 2.35/1.89 ((W1!8 = X!1) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3166])).
% 2.35/1.89 tff(3646,plain,
% 2.35/1.89 (tptp_fun_X_2(Y!0) = W1!8),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[1289, 3645])).
% 2.35/1.89 tff(3647,plain,
% 2.35/1.89 ($false),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3169, 3646])).
% 2.35/1.89 tff(3648,plain,((~(W1!8 = X!1)) | (tptp_fun_X_2(Y!0) = W1!8) | (~(tptp_fun_X_2(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.89 tff(3649,plain,
% 2.35/1.89 (~(W1!8 = X!1)),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3648, 3644, 2935])).
% 2.35/1.89 tff(3650,plain,
% 2.35/1.89 (W1!8 = Y!0),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[19, 3649])).
% 2.35/1.89 tff(3651,plain,
% 2.35/1.89 (Y!0 = tptp_fun_X_2(X!1)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3612])).
% 2.35/1.89 tff(3652,plain,
% 2.35/1.89 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3651, 3650])).
% 2.35/1.89 tff(3653,plain,
% 2.35/1.89 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, W1!8)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3652])).
% 2.35/1.89 tff(3654,plain,
% 2.35/1.89 ((~big_f(tptp_fun_X_2(X!1), Y!0)) <=> (~big_f(Y!0, W1!8))),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3653])).
% 2.35/1.89 tff(3655,plain,
% 2.35/1.89 (~big_f(Y!0, W1!8)),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[3622, 3654])).
% 2.35/1.89 tff(3656,plain,
% 2.35/1.89 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[516, 3655, 3637])).
% 2.35/1.89 tff(3657,plain,
% 2.35/1.89 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[3656, 44])).
% 2.35/1.89 tff(3658,plain,
% 2.35/1.89 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(Y!0)),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3650])).
% 2.35/1.89 tff(3659,plain,
% 2.35/1.89 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_Z1_9(Y!0) = X!1)),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3658])).
% 2.35/1.89 tff(3660,plain,
% 2.35/1.89 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.35/1.89 inference(transitivity,[status(thm)],[3659, 3279])).
% 2.35/1.89 tff(3661,plain,
% 2.35/1.89 ((X!1 = tptp_fun_Z1_9(Y!0)) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.35/1.89 inference(symmetry,[status(thm)],[3660])).
% 2.35/1.89 tff(3662,plain,
% 2.35/1.89 ((~(X!1 = tptp_fun_Z1_9(Y!0))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.35/1.89 inference(monotonicity,[status(thm)],[3661])).
% 2.35/1.89 tff(3663,plain,
% 2.35/1.89 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3003, 3635])).
% 2.35/1.89 tff(3664,plain,
% 2.35/1.89 ((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.89 inference(unit_resolution,[status(thm)],[3286, 3663])).
% 2.35/1.89 tff(3665,plain,
% 2.35/1.89 (Y!0 = W1!8),
% 2.35/1.89 inference(modus_ponens,[status(thm)],[3650, 2])).
% 2.35/1.90 tff(3666,plain,
% 2.35/1.90 (![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3289, 3665, 3664])).
% 2.35/1.90 tff(3667,plain,
% 2.35/1.90 (big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3291, 3666])).
% 2.35/1.90 tff(3668,plain,
% 2.35/1.90 (~(X!1 = tptp_fun_Z1_9(Y!0))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3294, 3667])).
% 2.35/1.90 tff(3669,plain,
% 2.35/1.90 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[3668, 3662])).
% 2.35/1.90 tff(3670,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[522, 3669, 3657])).
% 2.35/1.90 tff(3671,plain,(big_f(X!1, Y!0) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3672,plain,
% 2.35/1.90 (big_f(X!1, Y!0)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3671, 34])).
% 2.35/1.90 tff(3673,plain,
% 2.35/1.90 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[52, 2666, 30])).
% 2.35/1.90 tff(3674,plain,
% 2.35/1.90 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[50, 3673])).
% 2.35/1.90 tff(3675,plain,
% 2.35/1.90 (big_f(X!1, Y!0)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[2933, 30])).
% 2.35/1.90 tff(3676,plain,
% 2.35/1.90 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[220, 2661])).
% 2.35/1.90 tff(3677,plain,
% 2.35/1.90 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[1713, 3676])).
% 2.35/1.90 tff(3678,assumption,(big_f(X!1, Y!0)), introduced(assumption)).
% 2.35/1.90 tff(3679,plain,
% 2.35/1.90 ((~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))) | ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0))),
% 2.35/1.90 inference(quant_inst,[status(thm)],[])).
% 2.35/1.90 tff(3680,plain,
% 2.35/1.90 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3679, 2621])).
% 2.35/1.90 tff(3681,assumption,(tptp_fun_Y_4(Y!0, X!1) = Y!0), introduced(assumption)).
% 2.35/1.90 tff(3682,plain,
% 2.35/1.90 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(X!1, Y!0)),
% 2.35/1.90 inference(monotonicity,[status(thm)],[1663, 3681])).
% 2.35/1.90 tff(3683,plain,
% 2.35/1.90 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.35/1.90 inference(symmetry,[status(thm)],[3682])).
% 2.35/1.90 tff(3684,plain,
% 2.35/1.90 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[3678, 3683])).
% 2.35/1.90 tff(3685,assumption,((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)), introduced(assumption)).
% 2.35/1.90 tff(3686,plain,
% 2.35/1.90 ((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0))) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) | (~(tptp_fun_Y_4(Y!0, X!1) = Y!0))),
% 2.35/1.90 inference(tautology,[status(thm)],[])).
% 2.35/1.90 tff(3687,plain,
% 2.35/1.90 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3686, 3681, 3685])).
% 2.35/1.90 tff(3688,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3687, 3684])).
% 2.35/1.90 tff(3689,plain,((~(tptp_fun_Y_4(Y!0, X!1) = Y!0)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3690,plain,
% 2.35/1.90 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3689, 3680, 3678, 1663])).
% 2.35/1.90 tff(3691,plain,
% 2.35/1.90 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(Y!0, X!1) = Y!0) | (tptp_fun_Y_4(Y!0, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(Y!0, X!1) = Y!0) | (tptp_fun_Y_4(Y!0, X!1) = X!1))),
% 2.35/1.90 inference(rewrite,[status(thm)],[])).
% 2.35/1.90 tff(3692,plain,
% 2.35/1.90 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_4(Y!0, X!1) = Y!0) | (tptp_fun_Y_4(Y!0, X!1) = X!1))),
% 2.35/1.90 inference(quant_inst,[status(thm)],[])).
% 2.35/1.90 tff(3693,plain,
% 2.35/1.90 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_4(Y!0, X!1) = Y!0) | (tptp_fun_Y_4(Y!0, X!1) = X!1)),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[3692, 3691])).
% 2.35/1.90 tff(3694,plain,
% 2.35/1.90 ((tptp_fun_Y_4(Y!0, X!1) = Y!0) | (tptp_fun_Y_4(Y!0, X!1) = X!1)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3693, 12])).
% 2.35/1.90 tff(3695,plain,
% 2.35/1.90 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3694, 3690])).
% 2.35/1.90 tff(3696,plain,
% 2.35/1.90 (tptp_fun_Y_4(Y!0, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.35/1.90 inference(transitivity,[status(thm)],[3695, 599])).
% 2.35/1.90 tff(3697,plain,
% 2.35/1.90 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[1663, 3696])).
% 2.35/1.90 tff(3698,plain,
% 2.35/1.90 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.35/1.90 inference(symmetry,[status(thm)],[3697])).
% 2.35/1.90 tff(3699,plain,
% 2.35/1.90 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[3698])).
% 2.35/1.90 tff(3700,plain,
% 2.35/1.90 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[42, 3699])).
% 2.35/1.90 tff(3701,plain,
% 2.35/1.90 ((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0))) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) | (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.35/1.90 inference(tautology,[status(thm)],[])).
% 2.35/1.90 tff(3702,plain,
% 2.35/1.90 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3701, 3690, 3680])).
% 2.35/1.90 tff(3703,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3702, 3700])).
% 2.35/1.90 tff(3704,plain,((~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(X!1, Y!0)) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3705,plain,
% 2.35/1.90 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3704, 3677, 40, 3675, 42])).
% 2.35/1.90 tff(3706,plain,
% 2.35/1.90 ((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[958, 114])).
% 2.35/1.90 tff(3707,plain,
% 2.35/1.90 (tptp_fun_X1_13(X!1, Y!0) = X!1),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[977, 973, 41])).
% 2.35/1.90 tff(3708,plain,
% 2.35/1.90 (big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, Y!0)),
% 2.35/1.90 inference(monotonicity,[status(thm)],[3707, 109])).
% 2.35/1.90 tff(3709,plain,
% 2.35/1.90 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(symmetry,[status(thm)],[3708])).
% 2.35/1.90 tff(3710,plain,
% 2.35/1.90 (big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[3678, 3709])).
% 2.35/1.90 tff(3711,plain,
% 2.35/1.90 ((~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))) | (~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.35/1.90 inference(tautology,[status(thm)],[])).
% 2.35/1.90 tff(3712,plain,
% 2.35/1.90 (~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3711, 973, 3707])).
% 2.35/1.90 tff(3713,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3712, 3710])).
% 2.35/1.90 tff(3714,plain,((~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3715,plain,
% 2.35/1.90 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3714, 3706, 3678, 109])).
% 2.35/1.90 tff(3716,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3715, 1434])).
% 2.35/1.90 tff(3717,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(X!1, Y!0)) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3718,plain,
% 2.35/1.90 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3717, 109, 30, 3675, 35])).
% 2.35/1.90 tff(3719,plain,
% 2.35/1.90 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[86, 3718])).
% 2.35/1.90 tff(3720,plain,
% 2.35/1.90 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[1449, 109, 30, 35, 47])).
% 2.35/1.90 tff(3721,plain,
% 2.35/1.90 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[82, 3720])).
% 2.35/1.90 tff(3722,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[84, 3721, 3719])).
% 2.35/1.90 tff(3723,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3724,plain,
% 2.35/1.90 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3723, 47, 35, 30])).
% 2.35/1.90 tff(3725,plain,
% 2.35/1.90 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[39, 3724])).
% 2.35/1.90 tff(3726,plain,
% 2.35/1.90 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[1413, 828, 106, 3725])).
% 2.35/1.90 tff(3727,plain,
% 2.35/1.90 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.90 inference(monotonicity,[status(thm)],[31, 154])).
% 2.35/1.90 tff(3728,plain,
% 2.35/1.90 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.90 inference(symmetry,[status(thm)],[3727])).
% 2.35/1.90 tff(3729,plain,
% 2.35/1.90 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_Y1_11(X!1)))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[3728])).
% 2.35/1.90 tff(3730,plain,
% 2.35/1.90 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[35, 3729])).
% 2.35/1.90 tff(3731,plain,
% 2.35/1.90 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[106, 1786])).
% 2.35/1.90 tff(3732,plain,
% 2.35/1.90 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.90 inference(symmetry,[status(thm)],[3731])).
% 2.35/1.90 tff(3733,plain,
% 2.35/1.90 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X_2(X!1), Y!0))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[3732])).
% 2.35/1.90 tff(3734,plain,
% 2.35/1.90 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[2501, 3733])).
% 2.35/1.90 tff(3735,plain,
% 2.35/1.90 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[1588, 3384, 41, 598, 106])).
% 2.35/1.90 tff(3736,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3735, 3734])).
% 2.35/1.90 tff(3737,plain,((tptp_fun_X_2(X!1) = X!1) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3738,plain,
% 2.35/1.90 (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3737, 3726, 154, 3725, 3730, 47])).
% 2.35/1.90 tff(3739,plain,
% 2.35/1.90 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[222, 3738])).
% 2.35/1.90 tff(3740,plain,
% 2.35/1.90 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[220, 3739])).
% 2.35/1.90 tff(3741,plain,
% 2.35/1.90 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[82, 3740])).
% 2.35/1.90 tff(3742,plain,
% 2.35/1.90 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[84, 3741])).
% 2.35/1.90 tff(3743,plain,
% 2.35/1.90 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[561, 3742])).
% 2.35/1.90 tff(3744,plain,
% 2.35/1.90 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[563, 3743, 3724])).
% 2.35/1.90 tff(3745,plain,
% 2.35/1.90 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[596, 3744, 3726])).
% 2.35/1.90 tff(3746,plain,
% 2.35/1.90 ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (big_f(X!1, X!1) <=> (X!1 = tptp_fun_W_6(X!1)))),
% 2.35/1.90 inference(quant_inst,[status(thm)],[])).
% 2.35/1.90 tff(3747,plain,
% 2.35/1.90 (big_f(X!1, X!1) <=> (X!1 = tptp_fun_W_6(X!1))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3746, 298])).
% 2.35/1.90 tff(3748,plain,
% 2.35/1.90 (big_f(X!1, X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[599])).
% 2.35/1.90 tff(3749,plain,
% 2.35/1.90 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, X!1)),
% 2.35/1.90 inference(symmetry,[status(thm)],[3748])).
% 2.35/1.90 tff(3750,plain,
% 2.35/1.90 (big_f(X!1, X!1)),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[622, 3749])).
% 2.35/1.90 tff(3751,plain,
% 2.35/1.90 ((~(big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1)))) | (~big_f(X!1, Y!0)) | (Y!0 = tptp_fun_W_6(X!1))),
% 2.35/1.90 inference(tautology,[status(thm)],[])).
% 2.35/1.90 tff(3752,plain,
% 2.35/1.90 (Y!0 = tptp_fun_W_6(X!1)),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3751, 322, 3678])).
% 2.35/1.90 tff(3753,plain,
% 2.35/1.90 (tptp_fun_W_6(X!1) = Y!0),
% 2.35/1.90 inference(symmetry,[status(thm)],[3752])).
% 2.35/1.90 tff(3754,plain,
% 2.35/1.90 ((X!1 = tptp_fun_W_6(X!1)) <=> (X!1 = Y!0)),
% 2.35/1.90 inference(monotonicity,[status(thm)],[3753])).
% 2.35/1.90 tff(3755,plain,
% 2.35/1.90 ((X!1 = Y!0) <=> (X!1 = tptp_fun_W_6(X!1))),
% 2.35/1.90 inference(symmetry,[status(thm)],[3754])).
% 2.35/1.90 tff(3756,plain,
% 2.35/1.90 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_W_6(X!1)))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[3755])).
% 2.35/1.90 tff(3757,plain,
% 2.35/1.90 (~(X!1 = tptp_fun_W_6(X!1))),
% 2.35/1.90 inference(modus_ponens,[status(thm)],[741, 3756])).
% 2.35/1.90 tff(3758,plain,
% 2.35/1.90 ((~(big_f(X!1, X!1) <=> (X!1 = tptp_fun_W_6(X!1)))) | (~big_f(X!1, X!1)) | (X!1 = tptp_fun_W_6(X!1))),
% 2.35/1.90 inference(tautology,[status(thm)],[])).
% 2.35/1.90 tff(3759,plain,
% 2.35/1.90 ($false),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3758, 3757, 3750, 3747])).
% 2.35/1.90 tff(3760,plain,((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.90 tff(3761,plain,
% 2.35/1.90 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.35/1.90 inference(unit_resolution,[status(thm)],[3760, 3745, 3725, 3675])).
% 2.35/1.90 tff(3762,plain,
% 2.35/1.90 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (Y!0 = W1!8)),
% 2.35/1.90 inference(monotonicity,[status(thm)],[154])).
% 2.35/1.90 tff(3763,plain,
% 2.35/1.90 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (W1!8 = Y!0)),
% 2.35/1.90 inference(transitivity,[status(thm)],[3762, 1])).
% 2.35/1.90 tff(3764,plain,
% 2.35/1.90 ((W1!8 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.35/1.90 inference(symmetry,[status(thm)],[3763])).
% 2.35/1.90 tff(3765,plain,
% 2.35/1.90 ((~(tptp_fun_Z1_12(Y!0) = Y!0)) <=> (~(tptp_fun_Z1_12(Y!0) = W1!8))),
% 2.35/1.90 inference(monotonicity,[status(thm)],[1283])).
% 2.35/1.90 tff(3766,plain,
% 2.35/1.90 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[31, 796])).
% 2.35/1.91 tff(3767,plain,
% 2.35/1.91 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.91 inference(symmetry,[status(thm)],[3766])).
% 2.35/1.91 tff(3768,plain,
% 2.35/1.91 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_Y1_11(X!1)))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3767])).
% 2.35/1.91 tff(3769,plain,
% 2.35/1.91 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[35, 3768])).
% 2.35/1.91 tff(3770,plain,
% 2.35/1.91 (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3737, 3726, 796, 3725, 3769, 47])).
% 2.35/1.91 tff(3771,plain,
% 2.35/1.91 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[222, 3770])).
% 2.35/1.91 tff(3772,plain,
% 2.35/1.91 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[220, 3771])).
% 2.35/1.91 tff(3773,plain,
% 2.35/1.91 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[82, 3772])).
% 2.35/1.91 tff(3774,plain,
% 2.35/1.91 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[84, 3773])).
% 2.35/1.91 tff(3775,plain,
% 2.35/1.91 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[561, 3774])).
% 2.35/1.91 tff(3776,plain,
% 2.35/1.91 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[563, 3775, 3724])).
% 2.35/1.91 tff(3777,plain,
% 2.35/1.91 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[576, 3776])).
% 2.35/1.91 tff(3778,plain,
% 2.35/1.91 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[596, 3776, 3726])).
% 2.35/1.91 tff(3779,plain,
% 2.35/1.91 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[751, 3778, 3777])).
% 2.35/1.91 tff(3780,plain,
% 2.35/1.91 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[1191, 3779])).
% 2.35/1.91 tff(3781,plain,
% 2.35/1.91 (~(tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[3780, 3765])).
% 2.35/1.91 tff(3782,plain,
% 2.35/1.91 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[839, 834, 240, 828, 598, 830])).
% 2.35/1.91 tff(3783,plain,
% 2.35/1.91 (X!1 = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.35/1.91 inference(symmetry,[status(thm)],[3782])).
% 2.35/1.91 tff(3784,plain,
% 2.35/1.91 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3783])).
% 2.35/1.91 tff(3785,plain,
% 2.35/1.91 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(symmetry,[status(thm)],[3784])).
% 2.35/1.91 tff(3786,plain,
% 2.35/1.91 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))) <=> (~big_f(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3785])).
% 2.35/1.91 tff(3787,plain,
% 2.35/1.91 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[1191, 830])).
% 2.35/1.91 tff(3788,plain,
% 2.35/1.91 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[594, 3787])).
% 2.35/1.91 tff(3789,plain,
% 2.35/1.91 (tptp_fun_Z1_12(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.35/1.91 inference(transitivity,[status(thm)],[3788, 599])).
% 2.35/1.91 tff(3790,plain,
% 2.35/1.91 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3789])).
% 2.35/1.91 tff(3791,plain,
% 2.35/1.91 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3790])).
% 2.35/1.91 tff(3792,plain,
% 2.35/1.91 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[849, 3782, 834])).
% 2.35/1.91 tff(3793,plain,
% 2.35/1.91 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[3792, 3791])).
% 2.35/1.91 tff(3794,plain,
% 2.35/1.91 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[3793, 3786])).
% 2.35/1.91 tff(3795,plain,
% 2.35/1.91 ($false),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[622, 3794])).
% 2.35/1.91 tff(3796,plain,((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(tptp_fun_X_2(X!1), X!1) | (~(X!1 = tptp_fun_Z1_12(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.91 tff(3797,plain,
% 2.35/1.91 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3796, 3778, 3725, 106, 828, 3779])).
% 2.35/1.91 tff(3798,plain,
% 2.35/1.91 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[813, 3797])).
% 2.35/1.91 tff(3799,plain,
% 2.35/1.91 (~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[811, 3798, 3781])).
% 2.35/1.91 tff(3800,plain,
% 2.35/1.91 ((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[748, 3799])).
% 2.35/1.91 tff(3801,plain,
% 2.35/1.91 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[746, 3800])).
% 2.35/1.91 tff(3802,plain,
% 2.35/1.91 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[462, 3801])).
% 2.35/1.91 tff(3803,plain,
% 2.35/1.91 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[342, 3802])).
% 2.35/1.91 tff(3804,plain,
% 2.35/1.91 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[344, 3803])).
% 2.35/1.91 tff(3805,plain,
% 2.35/1.91 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3760, 3778, 3725, 3675])).
% 2.35/1.91 tff(3806,plain,
% 2.35/1.91 (~(X!1 = Z!5)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[346, 3805, 3804])).
% 2.35/1.91 tff(3807,plain,
% 2.35/1.91 (~(Z!5 = X!1)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[353, 3806])).
% 2.35/1.91 tff(3808,plain,
% 2.35/1.91 (Z!5 = Y!0),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[361, 3807])).
% 2.35/1.91 tff(3809,plain,
% 2.35/1.91 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3808])).
% 2.35/1.91 tff(3810,plain,
% 2.35/1.91 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3809])).
% 2.35/1.91 tff(3811,plain,
% 2.35/1.91 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.35/1.91 inference(transitivity,[status(thm)],[3810, 339])).
% 2.35/1.91 tff(3812,plain,
% 2.35/1.91 ((~(Y!0 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3811])).
% 2.35/1.91 tff(3813,plain,
% 2.35/1.91 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[385, 3802])).
% 2.35/1.91 tff(3814,plain,
% 2.35/1.91 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[387, 3813])).
% 2.35/1.91 tff(3815,plain,
% 2.35/1.91 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.35/1.91 inference(transitivity,[status(thm)],[3808, 31])).
% 2.35/1.91 tff(3816,plain,
% 2.35/1.91 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3815])).
% 2.35/1.91 tff(3817,plain,
% 2.35/1.91 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.35/1.91 inference(symmetry,[status(thm)],[3816])).
% 2.35/1.91 tff(3818,plain,
% 2.35/1.91 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Z!5, Y!0))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3817])).
% 2.35/1.91 tff(3819,plain,
% 2.35/1.91 (~big_f(Z!5, Y!0)),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[35, 3818])).
% 2.35/1.91 tff(3820,plain,
% 2.35/1.91 (~(Y!0 = tptp_fun_W_6(Z!5))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[394, 3819, 3814])).
% 2.35/1.91 tff(3821,plain,
% 2.35/1.91 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[3820, 3812])).
% 2.35/1.91 tff(3822,plain,
% 2.35/1.91 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[983, 3813])).
% 2.35/1.91 tff(3823,plain,
% 2.35/1.91 (Z!5 = tptp_fun_X_2(X!1)),
% 2.35/1.91 inference(transitivity,[status(thm)],[3808, 527])).
% 2.35/1.91 tff(3824,plain,
% 2.35/1.91 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3823])).
% 2.35/1.91 tff(3825,plain,
% 2.35/1.91 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Z!5, X!1)),
% 2.35/1.91 inference(symmetry,[status(thm)],[3824])).
% 2.35/1.91 tff(3826,plain,
% 2.35/1.91 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Z!5, X!1))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3825])).
% 2.35/1.91 tff(3827,plain,
% 2.35/1.91 (~big_f(Z!5, X!1)),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[828, 3826])).
% 2.35/1.91 tff(3828,plain,
% 2.35/1.91 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[1547, 3827, 3822])).
% 2.35/1.91 tff(3829,plain,
% 2.35/1.91 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[412])).
% 2.35/1.91 tff(3830,plain,
% 2.35/1.91 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3829])).
% 2.35/1.91 tff(3831,plain,
% 2.35/1.91 ((X!1 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.35/1.91 inference(transitivity,[status(thm)],[3830, 1537])).
% 2.35/1.91 tff(3832,plain,
% 2.35/1.91 ((tptp_fun_W_6(Y!0) = X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.35/1.91 inference(symmetry,[status(thm)],[3831])).
% 2.35/1.91 tff(3833,assumption,(tptp_fun_W_6(Y!0) = X!1), introduced(assumption)).
% 2.35/1.91 tff(3834,plain,
% 2.35/1.91 (X!1 = tptp_fun_W_6(Z!5)),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[3833, 3832])).
% 2.35/1.91 tff(3835,assumption,(~(X!1 = tptp_fun_W_6(Z!5))), introduced(assumption)).
% 2.35/1.91 tff(3836,plain,
% 2.35/1.91 ($false),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3835, 3834])).
% 2.35/1.91 tff(3837,plain,((~(tptp_fun_W_6(Y!0) = X!1)) | (X!1 = tptp_fun_W_6(Z!5)) | (~(Z!5 = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.91 tff(3838,plain,
% 2.35/1.91 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3837, 3828, 3808])).
% 2.35/1.91 tff(3839,plain,
% 2.35/1.91 (tptp_fun_W_6(Y!0) = Y!0),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[403, 3838])).
% 2.35/1.91 tff(3840,plain,
% 2.35/1.91 ($false),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3839, 3821])).
% 2.35/1.91 tff(3841,plain,(big_f(tptp_fun_X_2(X!1), X!1) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(W1!8 = Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.91 tff(3842,plain,
% 2.35/1.91 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3841, 20, 30, 35, 796, 47])).
% 2.35/1.91 tff(3843,plain,
% 2.35/1.91 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[866, 3842, 30, 35, 106])).
% 2.35/1.91 tff(3844,plain,
% 2.35/1.91 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[198, 3843])).
% 2.35/1.91 tff(3845,plain,
% 2.35/1.91 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[52, 3844, 30])).
% 2.35/1.91 tff(3846,plain,
% 2.35/1.91 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[54, 3845])).
% 2.35/1.91 tff(3847,plain,
% 2.35/1.91 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[56, 3846])).
% 2.35/1.91 tff(3848,plain,
% 2.35/1.91 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[82, 3847])).
% 2.35/1.91 tff(3849,plain,
% 2.35/1.91 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[84, 3848])).
% 2.35/1.91 tff(3850,plain,
% 2.35/1.91 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[561, 3849])).
% 2.35/1.91 tff(3851,plain,
% 2.35/1.91 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[563, 3850, 3724])).
% 2.35/1.91 tff(3852,plain,
% 2.35/1.91 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[527, 3725])).
% 2.35/1.91 tff(3853,plain,
% 2.35/1.91 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(symmetry,[status(thm)],[3852])).
% 2.35/1.91 tff(3854,plain,
% 2.35/1.91 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[3842, 3853])).
% 2.35/1.91 tff(3855,plain,
% 2.35/1.91 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[1194, 3854, 3851])).
% 2.35/1.91 tff(3856,plain,
% 2.35/1.91 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[596, 42, 575])).
% 2.35/1.91 tff(3857,plain,
% 2.35/1.91 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[1108, 3856, 30, 35, 598])).
% 2.35/1.91 tff(3858,plain,
% 2.35/1.91 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[1110, 3857])).
% 2.35/1.91 tff(3859,plain,
% 2.35/1.91 (Y!0 = Z!5),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[725, 3858, 724])).
% 2.35/1.91 tff(3860,plain,
% 2.35/1.91 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y_7(Z!5, X!1)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3859])).
% 2.35/1.91 tff(3861,plain,
% 2.35/1.91 ((tptp_fun_Y_7(Y!0, X!1) = Y!0) <=> (tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3860])).
% 2.35/1.91 tff(3862,plain,
% 2.35/1.91 ((~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) <=> (~(tptp_fun_Y_7(Z!5, X!1) = Y!0))),
% 2.35/1.91 inference(monotonicity,[status(thm)],[3861])).
% 2.35/1.91 tff(3863,plain,
% 2.35/1.91 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[3366, 3858, 341])).
% 2.35/1.91 tff(3864,plain,
% 2.35/1.91 ((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.35/1.91 inference(unit_resolution,[status(thm)],[1842, 3863])).
% 2.35/1.91 tff(3865,plain,
% 2.35/1.91 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) <=> big_f(X!1, Y!0)),
% 2.35/1.91 inference(monotonicity,[status(thm)],[1903])).
% 2.35/1.91 tff(3866,plain,
% 2.35/1.91 (big_f(X!1, Y!0) <=> big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.35/1.91 inference(symmetry,[status(thm)],[3865])).
% 2.35/1.91 tff(3867,plain,
% 2.35/1.91 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.35/1.91 inference(modus_ponens,[status(thm)],[3678, 3866])).
% 2.35/1.91 tff(3868,assumption,((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)), introduced(assumption)).
% 2.35/1.92 tff(3869,plain,
% 2.35/1.92 ((~((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0))) | (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) | (~(tptp_fun_Y_7(Y!0, X!1) = Y!0))),
% 2.35/1.92 inference(tautology,[status(thm)],[])).
% 2.35/1.92 tff(3870,plain,
% 2.35/1.92 (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3869, 1903, 3868])).
% 2.35/1.92 tff(3871,plain,
% 2.35/1.92 ($false),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3870, 3867])).
% 2.35/1.92 tff(3872,plain,((~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) | (~big_f(X!1, Y!0)) | (~((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.92 tff(3873,plain,
% 2.35/1.92 (~(tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3872, 3864, 3678])).
% 2.35/1.92 tff(3874,plain,
% 2.35/1.92 (~(tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.35/1.92 inference(modus_ponens,[status(thm)],[3873, 3862])).
% 2.35/1.92 tff(3875,plain,
% 2.35/1.92 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(Z!5, X!1) = Y!0) | (tptp_fun_Y_7(Z!5, X!1) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(Z!5, X!1) = Y!0) | (tptp_fun_Y_7(Z!5, X!1) = X!1))),
% 2.35/1.92 inference(rewrite,[status(thm)],[])).
% 2.35/1.92 tff(3876,plain,
% 2.35/1.92 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_Y_7(Z!5, X!1) = Y!0) | (tptp_fun_Y_7(Z!5, X!1) = X!1))),
% 2.35/1.92 inference(quant_inst,[status(thm)],[])).
% 2.35/1.92 tff(3877,plain,
% 2.35/1.92 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_Y_7(Z!5, X!1) = Y!0) | (tptp_fun_Y_7(Z!5, X!1) = X!1)),
% 2.35/1.92 inference(modus_ponens,[status(thm)],[3876, 3875])).
% 2.35/1.92 tff(3878,plain,
% 2.35/1.92 ((tptp_fun_Y_7(Z!5, X!1) = Y!0) | (tptp_fun_Y_7(Z!5, X!1) = X!1)),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3877, 12])).
% 2.35/1.92 tff(3879,plain,
% 2.35/1.92 (tptp_fun_Y_7(Z!5, X!1) = X!1),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3878, 3874])).
% 2.35/1.92 tff(3880,plain,
% 2.35/1.92 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.35/1.92 inference(transitivity,[status(thm)],[3860, 3879, 599])).
% 2.35/1.92 tff(3881,plain,
% 2.35/1.92 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3880])).
% 2.35/1.92 tff(3882,plain,
% 2.35/1.92 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.35/1.92 inference(symmetry,[status(thm)],[3881])).
% 2.35/1.92 tff(3883,plain,
% 2.35/1.92 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1)))),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3882])).
% 2.35/1.92 tff(3884,plain,
% 2.35/1.92 (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.35/1.92 inference(modus_ponens,[status(thm)],[42, 3883])).
% 2.35/1.92 tff(3885,plain,
% 2.35/1.92 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[1844, 3864, 3873])).
% 2.35/1.92 tff(3886,plain,
% 2.35/1.92 ($false),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3885, 3884])).
% 2.35/1.92 tff(3887,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(X!1, Y!0)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.92 tff(3888,plain,
% 2.35/1.92 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3887, 3855, 3675, 35, 30, 3725, 3851])).
% 2.35/1.92 tff(3889,plain,
% 2.35/1.92 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[462, 3888])).
% 2.35/1.92 tff(3890,plain,
% 2.35/1.92 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[1269, 3889])).
% 2.35/1.92 tff(3891,plain,
% 2.35/1.92 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[1254, 3855, 3725, 3854])).
% 2.35/1.92 tff(3892,plain,
% 2.35/1.92 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[1256, 3891])).
% 2.35/1.92 tff(3893,plain,
% 2.35/1.92 (~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[1273, 3892, 29])).
% 2.35/1.92 tff(3894,plain,
% 2.35/1.92 ($false),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[1271, 3893, 3890])).
% 2.35/1.92 tff(3895,plain,((W1!8 = X!1) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.92 tff(3896,plain,
% 2.35/1.92 (W1!8 = X!1),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3895, 47, 30, 154, 35])).
% 2.35/1.92 tff(3897,plain,
% 2.35/1.92 ((W1!8 = Y!0) <=> (X!1 = Y!0)),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3896])).
% 2.35/1.92 tff(3898,plain,
% 2.35/1.92 ((X!1 = Y!0) <=> (W1!8 = Y!0)),
% 2.35/1.92 inference(symmetry,[status(thm)],[3897])).
% 2.35/1.92 tff(3899,plain,
% 2.35/1.92 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.35/1.92 inference(transitivity,[status(thm)],[3898, 3764])).
% 2.35/1.92 tff(3900,plain,
% 2.35/1.92 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = W1!8))),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3899])).
% 2.35/1.92 tff(3901,plain,
% 2.35/1.92 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.35/1.92 inference(modus_ponens,[status(thm)],[741, 3900])).
% 2.35/1.92 tff(3902,plain,
% 2.35/1.92 ((~(Y!0 = tptp_fun_Z1_12(X!1))) <=> (~(tptp_fun_Z1_12(X!1) = Y!0))),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3192])).
% 2.35/1.92 tff(3903,plain,
% 2.35/1.92 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[88, 3741])).
% 2.35/1.92 tff(3904,plain,
% 2.35/1.92 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[191, 3903])).
% 2.35/1.92 tff(3905,plain,
% 2.35/1.92 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[161, 3904, 144])).
% 2.35/1.92 tff(3906,plain,
% 2.35/1.92 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3195, 3905])).
% 2.35/1.92 tff(3907,plain,
% 2.35/1.92 (~(Y!0 = tptp_fun_Z1_12(X!1))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3197, 3906, 3730])).
% 2.35/1.92 tff(3908,plain,
% 2.35/1.92 (~(tptp_fun_Z1_12(X!1) = Y!0)),
% 2.35/1.92 inference(modus_ponens,[status(thm)],[3907, 3902])).
% 2.35/1.92 tff(3909,plain,
% 2.35/1.92 (tptp_fun_Z1_12(X!1) = X!1),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[187, 3908])).
% 2.35/1.92 tff(3910,plain,
% 2.35/1.92 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))),
% 2.35/1.92 inference(quant_inst,[status(thm)],[])).
% 2.35/1.92 tff(3911,plain,
% 2.35/1.92 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3910, 3905])).
% 2.35/1.92 tff(3912,plain,
% 2.35/1.92 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1))),
% 2.35/1.92 inference(monotonicity,[status(thm)],[1469, 1787])).
% 2.35/1.92 tff(3913,plain,
% 2.35/1.92 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.35/1.92 inference(symmetry,[status(thm)],[3912])).
% 2.35/1.92 tff(3914,assumption,(big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))), introduced(assumption)).
% 2.35/1.92 tff(3915,assumption,(![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))), introduced(assumption)).
% 2.35/1.92 tff(3916,plain,
% 2.35/1.92 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))) | ((~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8))),
% 2.35/1.92 inference(quant_inst,[status(thm)],[])).
% 2.35/1.92 tff(3917,plain,
% 2.35/1.92 ((~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3916, 3915])).
% 2.35/1.92 tff(3918,plain,
% 2.35/1.92 (tptp_fun_Y1_11(X!1) = tptp_fun_X_2(Y!0)),
% 2.35/1.92 inference(transitivity,[status(thm)],[796, 31])).
% 2.35/1.92 tff(3919,plain,
% 2.35/1.92 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.35/1.92 inference(monotonicity,[status(thm)],[1289, 3918])).
% 2.35/1.92 tff(3920,plain,
% 2.35/1.92 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3919, 176])).
% 2.35/1.92 tff(3921,plain,
% 2.35/1.92 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.35/1.92 inference(symmetry,[status(thm)],[3920])).
% 2.35/1.92 tff(3922,plain,
% 2.35/1.92 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3919])).
% 2.35/1.92 tff(3923,plain,
% 2.35/1.92 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.35/1.92 inference(transitivity,[status(thm)],[3922, 3921])).
% 2.35/1.92 tff(3924,plain,
% 2.35/1.92 ((~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)) <=> (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))),
% 2.35/1.92 inference(monotonicity,[status(thm)],[3923])).
% 2.35/1.92 tff(3925,assumption,(~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)), introduced(assumption)).
% 2.35/1.92 tff(3926,plain,
% 2.35/1.92 (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.35/1.92 inference(modus_ponens,[status(thm)],[3925, 3924])).
% 2.35/1.92 tff(3927,assumption,((~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)), introduced(assumption)).
% 2.35/1.92 tff(3928,plain,
% 2.35/1.92 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.35/1.92 inference(monotonicity,[status(thm)],[1289])).
% 2.35/1.92 tff(3929,assumption,(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8), introduced(assumption)).
% 2.35/1.92 tff(3930,plain,
% 2.35/1.92 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1),
% 2.35/1.92 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 2.35/1.92 tff(3931,plain,
% 2.35/1.92 ($false),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3925, 3930])).
% 2.35/1.92 tff(3932,plain,((~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (~(W1!8 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.92 tff(3933,plain,
% 2.35/1.92 (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3932, 3925, 1289])).
% 2.35/1.92 tff(3934,plain,
% 2.35/1.92 ((~((~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8))) | big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)),
% 2.35/1.92 inference(tautology,[status(thm)],[])).
% 2.35/1.92 tff(3935,plain,
% 2.35/1.92 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3934, 3933, 3927])).
% 2.35/1.92 tff(3936,plain,
% 2.35/1.92 ((~(big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.35/1.92 inference(tautology,[status(thm)],[])).
% 2.35/1.92 tff(3937,plain,
% 2.35/1.92 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3936, 3935, 3914])).
% 2.35/1.92 tff(3938,plain,
% 2.35/1.92 ($false),
% 2.35/1.92 inference(unit_resolution,[status(thm)],[3937, 3926])).
% 2.35/1.92 tff(3939,plain,((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (~(tptp_fun_Z1_12(X!1) = X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(W1!8 = X!1)) | (~(big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~((~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(3940,plain,
% 2.35/1.93 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3939, 3917, 796, 30, 1289, 3914, 176])).
% 2.35/1.93 tff(3941,plain,
% 2.35/1.93 (X!1 = tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1))),
% 2.35/1.93 inference(symmetry,[status(thm)],[3940])).
% 2.35/1.93 tff(3942,plain,
% 2.35/1.93 (X!1 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.35/1.93 inference(transitivity,[status(thm)],[3941, 3913])).
% 2.35/1.93 tff(3943,plain,
% 2.35/1.93 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3942, 31])).
% 2.35/1.93 tff(3944,plain,
% 2.35/1.93 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(X!1, Y!0)),
% 2.35/1.93 inference(symmetry,[status(thm)],[3943])).
% 2.35/1.93 tff(3945,plain,
% 2.35/1.93 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (~big_f(X!1, Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3944])).
% 2.35/1.93 tff(3946,plain,
% 2.35/1.93 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3918])).
% 2.35/1.93 tff(3947,plain,
% 2.35/1.93 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3946, 3918])).
% 2.35/1.93 tff(3948,plain,
% 2.35/1.93 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3947])).
% 2.35/1.93 tff(3949,plain,
% 2.35/1.93 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3101, 3915])).
% 2.35/1.93 tff(3950,plain,
% 2.35/1.93 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[1289])).
% 2.35/1.93 tff(3951,plain,
% 2.35/1.93 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3950])).
% 2.35/1.93 tff(3952,assumption,(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1), introduced(assumption)).
% 2.35/1.93 tff(3953,plain,
% 2.35/1.93 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[3952, 3951])).
% 2.35/1.93 tff(3954,assumption,(~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)), introduced(assumption)).
% 2.35/1.93 tff(3955,plain,
% 2.35/1.93 ($false),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3954, 3953])).
% 2.35/1.93 tff(3956,plain,((~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)) | (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) | (~(W1!8 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(3957,plain,
% 2.35/1.93 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3956, 3940, 1289])).
% 2.35/1.93 tff(3958,plain,
% 2.35/1.93 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3099, 3957, 3949])).
% 2.35/1.93 tff(3959,plain,
% 2.35/1.93 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[3958, 3948])).
% 2.35/1.93 tff(3960,plain,
% 2.35/1.93 (~big_f(X!1, Y!0)),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[3959, 3945])).
% 2.35/1.93 tff(3961,plain,
% 2.35/1.93 ($false),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3675, 3960])).
% 2.35/1.93 tff(3962,plain,((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(W1!8 = X!1)) | (~(big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~(tptp_fun_Z1_12(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(3963,plain,
% 2.35/1.93 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3962, 3911, 154, 3896, 30, 3909])).
% 2.35/1.93 tff(3964,plain,
% 2.35/1.93 (~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[794, 3963, 3901])).
% 2.35/1.93 tff(3965,plain,
% 2.35/1.93 ((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[792, 3964])).
% 2.35/1.93 tff(3966,plain,
% 2.35/1.93 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[790, 3965])).
% 2.35/1.93 tff(3967,plain,
% 2.35/1.93 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[462, 3966])).
% 2.35/1.93 tff(3968,plain,
% 2.35/1.93 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[342, 3967])).
% 2.35/1.93 tff(3969,plain,
% 2.35/1.93 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[344, 3968])).
% 2.35/1.93 tff(3970,plain,
% 2.35/1.93 (~(X!1 = Z!5)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[346, 3969, 3761])).
% 2.35/1.93 tff(3971,plain,
% 2.35/1.93 (~(Z!5 = X!1)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[353, 3970])).
% 2.35/1.93 tff(3972,plain,
% 2.35/1.93 (Z!5 = Y!0),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[361, 3971])).
% 2.35/1.93 tff(3973,plain,
% 2.35/1.93 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3972])).
% 2.35/1.93 tff(3974,plain,
% 2.35/1.93 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3973])).
% 2.35/1.93 tff(3975,plain,
% 2.35/1.93 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.35/1.93 inference(transitivity,[status(thm)],[3974, 339])).
% 2.35/1.93 tff(3976,plain,
% 2.35/1.93 ((~(Y!0 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3975])).
% 2.35/1.93 tff(3977,plain,
% 2.35/1.93 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[385, 3967])).
% 2.35/1.93 tff(3978,plain,
% 2.35/1.93 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[387, 3977])).
% 2.35/1.93 tff(3979,plain,
% 2.35/1.93 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.35/1.93 inference(transitivity,[status(thm)],[3972, 31])).
% 2.35/1.93 tff(3980,plain,
% 2.35/1.93 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3979])).
% 2.35/1.93 tff(3981,plain,
% 2.35/1.93 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.35/1.93 inference(symmetry,[status(thm)],[3980])).
% 2.35/1.93 tff(3982,plain,
% 2.35/1.93 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Z!5, Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3981])).
% 2.35/1.93 tff(3983,plain,
% 2.35/1.93 (~big_f(Z!5, Y!0)),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[35, 3982])).
% 2.35/1.93 tff(3984,plain,
% 2.35/1.93 (~(Y!0 = tptp_fun_W_6(Z!5))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[394, 3983, 3978])).
% 2.35/1.93 tff(3985,plain,
% 2.35/1.93 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[3984, 3976])).
% 2.35/1.93 tff(3986,plain,
% 2.35/1.93 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[983, 3977])).
% 2.35/1.93 tff(3987,plain,
% 2.35/1.93 (Z!5 = tptp_fun_X_2(X!1)),
% 2.35/1.93 inference(transitivity,[status(thm)],[3972, 527])).
% 2.35/1.93 tff(3988,plain,
% 2.35/1.93 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3987])).
% 2.35/1.93 tff(3989,plain,
% 2.35/1.93 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Z!5, X!1)),
% 2.35/1.93 inference(symmetry,[status(thm)],[3988])).
% 2.35/1.93 tff(3990,plain,
% 2.35/1.93 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Z!5, X!1))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[3989])).
% 2.35/1.93 tff(3991,plain,
% 2.35/1.93 (~big_f(Z!5, X!1)),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[828, 3990])).
% 2.35/1.93 tff(3992,plain,
% 2.35/1.93 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1547, 3991, 3986])).
% 2.35/1.93 tff(3993,plain,
% 2.35/1.93 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3837, 3992, 3972])).
% 2.35/1.93 tff(3994,plain,
% 2.35/1.93 (tptp_fun_W_6(Y!0) = Y!0),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[403, 3993])).
% 2.35/1.93 tff(3995,plain,
% 2.35/1.93 ($false),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3994, 3985])).
% 2.35/1.93 tff(3996,plain,(big_f(tptp_fun_X_2(X!1), X!1) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_X_2(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(3997,plain,
% 2.35/1.93 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3996, 47, 30, 144, 35])).
% 2.35/1.93 tff(3998,plain,
% 2.35/1.93 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[866, 3997, 30, 35, 106])).
% 2.35/1.93 tff(3999,plain,
% 2.35/1.93 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[198, 3998])).
% 2.35/1.93 tff(4000,plain,
% 2.35/1.93 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[52, 3999, 30])).
% 2.35/1.93 tff(4001,plain,
% 2.35/1.93 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[54, 4000])).
% 2.35/1.93 tff(4002,plain,
% 2.35/1.93 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[56, 4001])).
% 2.35/1.93 tff(4003,plain,
% 2.35/1.93 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[82, 4002])).
% 2.35/1.93 tff(4004,plain,
% 2.35/1.93 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[84, 4003])).
% 2.35/1.93 tff(4005,plain,
% 2.35/1.93 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[561, 4004])).
% 2.35/1.93 tff(4006,plain,
% 2.35/1.93 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[563, 4005, 3724])).
% 2.35/1.93 tff(4007,plain,
% 2.35/1.93 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[3997, 3853])).
% 2.35/1.93 tff(4008,plain,
% 2.35/1.93 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1194, 4007, 4006])).
% 2.35/1.93 tff(4009,plain,
% 2.35/1.93 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3887, 4008, 3675, 35, 30, 3725, 4006])).
% 2.35/1.93 tff(4010,plain,
% 2.35/1.93 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[462, 4009])).
% 2.35/1.93 tff(4011,plain,
% 2.35/1.93 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1254, 4008, 3725, 4007])).
% 2.35/1.93 tff(4012,plain,
% 2.35/1.93 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1256, 4011])).
% 2.35/1.93 tff(4013,plain,
% 2.35/1.93 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[88, 4003])).
% 2.35/1.93 tff(4014,plain,
% 2.35/1.93 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[191, 4013])).
% 2.35/1.93 tff(4015,plain,
% 2.35/1.93 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[161, 4014, 144])).
% 2.35/1.93 tff(4016,plain,
% 2.35/1.93 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3910, 4015])).
% 2.35/1.93 tff(4017,plain,
% 2.35/1.93 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3195, 4015])).
% 2.35/1.93 tff(4018,plain,
% 2.35/1.93 (~(Y!0 = tptp_fun_Z1_12(X!1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3197, 4017, 3730])).
% 2.35/1.93 tff(4019,plain,
% 2.35/1.93 (~(tptp_fun_Z1_12(X!1) = Y!0)),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[4018, 3902])).
% 2.35/1.93 tff(4020,plain,
% 2.35/1.93 (tptp_fun_Z1_12(X!1) = X!1),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[187, 4019])).
% 2.35/1.93 tff(4021,plain,
% 2.35/1.93 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3962, 4020, 154, 3896, 30, 4016])).
% 2.35/1.93 tff(4022,plain,
% 2.35/1.93 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[576, 4006])).
% 2.35/1.93 tff(4023,plain,
% 2.35/1.93 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[578, 4008, 4022])).
% 2.35/1.93 tff(4024,plain,
% 2.35/1.93 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1264, 4023])).
% 2.35/1.93 tff(4025,plain,
% 2.35/1.93 ($false),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1298, 4024, 4021, 154, 4012, 4010])).
% 2.35/1.93 tff(4026,plain,((tptp_fun_X_2(X!1) = X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(4027,plain,
% 2.35/1.93 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[4026, 3705, 30, 144])).
% 2.35/1.93 tff(4028,plain,
% 2.35/1.93 ($false),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1139, 4027, 3674, 30, 41])).
% 2.35/1.93 tff(4029,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(4030,plain,
% 2.35/1.93 (tptp_fun_Y1_11(X!1) = X!1),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[4029, 42, 41, 30, 34])).
% 2.35/1.93 tff(4031,plain,
% 2.35/1.93 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1562, 4030, 34, 41])).
% 2.35/1.93 tff(4032,plain,
% 2.35/1.93 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[82, 4031])).
% 2.35/1.93 tff(4033,plain,
% 2.35/1.93 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[220, 4032])).
% 2.35/1.93 tff(4034,plain,
% 2.35/1.93 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1713, 4033])).
% 2.35/1.93 tff(4035,plain,
% 2.35/1.93 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3704, 4034, 40, 3672, 42])).
% 2.35/1.93 tff(4036,plain,
% 2.35/1.93 (tptp_fun_X_2(X!1) = Y!0),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[105, 4035])).
% 2.35/1.93 tff(4037,plain,
% 2.35/1.93 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[222, 4033])).
% 2.35/1.93 tff(4038,plain,
% 2.35/1.93 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[224, 4035, 4037])).
% 2.35/1.93 tff(4039,plain,
% 2.35/1.93 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[2614, 4030, 30, 41])).
% 2.35/1.93 tff(4040,plain,
% 2.35/1.93 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1599, 4036, 30, 4039])).
% 2.35/1.93 tff(4041,plain,
% 2.35/1.93 ($false),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[1588, 4040, 4038, 40, 41, 4036])).
% 2.35/1.93 tff(4042,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(4043,plain,
% 2.35/1.93 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[4042, 41, 30, 34])).
% 2.35/1.93 tff(4044,plain,
% 2.35/1.93 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3671, 45])).
% 2.35/1.93 tff(4045,plain,
% 2.35/1.93 ((tptp_fun_Y1_11(Y!0) = X!1) <=> (Y!0 = X!1)),
% 2.35/1.93 inference(monotonicity,[status(thm)],[4044])).
% 2.35/1.93 tff(4046,plain,
% 2.35/1.93 ((tptp_fun_Y1_11(Y!0) = X!1) <=> (X!1 = Y!0)),
% 2.35/1.93 inference(transitivity,[status(thm)],[4045, 46])).
% 2.35/1.93 tff(4047,plain,
% 2.35/1.93 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(Y!0) = X!1)),
% 2.35/1.93 inference(symmetry,[status(thm)],[4046])).
% 2.35/1.93 tff(4048,plain,
% 2.35/1.93 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(Y!0) = X!1))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[4047])).
% 2.35/1.93 tff(4049,plain,
% 2.35/1.93 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[741, 4048])).
% 2.35/1.93 tff(4050,plain,
% 2.35/1.93 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[155])).
% 2.35/1.93 tff(4051,plain,
% 2.35/1.93 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.93 inference(symmetry,[status(thm)],[4050])).
% 2.35/1.93 tff(4052,plain,
% 2.35/1.93 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_Y1_11(X!1)))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[4051])).
% 2.35/1.93 tff(4053,plain,
% 2.35/1.93 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.35/1.93 inference(modus_ponens,[status(thm)],[41, 4052])).
% 2.35/1.93 tff(4054,plain,
% 2.35/1.93 ($false),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[3415, 4053])).
% 2.35/1.93 tff(4055,plain,((tptp_fun_Y1_11(X!1) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.35/1.93 tff(4056,plain,
% 2.35/1.93 (tptp_fun_Y1_11(X!1) = X!1),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[4055, 45, 41, 932])).
% 2.35/1.93 tff(4057,plain,
% 2.35/1.93 (tptp_fun_W_6(tptp_fun_Y1_11(Y!0)) = tptp_fun_W_6(Y!0)),
% 2.35/1.93 inference(monotonicity,[status(thm)],[109])).
% 2.35/1.93 tff(4058,plain,
% 2.35/1.93 ((Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[4057])).
% 2.35/1.93 tff(4059,plain,
% 2.35/1.93 ((Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.35/1.93 inference(transitivity,[status(thm)],[4058, 339])).
% 2.35/1.93 tff(4060,plain,
% 2.35/1.93 ((~(Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.35/1.93 inference(monotonicity,[status(thm)],[4059])).
% 2.35/1.93 tff(4061,plain,
% 2.35/1.93 (tptp_fun_Y1_11(X!1) = X!1),
% 2.35/1.93 inference(unit_resolution,[status(thm)],[4055, 41, 109, 45])).
% 2.35/1.93 tff(4062,plain,
% 2.35/1.93 ((tptp_fun_X_2(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.35/1.93 inference(monotonicity,[status(thm)],[1878])).
% 2.35/1.93 tff(4063,plain,
% 2.35/1.93 ((tptp_fun_X_2(Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.35/1.93 inference(transitivity,[status(thm)],[4062, 24])).
% 2.35/1.93 tff(4064,plain,
% 2.35/1.93 ((W1!8 = X!1) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.35/1.94 inference(symmetry,[status(thm)],[4063])).
% 2.35/1.94 tff(4065,assumption,(big_f(tptp_fun_Z1_9(W1!8), W1!8)), introduced(assumption)).
% 2.35/1.94 tff(4066,plain,
% 2.35/1.94 (W1!8 = tptp_fun_Y1_11(Y!0)),
% 2.35/1.94 inference(transitivity,[status(thm)],[486, 146])).
% 2.35/1.94 tff(4067,assumption,(tptp_fun_Z1_9(W1!8) = Y!0), introduced(assumption)).
% 2.35/1.94 tff(4068,plain,
% 2.35/1.94 (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.35/1.94 inference(monotonicity,[status(thm)],[4067, 4066])).
% 2.35/1.94 tff(4069,plain,
% 2.35/1.94 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.35/1.94 inference(symmetry,[status(thm)],[4068])).
% 2.35/1.94 tff(4070,plain,
% 2.35/1.94 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.35/1.94 inference(monotonicity,[status(thm)],[4069])).
% 2.35/1.94 tff(4071,plain,
% 2.35/1.94 (~big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.35/1.94 inference(modus_ponens,[status(thm)],[41, 4070])).
% 2.35/1.94 tff(4072,plain,
% 2.35/1.94 ($false),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[4065, 4071])).
% 2.35/1.94 tff(4073,plain,((~(tptp_fun_Z1_9(W1!8) = Y!0)) | (~big_f(tptp_fun_Z1_9(W1!8), W1!8)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(W1!8 = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.94 tff(4074,plain,
% 2.35/1.94 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[4073, 4065, 41, 486, 109])).
% 2.35/1.94 tff(4075,plain,
% 2.35/1.94 (tptp_fun_Z1_9(W1!8) = X!1),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[522, 4074])).
% 2.35/1.94 tff(4076,plain,
% 2.35/1.94 (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> big_f(X!1, Y!0)),
% 2.35/1.94 inference(monotonicity,[status(thm)],[4075, 486])).
% 2.35/1.94 tff(4077,plain,
% 2.35/1.94 (big_f(X!1, Y!0) <=> big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.35/1.94 inference(symmetry,[status(thm)],[4076])).
% 2.35/1.94 tff(4078,plain,
% 2.35/1.94 ((~big_f(X!1, Y!0)) <=> (~big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.35/1.94 inference(monotonicity,[status(thm)],[4077])).
% 2.35/1.94 tff(4079,plain,
% 2.35/1.94 (~big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.35/1.94 inference(modus_ponens,[status(thm)],[45, 4078])).
% 2.35/1.94 tff(4080,plain,
% 2.35/1.94 ($false),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[4065, 4079])).
% 2.35/1.94 tff(4081,plain,((~big_f(tptp_fun_Z1_9(W1!8), W1!8)) | big_f(X!1, Y!0) | (~(W1!8 = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.35/1.94 tff(4082,plain,
% 2.35/1.94 (~(W1!8 = Y!0)),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[4081, 1507, 45, 41, 109])).
% 2.35/1.94 tff(4083,plain,
% 2.35/1.94 (W1!8 = X!1),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[19, 4082])).
% 2.35/1.94 tff(4084,plain,
% 2.35/1.94 (tptp_fun_X_2(Y!0) = W1!8),
% 2.35/1.94 inference(modus_ponens,[status(thm)],[4083, 4064])).
% 2.35/1.94 tff(4085,plain,
% 2.35/1.94 (![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[3268, 4084, 3267])).
% 2.35/1.94 tff(4086,plain,
% 2.35/1.94 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[3235, 4085])).
% 2.35/1.94 tff(4087,plain,
% 2.35/1.94 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.35/1.94 inference(modus_ponens,[status(thm)],[4083, 1463])).
% 2.35/1.94 tff(4088,plain,
% 2.35/1.94 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.35/1.94 inference(unit_resolution,[status(thm)],[1465, 4087, 1460])).
% 2.35/1.94 tff(4089,plain,
% 2.35/1.94 (tptp_fun_Y1_11(X!1) = tptp_fun_X_2(Y!0)),
% 2.35/1.94 inference(transitivity,[status(thm)],[277, 2972])).
% 2.35/1.94 tff(4090,plain,
% 2.35/1.94 (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.35/1.94 inference(monotonicity,[status(thm)],[4089])).
% 2.35/1.94 tff(4091,plain,
% 2.35/1.94 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.35/1.94 inference(symmetry,[status(thm)],[4090])).
% 2.35/1.94 tff(4092,plain,
% 2.35/1.94 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.35/1.94 inference(transitivity,[status(thm)],[1289, 2972])).
% 2.35/1.94 tff(4093,plain,
% 2.35/1.94 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.35/1.94 inference(monotonicity,[status(thm)],[4092])).
% 2.35/1.94 tff(4094,plain,
% 2.35/1.94 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = X!1)),
% 2.35/1.94 inference(monotonicity,[status(thm)],[4093])).
% 2.35/1.94 tff(4095,plain,
% 2.35/1.94 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.35/1.94 inference(transitivity,[status(thm)],[4094, 485])).
% 2.35/1.94 tff(4096,plain,
% 2.35/1.94 ((X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.43/1.94 inference(symmetry,[status(thm)],[4095])).
% 2.43/1.94 tff(4097,plain,
% 2.43/1.94 ((~(X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4096])).
% 2.43/1.94 tff(4098,assumption,(![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))), introduced(assumption)).
% 2.43/1.94 tff(4099,assumption,(![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))), introduced(assumption)).
% 2.43/1.94 tff(4100,plain,
% 2.43/1.94 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[271, 4099])).
% 2.43/1.94 tff(4101,assumption,(X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))), introduced(assumption)).
% 2.43/1.94 tff(4102,plain,
% 2.43/1.94 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = X!1),
% 2.43/1.94 inference(symmetry,[status(thm)],[4101])).
% 2.43/1.94 tff(4103,plain,
% 2.43/1.94 (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = X!1),
% 2.43/1.94 inference(transitivity,[status(thm)],[4090, 4102])).
% 2.43/1.94 tff(4104,plain,
% 2.43/1.94 ((tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4103])).
% 2.43/1.94 tff(4105,plain,
% 2.43/1.94 ((tptp_fun_X1_13(X!1, X!1) = X!1) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(symmetry,[status(thm)],[4104])).
% 2.43/1.94 tff(4106,plain,
% 2.43/1.94 (tptp_fun_Z1_9(W1!8) = X!1),
% 2.43/1.94 inference(modus_ponens,[status(thm)],[4101, 4096])).
% 2.43/1.94 tff(4107,plain,
% 2.43/1.94 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[1467, 4098])).
% 2.43/1.94 tff(4108,plain,
% 2.43/1.94 (tptp_fun_X_2(Y!0) = W1!8),
% 2.43/1.94 inference(transitivity,[status(thm)],[1906, 1469])).
% 2.43/1.94 tff(4109,plain,
% 2.43/1.94 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = tptp_fun_Z1_9(W1!8)),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4108])).
% 2.43/1.94 tff(4110,plain,
% 2.43/1.94 (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = X!1),
% 2.43/1.94 inference(transitivity,[status(thm)],[4090, 4109, 1473])).
% 2.43/1.94 tff(4111,plain,
% 2.43/1.94 ((tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4110])).
% 2.43/1.94 tff(4112,plain,
% 2.43/1.94 ((tptp_fun_X1_13(X!1, X!1) = X!1) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(symmetry,[status(thm)],[4111])).
% 2.43/1.94 tff(4113,plain,
% 2.43/1.94 ((~(tptp_fun_X1_13(X!1, X!1) = X!1)) <=> (~(tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4112])).
% 2.43/1.94 tff(4114,plain,
% 2.43/1.94 (~(tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(modus_ponens,[status(thm)],[278, 4113])).
% 2.43/1.94 tff(4115,plain,
% 2.43/1.94 ($false),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[1481, 4114])).
% 2.43/1.94 tff(4116,plain,((tptp_fun_X1_13(X!1, X!1) = X!1) | (~(tptp_fun_Z1_9(W1!8) = X!1)) | (~(W1!8 = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.94 tff(4117,plain,
% 2.43/1.94 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4116, 4107, 1906, 4106, 277, 1289, 290])).
% 2.43/1.94 tff(4118,plain,
% 2.43/1.94 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.43/1.94 inference(modus_ponens,[status(thm)],[4117, 4105])).
% 2.43/1.94 tff(4119,plain,
% 2.43/1.94 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[316, 4117, 290])).
% 2.43/1.94 tff(4120,plain,
% 2.43/1.94 (~(tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[1487, 4119, 4107])).
% 2.43/1.94 tff(4121,plain,
% 2.43/1.94 ($false),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4120, 4118])).
% 2.43/1.94 tff(4122,plain,((~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | (~(X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(W1!8 = X!1)) | (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.94 tff(4123,plain,
% 2.43/1.94 (~(X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4122, 4100, 277, 1906, 1289, 4098])).
% 2.43/1.94 tff(4124,plain,
% 2.43/1.94 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.43/1.94 inference(modus_ponens,[status(thm)],[4123, 4097])).
% 2.43/1.94 tff(4125,plain,
% 2.43/1.94 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[522, 4124])).
% 2.43/1.94 tff(4126,plain,
% 2.43/1.94 (Y!0 = tptp_fun_Z1_9(W1!8)),
% 2.43/1.94 inference(symmetry,[status(thm)],[4125])).
% 2.43/1.94 tff(4127,plain,
% 2.43/1.94 (Y!0 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.43/1.94 inference(transitivity,[status(thm)],[4126, 4093, 4091])).
% 2.43/1.94 tff(4128,plain,
% 2.43/1.94 ((tptp_fun_X1_13(Y!0, X!1) = Y!0) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4127])).
% 2.43/1.94 tff(4129,plain,
% 2.43/1.94 ((~(tptp_fun_X1_13(Y!0, X!1) = Y!0)) <=> (~(tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4128])).
% 2.43/1.94 tff(4130,plain,
% 2.43/1.94 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[879, 4099])).
% 2.43/1.94 tff(4131,plain,
% 2.43/1.94 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.43/1.94 inference(quant_inst,[status(thm)],[])).
% 2.43/1.94 tff(4132,plain,
% 2.43/1.94 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4131, 4098])).
% 2.43/1.94 tff(4133,plain,
% 2.43/1.94 ((tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = Y!0) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.43/1.94 inference(commutativity,[status(thm)],[])).
% 2.43/1.94 tff(4134,plain,
% 2.43/1.94 ((tptp_fun_Z1_9(W1!8) = Y!0) <=> (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = Y!0)),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4093])).
% 2.43/1.94 tff(4135,plain,
% 2.43/1.94 ((tptp_fun_Z1_9(W1!8) = Y!0) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.43/1.94 inference(transitivity,[status(thm)],[4134, 4133])).
% 2.43/1.94 tff(4136,plain,
% 2.43/1.94 (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.43/1.94 inference(modus_ponens,[status(thm)],[4125, 4135])).
% 2.43/1.94 tff(4137,assumption,(Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))), introduced(assumption)).
% 2.43/1.94 tff(4138,plain,
% 2.43/1.94 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = Y!0),
% 2.43/1.94 inference(symmetry,[status(thm)],[4137])).
% 2.43/1.94 tff(4139,plain,
% 2.43/1.94 (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = Y!0),
% 2.43/1.94 inference(transitivity,[status(thm)],[4090, 4138])).
% 2.43/1.94 tff(4140,plain,
% 2.43/1.94 ((tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.43/1.94 inference(monotonicity,[status(thm)],[4139])).
% 2.43/1.94 tff(4141,plain,
% 2.43/1.94 ((tptp_fun_X1_13(Y!0, X!1) = Y!0) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(symmetry,[status(thm)],[4140])).
% 2.43/1.94 tff(4142,assumption,(~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))), introduced(assumption)).
% 2.43/1.94 tff(4143,plain,
% 2.43/1.94 (tptp_fun_X1_13(Y!0, X!1) = Y!0),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[920, 4142, 906])).
% 2.43/1.94 tff(4144,plain,
% 2.43/1.94 (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.43/1.94 inference(modus_ponens,[status(thm)],[4143, 4141])).
% 2.43/1.94 tff(4145,assumption,(big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))), introduced(assumption)).
% 2.43/1.94 tff(4146,plain,
% 2.43/1.94 ((~(big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) | (~(tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.43/1.94 inference(tautology,[status(thm)],[])).
% 2.43/1.94 tff(4147,plain,
% 2.43/1.94 (~(tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4146, 4142, 4145])).
% 2.43/1.94 tff(4148,plain,
% 2.43/1.94 ($false),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4147, 4144])).
% 2.43/1.94 tff(4149,plain,(big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) | (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.94 tff(4150,plain,
% 2.43/1.94 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4149, 4136, 277, 1906, 4130, 4132])).
% 2.43/1.94 tff(4151,plain,
% 2.43/1.94 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[907, 4150, 4130])).
% 2.43/1.94 tff(4152,plain,
% 2.43/1.94 (~(tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(modus_ponens,[status(thm)],[4151, 4129])).
% 2.43/1.94 tff(4153,plain,
% 2.43/1.94 ((~(big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))) | (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) | (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.43/1.94 inference(tautology,[status(thm)],[])).
% 2.43/1.94 tff(4154,plain,
% 2.43/1.94 (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4153, 4150, 4132])).
% 2.43/1.94 tff(4155,plain,
% 2.43/1.94 ($false),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4154, 4152])).
% 2.43/1.94 tff(4156,plain,((~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(W1!8 = X!1)) | (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.94 tff(4157,plain,
% 2.43/1.94 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[4156, 4083, 1878, 277, 4088])).
% 2.43/1.94 tff(4158,plain,
% 2.43/1.94 (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[269, 4157, 277])).
% 2.43/1.94 tff(4159,plain,
% 2.43/1.94 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[90, 4158])).
% 2.43/1.94 tff(4160,plain,
% 2.43/1.94 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[88, 4159])).
% 2.43/1.94 tff(4161,plain,
% 2.43/1.94 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[82, 4160])).
% 2.43/1.94 tff(4162,plain,
% 2.43/1.94 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[220, 4161])).
% 2.43/1.94 tff(4163,plain,
% 2.43/1.94 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[222, 4162])).
% 2.43/1.94 tff(4164,plain,
% 2.43/1.94 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[224, 4163, 47])).
% 2.43/1.94 tff(4165,plain,
% 2.43/1.94 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.43/1.94 inference(unit_resolution,[status(thm)],[234, 4164])).
% 2.43/1.94 tff(4166,plain,
% 2.43/1.94 (~(tptp_fun_W_3(X!1) = Y!0)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[247, 4165, 106, 41, 109])).
% 2.43/1.95 tff(4167,plain,
% 2.43/1.95 (tptp_fun_W_3(X!1) = X!1),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[252, 4166])).
% 2.43/1.95 tff(4168,plain,
% 2.43/1.95 (tptp_fun_W_3(X!1) = tptp_fun_X_2(Y!0)),
% 2.43/1.95 inference(transitivity,[status(thm)],[4167, 2967])).
% 2.43/1.95 tff(4169,plain,
% 2.43/1.95 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.95 inference(monotonicity,[status(thm)],[106, 4168])).
% 2.43/1.95 tff(4170,plain,
% 2.43/1.95 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.95 inference(modus_ponens,[status(thm)],[4165, 4169])).
% 2.43/1.95 tff(4171,plain,
% 2.43/1.95 (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[3237, 4170, 4086])).
% 2.43/1.95 tff(4172,plain,
% 2.43/1.95 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = Y!0),
% 2.43/1.95 inference(symmetry,[status(thm)],[4171])).
% 2.43/1.95 tff(4173,plain,
% 2.43/1.95 ((X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (X!1 = Y!0)),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4172])).
% 2.43/1.95 tff(4174,plain,
% 2.43/1.95 ((X!1 = Y!0) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.43/1.95 inference(symmetry,[status(thm)],[4173])).
% 2.43/1.95 tff(4175,plain,
% 2.43/1.95 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4174])).
% 2.43/1.95 tff(4176,plain,
% 2.43/1.95 (~(X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.43/1.95 inference(modus_ponens,[status(thm)],[741, 4175])).
% 2.43/1.95 tff(4177,plain,
% 2.43/1.95 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[56, 4161])).
% 2.43/1.95 tff(4178,plain,
% 2.43/1.95 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[2663, 4177])).
% 2.43/1.95 tff(4179,plain,
% 2.43/1.95 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[1858, 4178, 1857])).
% 2.43/1.95 tff(4180,plain,
% 2.43/1.95 (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[3258, 4179, 1878, 4085, 35])).
% 2.43/1.95 tff(4181,plain,
% 2.43/1.95 ($false),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4180, 4176])).
% 2.43/1.95 tff(4182,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_X_2(Y!0) = Y!0) | (~(tptp_fun_Y1_11(X!1) = X!1)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.43/1.95 tff(4183,plain,
% 2.43/1.95 (tptp_fun_X_2(X!1) = X!1),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4182, 1268, 109, 41, 2934, 2939, 4061, 45])).
% 2.43/1.95 tff(4184,plain,
% 2.43/1.95 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[3451, 4183, 45])).
% 2.43/1.95 tff(4185,plain,
% 2.43/1.95 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[82, 4184])).
% 2.43/1.95 tff(4186,plain,
% 2.43/1.95 (~(W1!8 = Y!0)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4081, 1507, 45, 109, 41])).
% 2.43/1.95 tff(4187,plain,
% 2.43/1.95 (W1!8 = X!1),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[19, 4186])).
% 2.43/1.95 tff(4188,plain,
% 2.43/1.95 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.43/1.95 inference(modus_ponens,[status(thm)],[4187, 1463])).
% 2.43/1.95 tff(4189,plain,
% 2.43/1.95 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4156, 4187, 4099, 2935, 277])).
% 2.43/1.95 tff(4190,plain,
% 2.43/1.95 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[1465, 4189, 1460])).
% 2.43/1.95 tff(4191,plain,
% 2.43/1.95 ($false),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4190, 4188])).
% 2.43/1.95 tff(4192,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))) | big_f(X!1, Y!0) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.95 tff(4193,plain,
% 2.43/1.95 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4192, 1268, 4061, 45, 109, 41])).
% 2.43/1.95 tff(4194,plain,
% 2.43/1.95 (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[269, 4193, 4061])).
% 2.43/1.95 tff(4195,plain,
% 2.43/1.95 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[90, 4194])).
% 2.43/1.95 tff(4196,plain,
% 2.43/1.95 ($false),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[88, 4195, 4185])).
% 2.43/1.95 tff(4197,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | big_f(X!1, Y!0) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.95 tff(4198,plain,
% 2.43/1.95 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4197, 45, 41, 109])).
% 2.43/1.95 tff(4199,plain,
% 2.43/1.95 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[462, 4198])).
% 2.43/1.95 tff(4200,plain,
% 2.43/1.95 (~((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[734, 4199])).
% 2.43/1.95 tff(4201,plain,
% 2.43/1.95 (((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))))) | ((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))),
% 2.43/1.95 inference(tautology,[status(thm)],[])).
% 2.43/1.95 tff(4202,plain,
% 2.43/1.95 ((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4201, 4200])).
% 2.43/1.95 tff(4203,plain,
% 2.43/1.95 ((tptp_fun_Y1_11(Y!0) = Z!5) <=> (Y!0 = Z!5)),
% 2.43/1.95 inference(monotonicity,[status(thm)],[109])).
% 2.43/1.95 tff(4204,plain,
% 2.43/1.95 ((Y!0 = Z!5) <=> (tptp_fun_Y1_11(Y!0) = Z!5)),
% 2.43/1.95 inference(symmetry,[status(thm)],[4203])).
% 2.43/1.95 tff(4205,plain,
% 2.43/1.95 (~(Z!5 = Y!0)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[438, 436])).
% 2.43/1.95 tff(4206,plain,
% 2.43/1.95 (Z!5 = X!1),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[361, 4205])).
% 2.43/1.95 tff(4207,plain,
% 2.43/1.95 (X!1 = Z!5),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[353, 349])).
% 2.43/1.95 tff(4208,plain,
% 2.43/1.95 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[3572, 144, 45, 34, 3548])).
% 2.43/1.95 tff(4209,plain,
% 2.43/1.95 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[627, 4208, 45, 40])).
% 2.43/1.95 tff(4210,plain,
% 2.43/1.95 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[629, 4209])).
% 2.43/1.95 tff(4211,plain,
% 2.43/1.95 (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[2624, 4208, 45, 1663, 40])).
% 2.43/1.95 tff(4212,plain,
% 2.43/1.95 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[1713, 4211])).
% 2.43/1.95 tff(4213,plain,
% 2.43/1.95 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[220, 4212])).
% 2.43/1.95 tff(4214,plain,
% 2.43/1.95 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[82, 4213])).
% 2.43/1.95 tff(4215,plain,
% 2.43/1.95 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[88, 4214])).
% 2.43/1.95 tff(4216,plain,
% 2.43/1.95 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[191, 4215])).
% 2.43/1.95 tff(4217,plain,
% 2.43/1.95 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[786, 4216, 45, 144])).
% 2.43/1.95 tff(4218,plain,
% 2.43/1.95 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[788, 4217])).
% 2.43/1.95 tff(4219,plain,
% 2.43/1.95 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[84, 4214])).
% 2.43/1.95 tff(4220,plain,
% 2.43/1.95 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[561, 4219])).
% 2.43/1.95 tff(4221,plain,
% 2.43/1.95 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[563, 4220, 34])).
% 2.43/1.95 tff(4222,plain,
% 2.43/1.95 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[576, 4221])).
% 2.43/1.95 tff(4223,plain,
% 2.43/1.95 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[751, 4222, 4208])).
% 2.43/1.95 tff(4224,plain,
% 2.43/1.95 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[1191, 4223])).
% 2.43/1.95 tff(4225,plain,
% 2.43/1.95 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[594, 4224])).
% 2.43/1.95 tff(4226,plain,
% 2.43/1.95 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[2232, 4208, 1663, 45, 34])).
% 2.43/1.95 tff(4227,plain,
% 2.43/1.95 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[3183, 154, 2935, 40, 4226, 4225, 4208, 4218])).
% 2.43/1.95 tff(4228,plain,
% 2.43/1.95 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[462, 4227])).
% 2.43/1.95 tff(4229,plain,
% 2.43/1.95 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[743, 4228, 40, 4210])).
% 2.43/1.95 tff(4230,plain,
% 2.43/1.95 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[720, 4229])).
% 2.43/1.95 tff(4231,plain,
% 2.43/1.95 (~(tptp_fun_Z1_12(X!1) = X!1)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[182, 4216, 45, 144])).
% 2.43/1.95 tff(4232,plain,
% 2.43/1.95 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[187, 4231])).
% 2.43/1.95 tff(4233,plain,
% 2.43/1.95 (tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1)) = tptp_fun_Y_7(Y!0, Y!0)),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4232])).
% 2.43/1.95 tff(4234,plain,
% 2.43/1.95 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1))) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4232, 4233])).
% 2.43/1.95 tff(4235,plain,
% 2.43/1.95 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y_7(Y!0, tptp_fun_Z1_12(X!1)))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[3427, 4230, 154, 3415, 4232])).
% 2.43/1.95 tff(4236,plain,
% 2.43/1.95 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.43/1.95 inference(modus_ponens,[status(thm)],[4235, 4234])).
% 2.43/1.95 tff(4237,plain,
% 2.43/1.95 (~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[699, 4236, 4230])).
% 2.43/1.95 tff(4238,plain,
% 2.43/1.95 (tptp_fun_Y_7(Y!0, Y!0) = X!1),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[708, 4237])).
% 2.43/1.95 tff(4239,plain,
% 2.43/1.95 (tptp_fun_Y_7(Y!0, Y!0) = tptp_fun_X_2(Y!0)),
% 2.43/1.95 inference(transitivity,[status(thm)],[4238, 3148])).
% 2.43/1.95 tff(4240,plain,
% 2.43/1.95 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4239])).
% 2.43/1.95 tff(4241,plain,
% 2.43/1.95 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.43/1.95 inference(symmetry,[status(thm)],[4240])).
% 2.43/1.95 tff(4242,plain,
% 2.43/1.95 ((~big_f(Y!0, tptp_fun_X_2(Y!0))) <=> (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)))),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4241])).
% 2.43/1.95 tff(4243,plain,
% 2.43/1.95 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.95 inference(modus_ponens,[status(thm)],[4226, 3438])).
% 2.43/1.95 tff(4244,plain,
% 2.43/1.95 (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.43/1.95 inference(modus_ponens,[status(thm)],[4243, 4242])).
% 2.43/1.95 tff(4245,plain,
% 2.43/1.95 ($false),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4236, 4244])).
% 2.43/1.95 tff(4246,plain,((tptp_fun_Y1_11(X!1) = X!1) | (tptp_fun_Y1_11(Y!0) = Y!0) | big_f(X!1, Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(X!1 = Z!5))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.95 tff(4247,plain,
% 2.43/1.95 (tptp_fun_Y1_11(X!1) = X!1),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[4246, 34, 45, 1663, 3548])).
% 2.43/1.95 tff(4248,plain,
% 2.43/1.95 ((tptp_fun_Y1_11(X!1) = Y!0) <=> (X!1 = Y!0)),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4247])).
% 2.43/1.95 tff(4249,plain,
% 2.43/1.95 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = Y!0)),
% 2.43/1.95 inference(symmetry,[status(thm)],[4248])).
% 2.43/1.95 tff(4250,plain,
% 2.43/1.95 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = Y!0))),
% 2.43/1.95 inference(monotonicity,[status(thm)],[4249])).
% 2.43/1.95 tff(4251,plain,
% 2.43/1.95 (~(tptp_fun_Y1_11(X!1) = Y!0)),
% 2.43/1.95 inference(modus_ponens,[status(thm)],[741, 4250])).
% 2.43/1.95 tff(4252,plain,
% 2.43/1.95 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[3141, 4251, 2934, 34, 45, 2939])).
% 2.43/1.95 tff(4253,plain,
% 2.43/1.95 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[2791, 4252, 40, 4247])).
% 2.43/1.95 tff(4254,plain,
% 2.43/1.95 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.95 inference(unit_resolution,[status(thm)],[2816, 4253, 4247, 1663, 45, 4252])).
% 2.43/1.95 tff(4255,plain,
% 2.43/1.95 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[82, 4254])).
% 2.43/1.96 tff(4256,plain,
% 2.43/1.96 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[2232, 4252, 1663, 45, 34])).
% 2.43/1.96 tff(4257,plain,
% 2.43/1.96 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1894, 4256, 2934, 2939, 40])).
% 2.43/1.96 tff(4258,plain,
% 2.43/1.96 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[2663, 4257])).
% 2.43/1.96 tff(4259,plain,
% 2.43/1.96 ($false),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[56, 4258, 4255])).
% 2.43/1.96 tff(4260,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0) | (~(X!1 = Z!5))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.96 tff(4261,plain,
% 2.43/1.96 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4260, 1663, 45, 4207])).
% 2.43/1.96 tff(4262,plain,
% 2.43/1.96 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[3451, 1663, 45])).
% 2.43/1.96 tff(4263,plain,
% 2.43/1.96 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[82, 4262])).
% 2.43/1.96 tff(4264,plain,
% 2.43/1.96 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[84, 4263])).
% 2.43/1.96 tff(4265,plain,
% 2.43/1.96 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[86, 4264])).
% 2.43/1.96 tff(4266,plain,
% 2.43/1.96 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1168, 4265, 45, 4261])).
% 2.43/1.96 tff(4267,plain,
% 2.43/1.96 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[88, 4263])).
% 2.43/1.96 tff(4268,plain,
% 2.43/1.96 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[191, 4267])).
% 2.43/1.96 tff(4269,plain,
% 2.43/1.96 (tptp_fun_Y1_11(X!1) = X!1),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[189, 4266, 45, 4261, 4268])).
% 2.43/1.96 tff(4270,assumption,((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))), introduced(assumption)).
% 2.43/1.96 tff(4271,plain,
% 2.43/1.96 ((Y!0 = Z!5) <=> (Y!0 = X!1)),
% 2.43/1.96 inference(monotonicity,[status(thm)],[349])).
% 2.43/1.96 tff(4272,plain,
% 2.43/1.96 ((Y!0 = Z!5) <=> (X!1 = Y!0)),
% 2.43/1.96 inference(transitivity,[status(thm)],[4271, 46])).
% 2.43/1.96 tff(4273,plain,
% 2.43/1.96 ((X!1 = Y!0) <=> (Y!0 = Z!5)),
% 2.43/1.96 inference(symmetry,[status(thm)],[4272])).
% 2.43/1.96 tff(4274,plain,
% 2.43/1.96 ((~(X!1 = Y!0)) <=> (~(Y!0 = Z!5))),
% 2.43/1.96 inference(monotonicity,[status(thm)],[4273])).
% 2.43/1.96 tff(4275,plain,
% 2.43/1.96 (~(Y!0 = Z!5)),
% 2.43/1.96 inference(modus_ponens,[status(thm)],[741, 4274])).
% 2.43/1.96 tff(4276,plain,
% 2.43/1.96 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[725, 4275, 4270])).
% 2.43/1.96 tff(4277,plain,
% 2.43/1.96 ((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1110, 4276])).
% 2.43/1.96 tff(4278,plain,
% 2.43/1.96 (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[3342, 4277, 109, 41])).
% 2.43/1.96 tff(4279,plain,
% 2.43/1.96 (X!1 = tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0))),
% 2.43/1.96 inference(symmetry,[status(thm)],[4278])).
% 2.43/1.96 tff(4280,plain,
% 2.43/1.96 (tptp_fun_X_2(Y!0) = tptp_fun_Y_7(X!1, Y!0)),
% 2.43/1.96 inference(transitivity,[status(thm)],[1906, 4279, 937])).
% 2.43/1.96 tff(4281,plain,
% 2.43/1.96 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.43/1.96 inference(monotonicity,[status(thm)],[4280])).
% 2.43/1.96 tff(4282,plain,
% 2.43/1.96 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.96 inference(symmetry,[status(thm)],[4281])).
% 2.43/1.96 tff(4283,plain,
% 2.43/1.96 ((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.43/1.96 inference(monotonicity,[status(thm)],[4282])).
% 2.43/1.96 tff(4284,assumption,((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))), introduced(assumption)).
% 2.43/1.96 tff(4285,plain,
% 2.43/1.96 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(Y!0) = Z!5)),
% 2.43/1.96 inference(transitivity,[status(thm)],[4273, 4204])).
% 2.43/1.96 tff(4286,plain,
% 2.43/1.96 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(Y!0) = Z!5))),
% 2.43/1.96 inference(monotonicity,[status(thm)],[4285])).
% 2.43/1.96 tff(4287,plain,
% 2.43/1.96 (~(tptp_fun_Y1_11(Y!0) = Z!5)),
% 2.43/1.96 inference(modus_ponens,[status(thm)],[741, 4286])).
% 2.43/1.96 tff(4288,plain,
% 2.43/1.96 (![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[738, 4287, 4284])).
% 2.43/1.96 tff(4289,plain,
% 2.43/1.96 ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[629, 4288])).
% 2.43/1.96 tff(4290,plain,
% 2.43/1.96 (~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[624, 4278, 4289])).
% 2.43/1.96 tff(4291,plain,
% 2.43/1.96 (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.43/1.96 inference(modus_ponens,[status(thm)],[4290, 952])).
% 2.43/1.96 tff(4292,plain,
% 2.43/1.96 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.96 inference(modus_ponens,[status(thm)],[4291, 4283])).
% 2.43/1.96 tff(4293,assumption,((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))), introduced(assumption)).
% 2.43/1.96 tff(4294,plain,
% 2.43/1.96 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[346, 4207, 4293])).
% 2.43/1.96 tff(4295,plain,
% 2.43/1.96 (~(tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[337, 4294, 277, 290, 45])).
% 2.43/1.96 tff(4296,plain,
% 2.43/1.96 (tptp_fun_X1_13(X!1, X!1) = Y!0),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[285, 4295])).
% 2.43/1.96 tff(4297,plain,
% 2.43/1.96 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.96 inference(monotonicity,[status(thm)],[4296, 4089])).
% 2.43/1.96 tff(4298,plain,
% 2.43/1.96 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[291, 4295, 290])).
% 2.43/1.96 tff(4299,plain,
% 2.43/1.96 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.96 inference(modus_ponens,[status(thm)],[4298, 4297])).
% 2.43/1.96 tff(4300,plain,
% 2.43/1.96 ($false),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4299, 4292])).
% 2.43/1.96 tff(4301,plain,((~(Z!5 = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~((tptp_fun_Y1_11(Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W)))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))) | big_f(X!1, Y!0) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.96 tff(4302,plain,
% 2.43/1.96 (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4301, 724, 2935, 277, 4261, 41, 349, 737, 45, 345])).
% 2.43/1.96 tff(4303,plain,
% 2.43/1.96 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[271, 4302])).
% 2.43/1.96 tff(4304,plain,
% 2.43/1.96 (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[269, 4303, 277])).
% 2.43/1.96 tff(4305,plain,
% 2.43/1.96 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[90, 4304])).
% 2.43/1.96 tff(4306,plain,
% 2.43/1.96 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[88, 4305])).
% 2.43/1.96 tff(4307,plain,
% 2.43/1.96 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[346, 345, 4207])).
% 2.43/1.96 tff(4308,plain,
% 2.43/1.96 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1707, 4307, 45, 1663])).
% 2.43/1.96 tff(4309,plain,
% 2.43/1.96 (~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1709, 4308])).
% 2.43/1.96 tff(4310,plain,
% 2.43/1.96 (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1711, 4309, 1663])).
% 2.43/1.96 tff(4311,plain,
% 2.43/1.96 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1713, 4310])).
% 2.43/1.96 tff(4312,plain,
% 2.43/1.96 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[220, 4311])).
% 2.43/1.96 tff(4313,plain,
% 2.43/1.96 ($false),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[82, 4312, 4306])).
% 2.43/1.96 tff(4314,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | big_f(X!1, Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(Z!5 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.96 tff(4315,plain,
% 2.43/1.96 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4314, 4269, 4266, 45, 1663, 349])).
% 2.43/1.96 tff(4316,plain,
% 2.43/1.96 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[462, 4315])).
% 2.43/1.96 tff(4317,plain,
% 2.43/1.96 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[481, 4316])).
% 2.43/1.96 tff(4318,plain,
% 2.43/1.96 (big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1506, 4317])).
% 2.43/1.96 tff(4319,plain,
% 2.43/1.96 (~(W1!8 = Y!0)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4081, 4318, 45, 4261, 4266])).
% 2.43/1.96 tff(4320,plain,
% 2.43/1.96 (W1!8 = X!1),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[19, 4319])).
% 2.43/1.96 tff(4321,plain,
% 2.43/1.96 (X!1 = W1!8),
% 2.43/1.96 inference(symmetry,[status(thm)],[4320])).
% 2.43/1.96 tff(4322,plain,
% 2.43/1.96 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.43/1.96 inference(transitivity,[status(thm)],[4269, 4321])).
% 2.43/1.96 tff(4323,plain,
% 2.43/1.96 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[790, 4316])).
% 2.43/1.96 tff(4324,plain,
% 2.43/1.96 ((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1459, 4323])).
% 2.43/1.96 tff(4325,plain,
% 2.43/1.96 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[90, 4267])).
% 2.43/1.96 tff(4326,plain,
% 2.43/1.96 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[269, 4269, 4325])).
% 2.43/1.96 tff(4327,plain,
% 2.43/1.96 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4156, 4320, 2935, 4269, 4326])).
% 2.43/1.96 tff(4328,plain,
% 2.43/1.96 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1465, 4327, 4324])).
% 2.43/1.96 tff(4329,plain,
% 2.43/1.96 ($false),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4328, 4322])).
% 2.43/1.96 tff(4330,plain,((~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, Y!0) | (~(Z!5 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.96 tff(4331,plain,
% 2.43/1.96 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[4330, 45, 4206])).
% 2.43/1.96 tff(4332,plain,
% 2.43/1.96 (X!1 = Z!5),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[353, 4206])).
% 2.43/1.96 tff(4333,plain,
% 2.43/1.96 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[3442, 4208, 34, 45, 144])).
% 2.43/1.96 tff(4334,plain,
% 2.43/1.96 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[82, 4333])).
% 2.43/1.96 tff(4335,plain,
% 2.43/1.96 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[220, 4334])).
% 2.43/1.96 tff(4336,plain,
% 2.43/1.96 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[222, 4335])).
% 2.43/1.96 tff(4337,plain,
% 2.43/1.96 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[224, 4336, 47])).
% 2.43/1.96 tff(4338,plain,
% 2.43/1.96 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[234, 4337])).
% 2.43/1.96 tff(4339,plain,
% 2.43/1.96 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.43/1.96 inference(monotonicity,[status(thm)],[527, 154])).
% 2.43/1.96 tff(4340,plain,
% 2.43/1.96 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.43/1.96 inference(modus_ponens,[status(thm)],[3415, 4339])).
% 2.43/1.96 tff(4341,plain,
% 2.43/1.96 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1157, 4337, 4340])).
% 2.43/1.96 tff(4342,plain,
% 2.43/1.96 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1413, 4341, 106, 40])).
% 2.43/1.96 tff(4343,plain,
% 2.43/1.96 (~(tptp_fun_W_3(X!1) = X!1)),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[1578, 4342, 40, 106, 4338])).
% 2.43/1.96 tff(4344,plain,
% 2.43/1.96 (tptp_fun_W_3(X!1) = Y!0),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[252, 4343])).
% 2.43/1.96 tff(4345,plain,
% 2.43/1.96 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.96 inference(monotonicity,[status(thm)],[106, 3148])).
% 2.43/1.96 tff(4346,plain,
% 2.43/1.96 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.43/1.96 inference(monotonicity,[status(thm)],[4345])).
% 2.43/1.96 tff(4347,plain,
% 2.43/1.96 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.96 inference(modus_ponens,[status(thm)],[4341, 4346])).
% 2.43/1.96 tff(4348,plain,
% 2.43/1.96 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[2996, 4347, 2935, 106, 4338, 4344])).
% 2.43/1.96 tff(4349,plain,
% 2.43/1.96 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[720, 4348])).
% 2.43/1.96 tff(4350,plain,
% 2.43/1.96 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.43/1.96 inference(unit_resolution,[status(thm)],[743, 4349, 40, 4210])).
% 2.43/1.96 tff(4351,plain,
% 2.43/1.96 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[462, 4350])).
% 2.43/1.97 tff(4352,plain,
% 2.43/1.97 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3017, 4351])).
% 2.43/1.97 tff(4353,plain,
% 2.43/1.97 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3019, 4352])).
% 2.43/1.97 tff(4354,plain,
% 2.43/1.97 (~((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3013, 4351])).
% 2.43/1.97 tff(4355,plain,
% 2.43/1.97 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3015, 4354])).
% 2.43/1.97 tff(4356,plain,
% 2.43/1.97 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3090, 4355, 2935, 106, 4347, 45, 4344, 4338, 4353])).
% 2.43/1.97 tff(4357,plain,
% 2.43/1.97 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4356, 3460])).
% 2.43/1.97 tff(4358,plain,
% 2.43/1.97 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.43/1.97 inference(symmetry,[status(thm)],[4357])).
% 2.43/1.97 tff(4359,plain,
% 2.43/1.97 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[4208, 4358])).
% 2.43/1.97 tff(4360,plain,
% 2.43/1.97 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3480, 4359, 4356])).
% 2.43/1.97 tff(4361,plain,
% 2.43/1.97 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3491, 4344, 106, 45, 4338])).
% 2.43/1.97 tff(4362,plain,
% 2.43/1.97 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3116, 4361])).
% 2.43/1.97 tff(4363,plain,
% 2.43/1.97 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3003, 4351])).
% 2.43/1.97 tff(4364,plain,
% 2.43/1.97 ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3005, 4363])).
% 2.43/1.97 tff(4365,plain,
% 2.43/1.97 (Y!0 = W1!8),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3114, 4364, 4362])).
% 2.43/1.97 tff(4366,plain,
% 2.43/1.97 (W1!8 = Y!0),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3112, 4365])).
% 2.43/1.97 tff(4367,plain,
% 2.43/1.97 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4366])).
% 2.43/1.97 tff(4368,plain,
% 2.43/1.97 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.43/1.97 inference(transitivity,[status(thm)],[4367, 46])).
% 2.43/1.97 tff(4369,plain,
% 2.43/1.97 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.43/1.97 inference(symmetry,[status(thm)],[4368])).
% 2.43/1.97 tff(4370,plain,
% 2.43/1.97 ((X!1 = Y!0) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.43/1.97 inference(transitivity,[status(thm)],[4369, 3484])).
% 2.43/1.97 tff(4371,plain,
% 2.43/1.97 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X_2(Y!0) = W1!8))),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4370])).
% 2.43/1.97 tff(4372,plain,
% 2.43/1.97 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[741, 4371])).
% 2.43/1.97 tff(4373,plain,
% 2.43/1.97 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3086, 4372, 4353])).
% 2.43/1.97 tff(4374,plain,
% 2.43/1.97 ($false),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3084, 4373, 4360])).
% 2.43/1.97 tff(4375,plain,((tptp_fun_Y1_11(X!1) = X!1) | big_f(X!1, Y!0) | (tptp_fun_X_2(X!1) = X!1) | (tptp_fun_Y1_11(Y!0) = Y!0) | (~(X!1 = Z!5))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.97 tff(4376,plain,
% 2.43/1.97 (tptp_fun_Y1_11(X!1) = X!1),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[4375, 34, 47, 45, 3548])).
% 2.43/1.97 tff(4377,plain,
% 2.43/1.97 ((tptp_fun_Y1_11(X!1) = Y!0) <=> (X!1 = Y!0)),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4376])).
% 2.43/1.97 tff(4378,plain,
% 2.43/1.97 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = Y!0)),
% 2.43/1.97 inference(symmetry,[status(thm)],[4377])).
% 2.43/1.97 tff(4379,plain,
% 2.43/1.97 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = Y!0))),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4378])).
% 2.43/1.97 tff(4380,plain,
% 2.43/1.97 (~(tptp_fun_Y1_11(X!1) = Y!0)),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[741, 4379])).
% 2.43/1.97 tff(4381,plain,
% 2.43/1.97 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3141, 4380, 2934, 34, 45, 2939])).
% 2.43/1.97 tff(4382,plain,
% 2.43/1.97 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1413, 4381, 106, 40])).
% 2.43/1.97 tff(4383,plain,
% 2.43/1.97 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1650, 4381, 106, 4376, 4382, 45])).
% 2.43/1.97 tff(4384,plain,
% 2.43/1.97 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[82, 4383])).
% 2.43/1.97 tff(4385,plain,
% 2.43/1.97 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[56, 4384])).
% 2.43/1.97 tff(4386,plain,
% 2.43/1.97 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[2663, 4385])).
% 2.43/1.97 tff(4387,plain,
% 2.43/1.97 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1894, 4386, 2934, 2939, 40])).
% 2.43/1.97 tff(4388,plain,
% 2.43/1.97 (~((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(X!1, tptp_fun_Y1_11(Y!0)) = X!1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[627, 4387, 45, 40])).
% 2.43/1.97 tff(4389,plain,
% 2.43/1.97 (~![W: $i] : ((~big_f(tptp_fun_Y1_11(Y!0), tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y1_11(Y!0)) = W))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[629, 4388])).
% 2.43/1.97 tff(4390,plain,
% 2.43/1.97 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[220, 4384])).
% 2.43/1.97 tff(4391,plain,
% 2.43/1.97 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[222, 4390])).
% 2.43/1.97 tff(4392,plain,
% 2.43/1.97 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[224, 4391, 47])).
% 2.43/1.97 tff(4393,plain,
% 2.43/1.97 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1157, 4392, 4382])).
% 2.43/1.97 tff(4394,plain,
% 2.43/1.97 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3631, 4393, 106, 40, 4381])).
% 2.43/1.97 tff(4395,plain,
% 2.43/1.97 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1110, 4394])).
% 2.43/1.97 tff(4396,plain,
% 2.43/1.97 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[743, 4395, 40, 4389])).
% 2.43/1.97 tff(4397,plain,
% 2.43/1.97 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[462, 4396])).
% 2.43/1.97 tff(4398,plain,
% 2.43/1.97 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[481, 4397])).
% 2.43/1.97 tff(4399,plain,
% 2.43/1.97 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[483, 4398])).
% 2.43/1.97 tff(4400,plain,
% 2.43/1.97 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1858, 4386, 2934])).
% 2.43/1.97 tff(4401,plain,
% 2.43/1.97 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[4382, 4345])).
% 2.43/1.97 tff(4402,plain,
% 2.43/1.97 (~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3262, 4401, 2935, 2939, 4400])).
% 2.43/1.97 tff(4403,plain,
% 2.43/1.97 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3017, 4397])).
% 2.43/1.97 tff(4404,plain,
% 2.43/1.97 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3266, 4403])).
% 2.43/1.97 tff(4405,plain,
% 2.43/1.97 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3268, 4404, 4402])).
% 2.43/1.97 tff(4406,plain,
% 2.43/1.97 (~(W1!8 = X!1)),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3648, 4405, 2935])).
% 2.43/1.97 tff(4407,plain,
% 2.43/1.97 (W1!8 = Y!0),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[19, 4406])).
% 2.43/1.97 tff(4408,plain,
% 2.43/1.97 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.43/1.97 inference(monotonicity,[status(thm)],[527, 4407])).
% 2.43/1.97 tff(4409,plain,
% 2.43/1.97 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, W1!8)),
% 2.43/1.97 inference(symmetry,[status(thm)],[4408])).
% 2.43/1.97 tff(4410,plain,
% 2.43/1.97 ((~big_f(tptp_fun_X_2(X!1), Y!0)) <=> (~big_f(Y!0, W1!8))),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4409])).
% 2.43/1.97 tff(4411,plain,
% 2.43/1.97 (~big_f(Y!0, W1!8)),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[4393, 4410])).
% 2.43/1.97 tff(4412,plain,
% 2.43/1.97 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[516, 4411, 4399])).
% 2.43/1.97 tff(4413,plain,
% 2.43/1.97 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[4412, 44])).
% 2.43/1.97 tff(4414,plain,
% 2.43/1.97 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(Y!0)),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4407])).
% 2.43/1.97 tff(4415,plain,
% 2.43/1.97 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (tptp_fun_Z1_9(Y!0) = X!1)),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4414])).
% 2.43/1.97 tff(4416,plain,
% 2.43/1.97 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.43/1.97 inference(transitivity,[status(thm)],[4415, 3279])).
% 2.43/1.97 tff(4417,plain,
% 2.43/1.97 ((X!1 = tptp_fun_Z1_9(Y!0)) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.43/1.97 inference(symmetry,[status(thm)],[4416])).
% 2.43/1.97 tff(4418,plain,
% 2.43/1.97 ((~(X!1 = tptp_fun_Z1_9(Y!0))) <=> (~(tptp_fun_Z1_9(W1!8) = X!1))),
% 2.43/1.97 inference(monotonicity,[status(thm)],[4417])).
% 2.43/1.97 tff(4419,plain,
% 2.43/1.97 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3003, 4397])).
% 2.43/1.97 tff(4420,plain,
% 2.43/1.97 ((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3286, 4419])).
% 2.43/1.97 tff(4421,plain,
% 2.43/1.97 (Y!0 = W1!8),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[4407, 2])).
% 2.43/1.97 tff(4422,plain,
% 2.43/1.97 (![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3289, 4421, 4420])).
% 2.43/1.97 tff(4423,plain,
% 2.43/1.97 (big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3291, 4422])).
% 2.43/1.97 tff(4424,plain,
% 2.43/1.97 (~(X!1 = tptp_fun_Z1_9(Y!0))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3294, 4423])).
% 2.43/1.97 tff(4425,plain,
% 2.43/1.97 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.43/1.97 inference(modus_ponens,[status(thm)],[4424, 4418])).
% 2.43/1.97 tff(4426,plain,
% 2.43/1.97 ($false),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[522, 4425, 4413])).
% 2.43/1.97 tff(4427,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | big_f(X!1, Y!0) | (tptp_fun_X_2(X!1) = X!1) | (~(X!1 = Z!5))), inference(lemma,lemma(discharge,[]))).
% 2.43/1.97 tff(4428,plain,
% 2.43/1.97 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[4427, 45, 4331, 4332])).
% 2.43/1.97 tff(4429,plain,
% 2.43/1.97 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1858, 3445, 2934])).
% 2.43/1.97 tff(4430,plain,
% 2.43/1.97 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3396, 1437, 2935, 4331, 4428, 41])).
% 2.43/1.97 tff(4431,plain,
% 2.43/1.97 (~![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3262, 4430, 2935, 2939, 4429])).
% 2.43/1.97 tff(4432,plain,
% 2.43/1.97 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3350, 4430, 2935, 4428, 41])).
% 2.43/1.97 tff(4433,plain,
% 2.43/1.97 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1110, 4432])).
% 2.43/1.97 tff(4434,plain,
% 2.43/1.97 (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[725, 4433, 436])).
% 2.43/1.97 tff(4435,plain,
% 2.43/1.97 ((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[723, 4434])).
% 2.43/1.97 tff(4436,plain,
% 2.43/1.97 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[428, 4435])).
% 2.43/1.97 tff(4437,plain,
% 2.43/1.97 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[462, 4436])).
% 2.43/1.97 tff(4438,plain,
% 2.43/1.97 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3017, 4437])).
% 2.43/1.97 tff(4439,plain,
% 2.43/1.97 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3266, 4438])).
% 2.43/1.97 tff(4440,plain,
% 2.43/1.97 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3268, 4439, 4431])).
% 2.43/1.97 tff(4441,plain,
% 2.43/1.97 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[481, 4437])).
% 2.43/1.97 tff(4442,plain,
% 2.43/1.97 (big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[1506, 4441])).
% 2.43/1.97 tff(4443,plain,
% 2.43/1.97 (~(W1!8 = Y!0)),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[4081, 4442, 45, 4428, 41])).
% 2.43/1.97 tff(4444,plain,
% 2.43/1.97 (W1!8 = X!1),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[19, 4443])).
% 2.43/1.97 tff(4445,plain,
% 2.43/1.97 ($false),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[3648, 4444, 4440, 2935])).
% 2.43/1.97 tff(4446,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | big_f(X!1, Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (Y!0 = Z!5)), inference(lemma,lemma(discharge,[]))).
% 2.43/1.97 tff(4447,plain,
% 2.43/1.97 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[4446, 41, 45, 436])).
% 2.43/1.97 tff(4448,plain,
% 2.43/1.97 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[82, 4447])).
% 2.43/1.97 tff(4449,plain,
% 2.43/1.97 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[88, 4448])).
% 2.43/1.97 tff(4450,plain,
% 2.43/1.97 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[191, 4449])).
% 2.43/1.97 tff(4451,plain,
% 2.43/1.97 (tptp_fun_Y1_11(X!1) = X!1),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[189, 4450, 45, 4428, 41])).
% 2.43/1.97 tff(4452,plain,
% 2.43/1.97 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[4182, 4451, 2934, 4331, 4428, 2939, 41, 45])).
% 2.43/1.97 tff(4453,plain,
% 2.43/1.97 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[462, 4452])).
% 2.43/1.97 tff(4454,plain,
% 2.43/1.97 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[342, 4453])).
% 2.43/1.97 tff(4455,plain,
% 2.43/1.97 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[344, 4454])).
% 2.43/1.97 tff(4456,plain,
% 2.43/1.97 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[90, 4449])).
% 2.43/1.97 tff(4457,plain,
% 2.43/1.97 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.43/1.97 inference(unit_resolution,[status(thm)],[269, 4451, 4456])).
% 2.43/1.98 tff(4458,plain,
% 2.43/1.98 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[271, 4457])).
% 2.43/1.98 tff(4459,plain,
% 2.43/1.98 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[84, 4448])).
% 2.43/1.98 tff(4460,plain,
% 2.43/1.98 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[86, 4459])).
% 2.43/1.98 tff(4461,plain,
% 2.43/1.98 ((tptp_fun_Y1_11(Y!0) = X!1) <=> (Y!0 = X!1)),
% 2.43/1.98 inference(monotonicity,[status(thm)],[4428])).
% 2.43/1.98 tff(4462,plain,
% 2.43/1.98 ((tptp_fun_Y1_11(Y!0) = X!1) <=> (X!1 = Y!0)),
% 2.43/1.98 inference(transitivity,[status(thm)],[4461, 46])).
% 2.43/1.98 tff(4463,plain,
% 2.43/1.98 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(Y!0) = X!1)),
% 2.43/1.98 inference(symmetry,[status(thm)],[4462])).
% 2.43/1.98 tff(4464,plain,
% 2.43/1.98 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(Y!0) = X!1))),
% 2.43/1.98 inference(monotonicity,[status(thm)],[4463])).
% 2.43/1.98 tff(4465,plain,
% 2.43/1.98 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.43/1.98 inference(modus_ponens,[status(thm)],[741, 4464])).
% 2.43/1.98 tff(4466,plain,
% 2.43/1.98 (tptp_fun_X_2(X!1) = Y!0),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[105, 4331])).
% 2.43/1.98 tff(4467,plain,
% 2.43/1.98 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[879, 4457])).
% 2.43/1.98 tff(4468,plain,
% 2.43/1.98 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[1067, 4467, 4466, 4465, 45, 4451, 4453, 4460])).
% 2.43/1.98 tff(4469,plain,
% 2.43/1.98 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[1518, 4458, 4466, 4468, 4451])).
% 2.43/1.98 tff(4470,plain,
% 2.43/1.98 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[337, 4469, 4451, 4458, 45])).
% 2.43/1.98 tff(4471,plain,
% 2.43/1.98 ($false),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[346, 4470, 4455, 4332])).
% 2.43/1.98 tff(4472,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(X!1, Y!0) | (Y!0 = Z!5)), inference(lemma,lemma(discharge,[]))).
% 2.43/1.98 tff(4473,plain,
% 2.43/1.98 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[4472, 45, 436])).
% 2.43/1.98 tff(4474,plain,
% 2.43/1.98 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[1168, 4473, 45, 4428])).
% 2.43/1.98 tff(4475,plain,
% 2.43/1.98 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[86, 4474])).
% 2.43/1.98 tff(4476,plain,
% 2.43/1.98 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[84, 4475])).
% 2.43/1.98 tff(4477,plain,
% 2.43/1.98 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[82, 4476])).
% 2.43/1.98 tff(4478,plain,
% 2.43/1.98 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[220, 4477])).
% 2.43/1.98 tff(4479,plain,
% 2.43/1.98 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[222, 4478])).
% 2.43/1.98 tff(4480,plain,
% 2.43/1.98 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[224, 4479, 4331])).
% 2.43/1.98 tff(4481,plain,
% 2.43/1.98 (big_f(tptp_fun_X_2(X!1), Y!0) <=> (Y!0 = tptp_fun_W_3(X!1))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[1146, 4480])).
% 2.43/1.98 tff(4482,plain,
% 2.43/1.98 (Y!0 = tptp_fun_X_2(X!1)),
% 2.43/1.98 inference(symmetry,[status(thm)],[4466])).
% 2.43/1.98 tff(4483,plain,
% 2.43/1.98 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.43/1.98 inference(monotonicity,[status(thm)],[4482, 4428])).
% 2.43/1.98 tff(4484,plain,
% 2.43/1.98 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.43/1.98 inference(modus_ponens,[status(thm)],[4473, 4483])).
% 2.43/1.98 tff(4485,plain,
% 2.43/1.98 (Y!0 = tptp_fun_W_3(X!1)),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[1148, 4484, 4481])).
% 2.43/1.98 tff(4486,plain,
% 2.43/1.98 (tptp_fun_W_3(X!1) = Y!0),
% 2.43/1.98 inference(modus_ponens,[status(thm)],[4485, 1581])).
% 2.43/1.98 tff(4487,plain,
% 2.43/1.98 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.43/1.98 inference(unit_resolution,[status(thm)],[234, 4480])).
% 2.47/1.98 tff(4488,plain,
% 2.47/1.98 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4466, 3148])).
% 2.47/1.98 tff(4489,plain,
% 2.47/1.98 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4488])).
% 2.47/1.98 tff(4490,plain,
% 2.47/1.98 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[1157, 4484, 4480])).
% 2.47/1.98 tff(4491,plain,
% 2.47/1.98 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.98 inference(modus_ponens,[status(thm)],[4490, 4489])).
% 2.47/1.98 tff(4492,plain,
% 2.47/1.98 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[2996, 4491, 2935, 4466, 4487, 4486])).
% 2.47/1.98 tff(4493,plain,
% 2.47/1.98 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[720, 4492])).
% 2.47/1.98 tff(4494,plain,
% 2.47/1.98 (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[725, 4493, 436])).
% 2.47/1.98 tff(4495,plain,
% 2.47/1.98 ((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[723, 4494])).
% 2.47/1.98 tff(4496,plain,
% 2.47/1.98 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[428, 4495])).
% 2.47/1.98 tff(4497,plain,
% 2.47/1.98 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[462, 4496])).
% 2.47/1.98 tff(4498,plain,
% 2.47/1.98 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3017, 4497])).
% 2.47/1.98 tff(4499,plain,
% 2.47/1.98 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3019, 4498])).
% 2.47/1.98 tff(4500,plain,
% 2.47/1.98 (~((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3013, 4497])).
% 2.47/1.98 tff(4501,plain,
% 2.47/1.98 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3015, 4500])).
% 2.47/1.98 tff(4502,plain,
% 2.47/1.98 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3090, 4501, 2935, 4466, 4491, 45, 4486, 4487, 4499])).
% 2.47/1.98 tff(4503,plain,
% 2.47/1.98 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[56, 4477])).
% 2.47/1.98 tff(4504,plain,
% 2.47/1.98 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[2663, 4503])).
% 2.47/1.98 tff(4505,plain,
% 2.47/1.98 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[1858, 4504, 2934])).
% 2.47/1.98 tff(4506,plain,
% 2.47/1.98 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[1860, 4505])).
% 2.47/1.98 tff(4507,plain,
% 2.47/1.98 (~(Y!0 = tptp_fun_W_3(Y!0))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[1862, 4506, 2939])).
% 2.47/1.98 tff(4508,assumption,(tptp_fun_W_3(Y!0) = Y!0), introduced(assumption)).
% 2.47/1.98 tff(4509,plain,
% 2.47/1.98 (Y!0 = tptp_fun_W_3(Y!0)),
% 2.47/1.98 inference(modus_ponens,[status(thm)],[4508, 1854])).
% 2.47/1.98 tff(4510,assumption,(~(Y!0 = tptp_fun_W_3(Y!0))), introduced(assumption)).
% 2.47/1.98 tff(4511,plain,
% 2.47/1.98 ($false),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[4510, 4509])).
% 2.47/1.98 tff(4512,plain,((~(tptp_fun_W_3(Y!0) = Y!0)) | (Y!0 = tptp_fun_W_3(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.47/1.98 tff(4513,plain,
% 2.47/1.98 (~(tptp_fun_W_3(Y!0) = Y!0)),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[4512, 4507])).
% 2.47/1.98 tff(4514,plain,
% 2.47/1.98 (tptp_fun_W_3(Y!0) = X!1),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[1871, 4513])).
% 2.47/1.98 tff(4515,plain,
% 2.47/1.98 (X!1 = tptp_fun_W_3(Y!0)),
% 2.47/1.98 inference(symmetry,[status(thm)],[4514])).
% 2.47/1.98 tff(4516,plain,
% 2.47/1.98 (tptp_fun_X_2(Y!0) = tptp_fun_W_3(Y!0)),
% 2.47/1.98 inference(transitivity,[status(thm)],[2935, 4515])).
% 2.47/1.98 tff(4517,plain,
% 2.47/1.98 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X_2(Y!0)),
% 2.47/1.98 inference(transitivity,[status(thm)],[4502, 3148])).
% 2.47/1.98 tff(4518,plain,
% 2.47/1.98 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4517, 4516])).
% 2.47/1.98 tff(4519,plain,
% 2.47/1.98 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.47/1.98 inference(symmetry,[status(thm)],[4518])).
% 2.47/1.98 tff(4520,plain,
% 2.47/1.98 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[1891, 4505])).
% 2.47/1.98 tff(4521,plain,
% 2.47/1.98 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.47/1.98 inference(modus_ponens,[status(thm)],[4520, 4519])).
% 2.47/1.98 tff(4522,plain,
% 2.47/1.98 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3480, 4521, 4502])).
% 2.47/1.98 tff(4523,plain,
% 2.47/1.98 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3491, 4486, 4466, 45, 4487])).
% 2.47/1.98 tff(4524,plain,
% 2.47/1.98 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3116, 4523])).
% 2.47/1.98 tff(4525,plain,
% 2.47/1.98 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3003, 4497])).
% 2.47/1.98 tff(4526,plain,
% 2.47/1.98 ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3005, 4525])).
% 2.47/1.98 tff(4527,plain,
% 2.47/1.98 (Y!0 = W1!8),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3114, 4526, 4524])).
% 2.47/1.98 tff(4528,plain,
% 2.47/1.98 (W1!8 = Y!0),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3112, 4527])).
% 2.47/1.98 tff(4529,plain,
% 2.47/1.98 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4528])).
% 2.47/1.98 tff(4530,plain,
% 2.47/1.98 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.47/1.98 inference(transitivity,[status(thm)],[4529, 46])).
% 2.47/1.98 tff(4531,plain,
% 2.47/1.98 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.47/1.98 inference(symmetry,[status(thm)],[4530])).
% 2.47/1.98 tff(4532,plain,
% 2.47/1.98 ((X!1 = Y!0) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.47/1.98 inference(transitivity,[status(thm)],[4531, 3484])).
% 2.47/1.98 tff(4533,plain,
% 2.47/1.98 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X_2(Y!0) = W1!8))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4532])).
% 2.47/1.98 tff(4534,plain,
% 2.47/1.98 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.47/1.98 inference(modus_ponens,[status(thm)],[741, 4533])).
% 2.47/1.98 tff(4535,plain,
% 2.47/1.98 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3086, 4534, 4499])).
% 2.47/1.98 tff(4536,plain,
% 2.47/1.98 ($false),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[3084, 4535, 4522])).
% 2.47/1.98 tff(4537,plain,(big_f(X!1, Y!0) | (Y!0 = Z!5)), inference(lemma,lemma(discharge,[]))).
% 2.47/1.98 tff(4538,plain,
% 2.47/1.98 (Y!0 = Z!5),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[4537, 45])).
% 2.47/1.98 tff(4539,plain,
% 2.47/1.98 (tptp_fun_Y1_11(Y!0) = Z!5),
% 2.47/1.98 inference(modus_ponens,[status(thm)],[4538, 4204])).
% 2.47/1.98 tff(4540,plain,
% 2.47/1.98 ((~((~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))))) | (~(tptp_fun_Y1_11(Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))),
% 2.47/1.98 inference(tautology,[status(thm)],[])).
% 2.47/1.98 tff(4541,plain,
% 2.47/1.98 (![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[4540, 4539, 4202])).
% 2.47/1.98 tff(4542,plain,
% 2.47/1.98 ((~![Y: $i] : (big_f(tptp_fun_Y1_11(Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))) | (big_f(tptp_fun_Y1_11(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))),
% 2.47/1.98 inference(quant_inst,[status(thm)],[])).
% 2.47/1.98 tff(4543,plain,
% 2.47/1.98 (big_f(tptp_fun_Y1_11(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[4542, 4541])).
% 2.47/1.98 tff(4544,plain,
% 2.47/1.98 (big_f(tptp_fun_Y1_11(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[109, 146])).
% 2.47/1.98 tff(4545,plain,
% 2.47/1.98 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_Y1_11(Y!0), Y!0)),
% 2.47/1.98 inference(symmetry,[status(thm)],[4544])).
% 2.47/1.98 tff(4546,plain,
% 2.47/1.98 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_Y1_11(Y!0), Y!0))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4545])).
% 2.47/1.98 tff(4547,plain,
% 2.47/1.98 (~big_f(tptp_fun_Y1_11(Y!0), Y!0)),
% 2.47/1.98 inference(modus_ponens,[status(thm)],[41, 4546])).
% 2.47/1.98 tff(4548,plain,
% 2.47/1.98 ((~(big_f(tptp_fun_Y1_11(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))) | big_f(tptp_fun_Y1_11(Y!0), Y!0) | (~(Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0))))),
% 2.47/1.98 inference(tautology,[status(thm)],[])).
% 2.47/1.98 tff(4549,plain,
% 2.47/1.98 (~(Y!0 = tptp_fun_W_6(tptp_fun_Y1_11(Y!0)))),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[4548, 4547, 4543])).
% 2.47/1.98 tff(4550,plain,
% 2.47/1.98 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.47/1.98 inference(modus_ponens,[status(thm)],[4549, 4060])).
% 2.47/1.98 tff(4551,plain,
% 2.47/1.98 (tptp_fun_W_6(Y!0) = X!1),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[403, 4550])).
% 2.47/1.98 tff(4552,plain,
% 2.47/1.98 (tptp_fun_W_6(Y!0) = tptp_fun_X_2(Y!0)),
% 2.47/1.98 inference(transitivity,[status(thm)],[4551, 2972])).
% 2.47/1.98 tff(4553,plain,
% 2.47/1.98 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4552])).
% 2.47/1.98 tff(4554,plain,
% 2.47/1.98 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.47/1.98 inference(symmetry,[status(thm)],[4553])).
% 2.47/1.98 tff(4555,plain,
% 2.47/1.98 ((~big_f(Y!0, tptp_fun_X_2(Y!0))) <=> (~big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.47/1.98 inference(monotonicity,[status(thm)],[4554])).
% 2.47/1.98 tff(4556,plain,
% 2.47/1.98 (tptp_fun_Y1_11(X!1) = X!1),
% 2.47/1.98 inference(unit_resolution,[status(thm)],[4055, 45, 41, 109])).
% 2.47/1.99 tff(4557,plain,
% 2.47/1.99 ((Y!0 = Z!5) <=> (Z!5 = Y!0)),
% 2.47/1.99 inference(symmetry,[status(thm)],[434])).
% 2.47/1.99 tff(4558,plain,
% 2.47/1.99 (Z!5 = Y!0),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[4538, 4557])).
% 2.47/1.99 tff(4559,plain,
% 2.47/1.99 (X!1 = tptp_fun_W_6(Z!5)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[3837, 4551, 4558])).
% 2.47/1.99 tff(4560,plain,
% 2.47/1.99 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[342, 4199])).
% 2.47/1.99 tff(4561,plain,
% 2.47/1.99 ((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[980, 4560])).
% 2.47/1.99 tff(4562,plain,
% 2.47/1.99 (Z!5 = Y!0),
% 2.47/1.99 inference(symmetry,[status(thm)],[4538])).
% 2.47/1.99 tff(4563,plain,
% 2.47/1.99 ((X!1 = Z!5) <=> (X!1 = Y!0)),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4562])).
% 2.47/1.99 tff(4564,plain,
% 2.47/1.99 ((X!1 = Y!0) <=> (X!1 = Z!5)),
% 2.47/1.99 inference(symmetry,[status(thm)],[4563])).
% 2.47/1.99 tff(4565,plain,
% 2.47/1.99 ((~(X!1 = Y!0)) <=> (~(X!1 = Z!5))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4564])).
% 2.47/1.99 tff(4566,plain,
% 2.47/1.99 (~(X!1 = Z!5)),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[741, 4565])).
% 2.47/1.99 tff(4567,plain,
% 2.47/1.99 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1008, 4566, 4561])).
% 2.47/1.99 tff(4568,plain,
% 2.47/1.99 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1010, 4567])).
% 2.47/1.99 tff(4569,plain,
% 2.47/1.99 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1034, 4559, 4538, 45, 4568])).
% 2.47/1.99 tff(4570,plain,
% 2.47/1.99 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1036, 4569, 4568])).
% 2.47/1.99 tff(4571,plain,
% 2.47/1.99 (tptp_fun_X1_13(Y!0, X!1) = Y!0),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1053, 4570, 4556, 4569, 4559, 4558, 906])).
% 2.47/1.99 tff(4572,plain,
% 2.47/1.99 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[901, 4089])).
% 2.47/1.99 tff(4573,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.47/1.99 inference(symmetry,[status(thm)],[4572])).
% 2.47/1.99 tff(4574,plain,
% 2.47/1.99 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[3230, 4573])).
% 2.47/1.99 tff(4575,plain,
% 2.47/1.99 ($false),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[908, 4574])).
% 2.47/1.99 tff(4576,plain,((~(tptp_fun_X1_13(Y!0, X!1) = Y!0)) | (~big_f(Y!0, tptp_fun_X_2(Y!0))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.47/1.99 tff(4577,plain,
% 2.47/1.99 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4576, 4571, 1906, 4556, 906])).
% 2.47/1.99 tff(4578,plain,
% 2.47/1.99 (~big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[4577, 4555])).
% 2.47/1.99 tff(4579,plain,
% 2.47/1.99 (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[428, 4199])).
% 2.47/1.99 tff(4580,plain,
% 2.47/1.99 ((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[430, 4579])).
% 2.47/1.99 tff(4581,plain,
% 2.47/1.99 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[432, 4580, 4538])).
% 2.47/1.99 tff(4582,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[451, 4581])).
% 2.47/1.99 tff(4583,plain,
% 2.47/1.99 ($false),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4582, 4578])).
% 2.47/1.99 tff(4584,plain,((~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(X!1, Y!0) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.47/1.99 tff(4585,plain,
% 2.47/1.99 (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4584, 45, 1878, 932, 41])).
% 2.47/1.99 tff(4586,plain,
% 2.47/1.99 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[879, 4585])).
% 2.47/1.99 tff(4587,plain,
% 2.47/1.99 (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[269, 4586, 4056])).
% 2.47/1.99 tff(4588,plain,
% 2.47/1.99 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[90, 4587])).
% 2.47/1.99 tff(4589,plain,
% 2.47/1.99 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[88, 4588])).
% 2.47/1.99 tff(4590,plain,
% 2.47/1.99 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[82, 4589])).
% 2.47/1.99 tff(4591,plain,
% 2.47/1.99 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[3451, 4590, 45])).
% 2.47/1.99 tff(4592,plain,
% 2.47/1.99 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4562, 2967])).
% 2.47/1.99 tff(4593,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Z!5, X!1)),
% 2.47/1.99 inference(symmetry,[status(thm)],[4592])).
% 2.47/1.99 tff(4594,plain,
% 2.47/1.99 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4197, 45, 41, 932])).
% 2.47/1.99 tff(4595,plain,
% 2.47/1.99 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[462, 4594])).
% 2.47/1.99 tff(4596,assumption,(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0), introduced(assumption)).
% 2.47/1.99 tff(4597,plain,
% 2.47/1.99 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(X!1, Y!0)),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4596])).
% 2.47/1.99 tff(4598,plain,
% 2.47/1.99 (big_f(X!1, Y!0) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/1.99 inference(symmetry,[status(thm)],[4597])).
% 2.47/1.99 tff(4599,plain,
% 2.47/1.99 ((~big_f(X!1, Y!0)) <=> (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4598])).
% 2.47/1.99 tff(4600,plain,
% 2.47/1.99 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[45, 4599])).
% 2.47/1.99 tff(4601,plain,
% 2.47/1.99 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4197, 41, 109, 45])).
% 2.47/1.99 tff(4602,plain,
% 2.47/1.99 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[462, 4601])).
% 2.47/1.99 tff(4603,plain,
% 2.47/1.99 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[342, 4602])).
% 2.47/1.99 tff(4604,plain,
% 2.47/1.99 ((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[980, 4603])).
% 2.47/1.99 tff(4605,plain,
% 2.47/1.99 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1008, 4566, 4604])).
% 2.47/1.99 tff(4606,plain,
% 2.47/1.99 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1010, 4605])).
% 2.47/1.99 tff(4607,plain,
% 2.47/1.99 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1036, 4606, 4600])).
% 2.47/1.99 tff(4608,plain,
% 2.47/1.99 (tptp_fun_W_6(Y!0) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.47/1.99 inference(symmetry,[status(thm)],[4607])).
% 2.47/1.99 tff(4609,plain,
% 2.47/1.99 (tptp_fun_W_6(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.47/1.99 inference(transitivity,[status(thm)],[4608, 4596, 146])).
% 2.47/1.99 tff(4610,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4609])).
% 2.47/1.99 tff(4611,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(symmetry,[status(thm)],[4610])).
% 2.47/1.99 tff(4612,plain,
% 2.47/1.99 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_W_6(Y!0)))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4611])).
% 2.47/1.99 tff(4613,plain,
% 2.47/1.99 (~big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[41, 4612])).
% 2.47/1.99 tff(4614,plain,
% 2.47/1.99 (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[428, 4602])).
% 2.47/1.99 tff(4615,plain,
% 2.47/1.99 ((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[430, 4614])).
% 2.47/1.99 tff(4616,plain,
% 2.47/1.99 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[432, 4615, 4538])).
% 2.47/1.99 tff(4617,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[451, 4616])).
% 2.47/1.99 tff(4618,plain,
% 2.47/1.99 ($false),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4617, 4613])).
% 2.47/1.99 tff(4619,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.47/1.99 tff(4620,plain,
% 2.47/1.99 (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = Y!0)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4619, 45, 41, 932])).
% 2.47/1.99 tff(4621,plain,
% 2.47/1.99 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1027, 4620])).
% 2.47/1.99 tff(4622,plain,
% 2.47/1.99 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[240, 2972])).
% 2.47/1.99 tff(4623,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.47/1.99 inference(symmetry,[status(thm)],[4622])).
% 2.47/1.99 tff(4624,plain,
% 2.47/1.99 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1008, 4566, 981])).
% 2.47/1.99 tff(4625,plain,
% 2.47/1.99 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1010, 4624])).
% 2.47/1.99 tff(4626,plain,
% 2.47/1.99 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_Y1_11(X!1)),
% 2.47/1.99 inference(transitivity,[status(thm)],[1807, 889])).
% 2.47/1.99 tff(4627,plain,
% 2.47/1.99 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4626])).
% 2.47/1.99 tff(4628,plain,
% 2.47/1.99 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/1.99 inference(symmetry,[status(thm)],[4627])).
% 2.47/1.99 tff(4629,plain,
% 2.47/1.99 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[271, 1644])).
% 2.47/1.99 tff(4630,plain,
% 2.47/1.99 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1067, 1645, 931, 240, 45, 277, 341, 1641])).
% 2.47/1.99 tff(4631,plain,
% 2.47/1.99 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1518, 4630, 277, 240, 4629])).
% 2.47/1.99 tff(4632,plain,
% 2.47/1.99 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4631])).
% 2.47/1.99 tff(4633,plain,
% 2.47/1.99 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/1.99 inference(transitivity,[status(thm)],[4632, 4628])).
% 2.47/1.99 tff(4634,plain,
% 2.47/1.99 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4633])).
% 2.47/1.99 tff(4635,plain,
% 2.47/1.99 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[316, 4631, 4629])).
% 2.47/1.99 tff(4636,plain,
% 2.47/1.99 (~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[4635, 4634])).
% 2.47/1.99 tff(4637,plain,
% 2.47/1.99 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0)),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[1036, 4636, 4625])).
% 2.47/1.99 tff(4638,plain,
% 2.47/1.99 (tptp_fun_W_6(Y!0) = tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)),
% 2.47/1.99 inference(symmetry,[status(thm)],[4637])).
% 2.47/1.99 tff(4639,plain,
% 2.47/1.99 (tptp_fun_W_6(Y!0) = tptp_fun_X_2(Y!0)),
% 2.47/1.99 inference(transitivity,[status(thm)],[4638, 1807, 2972])).
% 2.47/1.99 tff(4640,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.99 inference(monotonicity,[status(thm)],[4639])).
% 2.47/1.99 tff(4641,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_W_6(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.47/1.99 inference(transitivity,[status(thm)],[4640, 4623])).
% 2.47/1.99 tff(4642,plain,
% 2.47/1.99 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[432, 431, 4538])).
% 2.47/1.99 tff(4643,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_W_6(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[451, 4642])).
% 2.47/1.99 tff(4644,plain,
% 2.47/1.99 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[4643, 4641])).
% 2.47/1.99 tff(4645,plain,
% 2.47/1.99 ($false),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4630, 4644])).
% 2.47/1.99 tff(4646,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (tptp_fun_Y1_11(Y!0) = X!1) | big_f(X!1, Y!0) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))), inference(lemma,lemma(discharge,[]))).
% 2.47/1.99 tff(4647,plain,
% 2.47/1.99 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[4646, 106, 1878, 4621, 4056, 931, 45, 4595])).
% 2.47/1.99 tff(4648,plain,
% 2.47/1.99 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[82, 4647])).
% 2.47/1.99 tff(4649,plain,
% 2.47/1.99 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[220, 4648])).
% 2.47/1.99 tff(4650,plain,
% 2.47/1.99 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[222, 4649])).
% 2.47/1.99 tff(4651,plain,
% 2.47/1.99 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/1.99 inference(unit_resolution,[status(thm)],[3396, 4650, 41, 932, 1878, 47])).
% 2.47/1.99 tff(4652,plain,
% 2.47/1.99 (big_f(Z!5, X!1)),
% 2.47/1.99 inference(modus_ponens,[status(thm)],[4651, 4593])).
% 2.47/2.00 tff(4653,plain,
% 2.47/2.00 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[385, 4595])).
% 2.47/2.00 tff(4654,plain,
% 2.47/2.00 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[983, 4653])).
% 2.47/2.00 tff(4655,plain,
% 2.47/2.00 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[342, 4595])).
% 2.47/2.00 tff(4656,plain,
% 2.47/2.00 ((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[980, 4655])).
% 2.47/2.00 tff(4657,plain,
% 2.47/2.00 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1008, 4566, 4656])).
% 2.47/2.00 tff(4658,plain,
% 2.47/2.00 ((~big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))) <=> (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_W_6(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1010, 4657])).
% 2.47/2.00 tff(4659,plain,
% 2.47/2.00 (X!1 = tptp_fun_Y1_11(X!1)),
% 2.47/2.00 inference(symmetry,[status(thm)],[4056])).
% 2.47/2.00 tff(4660,plain,
% 2.47/2.00 (tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1) = tptp_fun_Y1_11(X!1)),
% 2.47/2.00 inference(transitivity,[status(thm)],[4621, 4659])).
% 2.47/2.00 tff(4661,plain,
% 2.47/2.00 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4660])).
% 2.47/2.00 tff(4662,plain,
% 2.47/2.00 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/2.00 inference(symmetry,[status(thm)],[4661])).
% 2.47/2.00 tff(4663,plain,
% 2.47/2.00 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[56, 4648])).
% 2.47/2.00 tff(4664,plain,
% 2.47/2.00 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[2663, 4663])).
% 2.47/2.00 tff(4665,plain,
% 2.47/2.00 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1858, 4664, 1857])).
% 2.47/2.00 tff(4666,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1860, 4665])).
% 2.47/2.00 tff(4667,plain,
% 2.47/2.00 (~(Y!0 = tptp_fun_W_3(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1862, 4666, 35])).
% 2.47/2.00 tff(4668,plain,
% 2.47/2.00 (~(tptp_fun_W_3(Y!0) = Y!0)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4512, 4667])).
% 2.47/2.00 tff(4669,plain,
% 2.47/2.00 (tptp_fun_W_3(Y!0) = X!1),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1871, 4668])).
% 2.47/2.00 tff(4670,plain,
% 2.47/2.00 (tptp_fun_W_3(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.47/2.00 inference(transitivity,[status(thm)],[4669, 4659])).
% 2.47/2.00 tff(4671,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[1878, 4670])).
% 2.47/2.00 tff(4672,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/2.00 inference(transitivity,[status(thm)],[4671, 4662])).
% 2.47/2.00 tff(4673,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1891, 4665])).
% 2.47/2.00 tff(4674,plain,
% 2.47/2.00 (big_f(X!1, tptp_fun_Y_7(tptp_fun_W_6(Y!0), X!1))),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[4673, 4672])).
% 2.47/2.00 tff(4675,plain,
% 2.47/2.00 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1034, 4674, 4538, 45, 4658])).
% 2.47/2.00 tff(4676,plain,
% 2.47/2.00 (~big_f(Z!5, X!1)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[989, 4675, 4654])).
% 2.47/2.00 tff(4677,plain,
% 2.47/2.00 ($false),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4676, 4652])).
% 2.47/2.00 tff(4678,plain,((tptp_fun_X_2(X!1) = X!1) | big_f(X!1, Y!0) | big_f(tptp_fun_X_2(Y!0), Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.47/2.00 tff(4679,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4678, 4591, 45, 41, 1857, 931])).
% 2.47/2.00 tff(4680,plain,
% 2.47/2.00 ($false),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4679, 3213])).
% 2.47/2.00 tff(4681,plain,(big_f(X!1, Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_X_2(Y!0) = Y!0) | (tptp_fun_Y1_11(Y!0) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.47/2.00 tff(4682,plain,
% 2.47/2.00 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4681, 4049, 2934, 45])).
% 2.47/2.00 tff(4683,plain,
% 2.47/2.00 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1168, 4682, 4044, 45])).
% 2.47/2.00 tff(4684,plain,
% 2.47/2.00 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[86, 4683])).
% 2.47/2.00 tff(4685,plain,
% 2.47/2.00 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[84, 4684])).
% 2.47/2.00 tff(4686,plain,
% 2.47/2.00 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[82, 4685])).
% 2.47/2.00 tff(4687,plain,
% 2.47/2.00 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[220, 4686])).
% 2.47/2.00 tff(4688,plain,
% 2.47/2.00 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[222, 4687])).
% 2.47/2.00 tff(4689,plain,
% 2.47/2.00 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3451, 4686, 45])).
% 2.47/2.00 tff(4690,plain,
% 2.47/2.00 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[224, 4689, 4688])).
% 2.47/2.00 tff(4691,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[234, 4690])).
% 2.47/2.00 tff(4692,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(X!1), Y!0) <=> (Y!0 = tptp_fun_W_3(X!1))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1146, 4690])).
% 2.47/2.00 tff(4693,plain,
% 2.47/2.00 (Y!0 = tptp_fun_Y1_11(Y!0)),
% 2.47/2.00 inference(symmetry,[status(thm)],[4044])).
% 2.47/2.00 tff(4694,plain,
% 2.47/2.00 (tptp_fun_X_2(X!1) = Y!0),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[105, 4689])).
% 2.47/2.00 tff(4695,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4694, 4693])).
% 2.47/2.00 tff(4696,plain,
% 2.47/2.00 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.47/2.00 inference(symmetry,[status(thm)],[4695])).
% 2.47/2.00 tff(4697,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[4682, 4696])).
% 2.47/2.00 tff(4698,plain,
% 2.47/2.00 (Y!0 = tptp_fun_W_3(X!1)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1148, 4697, 4692])).
% 2.47/2.00 tff(4699,plain,
% 2.47/2.00 (tptp_fun_W_3(X!1) = Y!0),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[4698, 1581])).
% 2.47/2.00 tff(4700,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4694, 3148])).
% 2.47/2.00 tff(4701,plain,
% 2.47/2.00 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4700])).
% 2.47/2.00 tff(4702,plain,
% 2.47/2.00 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1157, 4697, 4690])).
% 2.47/2.00 tff(4703,plain,
% 2.47/2.00 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[4702, 4701])).
% 2.47/2.00 tff(4704,plain,
% 2.47/2.00 (~((~((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1)))) | (~((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3013, 1268])).
% 2.47/2.00 tff(4705,plain,
% 2.47/2.00 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))), tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) = Z1))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3015, 4704])).
% 2.47/2.00 tff(4706,plain,
% 2.47/2.00 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3090, 4705, 45, 4694, 2935, 4703, 4699, 4691, 3160])).
% 2.47/2.00 tff(4707,plain,
% 2.47/2.00 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X_2(Y!0)),
% 2.47/2.00 inference(transitivity,[status(thm)],[4706, 3148])).
% 2.47/2.00 tff(4708,plain,
% 2.47/2.00 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4707, 2935])).
% 2.47/2.00 tff(4709,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.47/2.00 inference(symmetry,[status(thm)],[4708])).
% 2.47/2.00 tff(4710,plain,
% 2.47/2.00 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[56, 4686])).
% 2.47/2.00 tff(4711,plain,
% 2.47/2.00 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[2663, 4710])).
% 2.47/2.00 tff(4712,plain,
% 2.47/2.00 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1858, 4711, 2934])).
% 2.47/2.00 tff(4713,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1860, 4712])).
% 2.47/2.00 tff(4714,plain,
% 2.47/2.00 (~(Y!0 = tptp_fun_W_3(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1862, 4713, 2939])).
% 2.47/2.00 tff(4715,plain,
% 2.47/2.00 (~(tptp_fun_W_3(Y!0) = Y!0)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4512, 4714])).
% 2.47/2.00 tff(4716,plain,
% 2.47/2.00 (tptp_fun_W_3(Y!0) = X!1),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1871, 4715])).
% 2.47/2.00 tff(4717,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4716])).
% 2.47/2.00 tff(4718,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_W_3(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1891, 4712])).
% 2.47/2.00 tff(4719,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[4718, 4717])).
% 2.47/2.00 tff(4720,plain,
% 2.47/2.00 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[4719, 4709])).
% 2.47/2.00 tff(4721,plain,
% 2.47/2.00 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3480, 4720, 4706])).
% 2.47/2.00 tff(4722,plain,
% 2.47/2.00 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X_2(X!1)))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3491, 4699, 45, 4694, 4691])).
% 2.47/2.00 tff(4723,plain,
% 2.47/2.00 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3116, 4722])).
% 2.47/2.00 tff(4724,plain,
% 2.47/2.00 ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3005, 3285])).
% 2.47/2.00 tff(4725,plain,
% 2.47/2.00 (Y!0 = W1!8),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3114, 4724, 4723])).
% 2.47/2.00 tff(4726,plain,
% 2.47/2.00 (W1!8 = Y!0),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3112, 4725])).
% 2.47/2.00 tff(4727,plain,
% 2.47/2.00 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4726])).
% 2.47/2.00 tff(4728,plain,
% 2.47/2.00 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.47/2.00 inference(transitivity,[status(thm)],[4727, 46])).
% 2.47/2.00 tff(4729,plain,
% 2.47/2.00 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.47/2.00 inference(symmetry,[status(thm)],[4728])).
% 2.47/2.00 tff(4730,plain,
% 2.47/2.00 ((X!1 = Y!0) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.47/2.00 inference(transitivity,[status(thm)],[4729, 3484])).
% 2.47/2.00 tff(4731,plain,
% 2.47/2.00 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X_2(Y!0) = W1!8))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4730])).
% 2.47/2.00 tff(4732,plain,
% 2.47/2.00 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[741, 4731])).
% 2.47/2.00 tff(4733,plain,
% 2.47/2.00 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3086, 4732, 3160])).
% 2.47/2.00 tff(4734,plain,
% 2.47/2.00 ($false),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[3084, 4733, 4721])).
% 2.47/2.00 tff(4735,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.47/2.00 tff(4736,plain,
% 2.47/2.00 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4735, 45])).
% 2.47/2.00 tff(4737,plain,
% 2.47/2.00 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[462, 4736])).
% 2.47/2.00 tff(4738,plain,
% 2.47/2.00 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[342, 4737])).
% 2.47/2.00 tff(4739,plain,
% 2.47/2.00 ((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[980, 4738])).
% 2.47/2.00 tff(4740,plain,
% 2.47/2.00 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[1008, 4566, 4739])).
% 2.47/2.00 tff(4741,plain,
% 2.47/2.00 ((~![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))) | ((~big_f(X!1, tptp_fun_Y_7(X!1, X!1))) <=> (tptp_fun_Y_7(X!1, X!1) = X!1))),
% 2.47/2.00 inference(quant_inst,[status(thm)],[])).
% 2.47/2.00 tff(4742,plain,
% 2.47/2.00 ((~big_f(X!1, tptp_fun_Y_7(X!1, X!1))) <=> (tptp_fun_Y_7(X!1, X!1) = X!1)),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4741, 4740])).
% 2.47/2.00 tff(4743,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> big_f(X!1, tptp_fun_Y_7(X!1, X!1))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[2935])).
% 2.47/2.00 tff(4744,plain,
% 2.47/2.00 ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0)))),
% 2.47/2.00 inference(quant_inst,[status(thm)],[])).
% 2.47/2.00 tff(4745,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0))),
% 2.47/2.00 inference(unit_resolution,[status(thm)],[4744, 4712])).
% 2.47/2.00 tff(4746,assumption,((~big_f(X!1, tptp_fun_Y_7(X!1, X!1))) <=> (tptp_fun_Y_7(X!1, X!1) = X!1)), introduced(assumption)).
% 2.47/2.00 tff(4747,plain,
% 2.47/2.00 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> big_f(X!1, tptp_fun_Y_7(X!1, X!1))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[1906])).
% 2.47/2.00 tff(4748,plain,
% 2.47/2.00 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1))) <=> (~big_f(X!1, tptp_fun_Y_7(X!1, X!1)))),
% 2.47/2.00 inference(monotonicity,[status(thm)],[4747])).
% 2.47/2.00 tff(4749,assumption,(~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1))), introduced(assumption)).
% 2.47/2.00 tff(4750,plain,
% 2.47/2.00 (~big_f(X!1, tptp_fun_Y_7(X!1, X!1))),
% 2.47/2.00 inference(modus_ponens,[status(thm)],[4749, 4748])).
% 2.47/2.00 tff(4751,assumption,(tptp_fun_W_3(Y!0) = X!1), introduced(assumption)).
% 2.47/2.01 tff(4752,plain,
% 2.47/2.01 ((tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0)) <=> (tptp_fun_Y_7(X!1, X!1) = X!1)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4751])).
% 2.47/2.01 tff(4753,plain,
% 2.47/2.01 ((~(tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0))) <=> (~(tptp_fun_Y_7(X!1, X!1) = X!1))),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4752])).
% 2.47/2.01 tff(4754,assumption,(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0))), introduced(assumption)).
% 2.47/2.01 tff(4755,plain,
% 2.47/2.01 ((~(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0)))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) | (~(tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0)))),
% 2.47/2.01 inference(tautology,[status(thm)],[])).
% 2.47/2.01 tff(4756,plain,
% 2.47/2.01 (~(tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4755, 4749, 4754])).
% 2.47/2.01 tff(4757,plain,
% 2.47/2.01 (~(tptp_fun_Y_7(X!1, X!1) = X!1)),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[4756, 4753])).
% 2.47/2.01 tff(4758,plain,
% 2.47/2.01 ((~((~big_f(X!1, tptp_fun_Y_7(X!1, X!1))) <=> (tptp_fun_Y_7(X!1, X!1) = X!1))) | big_f(X!1, tptp_fun_Y_7(X!1, X!1)) | (tptp_fun_Y_7(X!1, X!1) = X!1)),
% 2.47/2.01 inference(tautology,[status(thm)],[])).
% 2.47/2.01 tff(4759,plain,
% 2.47/2.01 ($false),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4758, 4757, 4750, 4746])).
% 2.47/2.01 tff(4760,plain,(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) | (~((~big_f(X!1, tptp_fun_Y_7(X!1, X!1))) <=> (tptp_fun_Y_7(X!1, X!1) = X!1))) | (~(tptp_fun_W_3(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0))))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.01 tff(4761,plain,
% 2.47/2.01 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4760, 4742, 4716, 2935, 4745])).
% 2.47/2.01 tff(4762,plain,
% 2.47/2.01 (big_f(X!1, tptp_fun_Y_7(X!1, X!1))),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[4761, 4743])).
% 2.47/2.01 tff(4763,plain,
% 2.47/2.01 ((tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0)) <=> (tptp_fun_Y_7(X!1, X!1) = X!1)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4716])).
% 2.47/2.01 tff(4764,plain,
% 2.47/2.01 ((~(big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1)) <=> (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0)))) | (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_7(X!1, X!1))) | (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0))),
% 2.47/2.01 inference(tautology,[status(thm)],[])).
% 2.47/2.01 tff(4765,plain,
% 2.47/2.01 (tptp_fun_Y_7(X!1, X!1) = tptp_fun_W_3(Y!0)),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4764, 4761, 4745])).
% 2.47/2.01 tff(4766,plain,
% 2.47/2.01 (tptp_fun_Y_7(X!1, X!1) = X!1),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[4765, 4763])).
% 2.47/2.01 tff(4767,plain,
% 2.47/2.01 ((~((~big_f(X!1, tptp_fun_Y_7(X!1, X!1))) <=> (tptp_fun_Y_7(X!1, X!1) = X!1))) | (~big_f(X!1, tptp_fun_Y_7(X!1, X!1))) | (~(tptp_fun_Y_7(X!1, X!1) = X!1))),
% 2.47/2.01 inference(tautology,[status(thm)],[])).
% 2.47/2.01 tff(4768,plain,
% 2.47/2.01 ($false),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4767, 4766, 4762, 4742])).
% 2.47/2.01 tff(4769,plain,(big_f(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.47/2.01 tff(4770,plain,
% 2.47/2.01 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1139, 2847, 30, 41])).
% 2.47/2.01 tff(4771,plain,
% 2.47/2.01 (tptp_fun_X_2(X!1) = X!1),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4026, 144, 30, 35])).
% 2.47/2.01 tff(4772,plain,
% 2.47/2.01 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1711, 4771, 2620])).
% 2.47/2.01 tff(4773,plain,
% 2.47/2.01 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3679, 4772])).
% 2.47/2.01 tff(4774,plain,
% 2.47/2.01 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3689, 4773, 3678, 4771])).
% 2.47/2.01 tff(4775,plain,
% 2.47/2.01 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3694, 4774])).
% 2.47/2.01 tff(4776,plain,
% 2.47/2.01 (tptp_fun_Y_4(Y!0, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.47/2.01 inference(transitivity,[status(thm)],[4775, 599])).
% 2.47/2.01 tff(4777,plain,
% 2.47/2.01 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4771])).
% 2.47/2.01 tff(4778,plain,
% 2.47/2.01 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1))),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4777])).
% 2.47/2.01 tff(4779,plain,
% 2.47/2.01 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.47/2.01 inference(symmetry,[status(thm)],[1765])).
% 2.47/2.01 tff(4780,plain,
% 2.47/2.01 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4779])).
% 2.47/2.01 tff(4781,plain,
% 2.47/2.01 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.47/2.01 inference(symmetry,[status(thm)],[4780])).
% 2.47/2.01 tff(4782,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[1785, 796])).
% 2.47/2.01 tff(4783,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.47/2.01 inference(symmetry,[status(thm)],[4782])).
% 2.47/2.01 tff(4784,plain,
% 2.47/2.01 (X!1 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.47/2.01 inference(transitivity,[status(thm)],[1789, 1671])).
% 2.47/2.01 tff(4785,plain,
% 2.47/2.01 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4784])).
% 2.47/2.01 tff(4786,plain,
% 2.47/2.01 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.47/2.01 inference(transitivity,[status(thm)],[4785, 4783])).
% 2.47/2.01 tff(4787,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[3678, 4786])).
% 2.47/2.01 tff(4788,plain,
% 2.47/2.01 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[1785])).
% 2.47/2.01 tff(4789,plain,
% 2.47/2.01 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.47/2.01 inference(symmetry,[status(thm)],[4788])).
% 2.47/2.01 tff(4790,plain,
% 2.47/2.01 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[1671])).
% 2.47/2.01 tff(4791,plain,
% 2.47/2.01 ((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.47/2.01 inference(transitivity,[status(thm)],[4790, 4789])).
% 2.47/2.01 tff(4792,plain,
% 2.47/2.01 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[1672, 4791])).
% 2.47/2.01 tff(4793,plain,
% 2.47/2.01 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3099, 4792, 4787])).
% 2.47/2.01 tff(4794,plain,
% 2.47/2.01 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3101, 4793])).
% 2.47/2.01 tff(4795,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[3678, 4785])).
% 2.47/2.01 tff(4796,plain,
% 2.47/2.01 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(monotonicity,[status(thm)],[1789])).
% 2.47/2.01 tff(4797,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(symmetry,[status(thm)],[4796])).
% 2.47/2.01 tff(4798,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[1671, 109])).
% 2.47/2.01 tff(4799,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(symmetry,[status(thm)],[4798])).
% 2.47/2.01 tff(4800,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(transitivity,[status(thm)],[4799, 4797])).
% 2.47/2.01 tff(4801,assumption,(big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)), introduced(assumption)).
% 2.47/2.01 tff(4802,plain,
% 2.47/2.01 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[4801, 4800])).
% 2.47/2.01 tff(4803,plain,
% 2.47/2.01 ($false),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[42, 4802])).
% 2.47/2.01 tff(4804,plain,((~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.01 tff(4805,plain,
% 2.47/2.01 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4804, 42, 4795, 30, 1663, 1672])).
% 2.47/2.01 tff(4806,plain,
% 2.47/2.01 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[39, 4805])).
% 2.47/2.01 tff(4807,plain,
% 2.47/2.01 (X!1 = tptp_fun_Y1_11(Y!0)),
% 2.47/2.01 inference(symmetry,[status(thm)],[4806])).
% 2.47/2.01 tff(4808,plain,
% 2.47/2.01 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)))),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4796])).
% 2.47/2.01 tff(4809,plain,
% 2.47/2.01 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[42, 4808])).
% 2.47/2.01 tff(4810,plain,
% 2.47/2.01 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3689, 3685, 1663, 3678])).
% 2.47/2.01 tff(4811,plain,
% 2.47/2.01 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3694, 4810])).
% 2.47/2.01 tff(4812,plain,
% 2.47/2.01 (tptp_fun_Y_4(Y!0, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.47/2.01 inference(transitivity,[status(thm)],[4811, 599])).
% 2.47/2.01 tff(4813,plain,
% 2.47/2.01 (tptp_fun_X_2(X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.47/2.01 inference(transitivity,[status(thm)],[1663, 1789])).
% 2.47/2.01 tff(4814,plain,
% 2.47/2.01 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4813, 4812])).
% 2.47/2.01 tff(4815,plain,
% 2.47/2.01 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.01 inference(symmetry,[status(thm)],[4814])).
% 2.47/2.01 tff(4816,plain,
% 2.47/2.01 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4815])).
% 2.47/2.01 tff(4817,assumption,(~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))), introduced(assumption)).
% 2.47/2.01 tff(4818,plain,
% 2.47/2.01 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.01 inference(modus_ponens,[status(thm)],[4817, 4816])).
% 2.47/2.01 tff(4819,plain,
% 2.47/2.01 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3701, 3685, 4810])).
% 2.47/2.01 tff(4820,plain,
% 2.47/2.01 ($false),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4819, 4818])).
% 2.47/2.01 tff(4821,plain,((~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0))) | big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~big_f(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.01 tff(4822,plain,
% 2.47/2.01 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[4821, 4809, 4806, 1663, 1672, 3678])).
% 2.47/2.01 tff(4823,plain,
% 2.47/2.01 (~![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[3679, 4822])).
% 2.47/2.01 tff(4824,plain,
% 2.47/2.01 (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1711, 4823, 1663])).
% 2.47/2.01 tff(4825,plain,
% 2.47/2.01 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1713, 4824])).
% 2.47/2.01 tff(4826,plain,
% 2.47/2.01 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[220, 4825])).
% 2.47/2.01 tff(4827,plain,
% 2.47/2.01 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[82, 4826])).
% 2.47/2.01 tff(4828,plain,
% 2.47/2.01 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[84, 4827])).
% 2.47/2.01 tff(4829,plain,
% 2.47/2.01 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[561, 4828])).
% 2.47/2.01 tff(4830,plain,
% 2.47/2.01 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[563, 4829, 4805])).
% 2.47/2.01 tff(4831,plain,
% 2.47/2.01 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[596, 4830, 42])).
% 2.47/2.01 tff(4832,plain,
% 2.47/2.01 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1108, 4831, 30, 35, 4806])).
% 2.47/2.01 tff(4833,plain,
% 2.47/2.01 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1110, 4832])).
% 2.47/2.01 tff(4834,plain,
% 2.47/2.01 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1254, 4831, 42, 4806])).
% 2.47/2.01 tff(4835,plain,
% 2.47/2.01 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1256, 4834])).
% 2.47/2.01 tff(4836,plain,
% 2.47/2.01 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[576, 4830])).
% 2.47/2.01 tff(4837,plain,
% 2.47/2.01 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[578, 4836, 42])).
% 2.47/2.01 tff(4838,plain,
% 2.47/2.01 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1264, 4837])).
% 2.47/2.01 tff(4839,plain,
% 2.47/2.01 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[1298, 4838, 796, 4835, 4794])).
% 2.47/2.01 tff(4840,plain,
% 2.47/2.01 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[462, 4839])).
% 2.47/2.01 tff(4841,plain,
% 2.47/2.01 (~((~((~(Y!0 = Z!5)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0))))) | (~((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)))))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[428, 4840])).
% 2.47/2.01 tff(4842,plain,
% 2.47/2.01 ((Y!0 = Z!5) | ![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[723, 4841])).
% 2.47/2.01 tff(4843,plain,
% 2.47/2.01 (Y!0 = Z!5),
% 2.47/2.01 inference(unit_resolution,[status(thm)],[725, 4842, 4833])).
% 2.47/2.01 tff(4844,plain,
% 2.47/2.01 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y_7(Z!5, X!1)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4843])).
% 2.47/2.01 tff(4845,plain,
% 2.47/2.01 ((tptp_fun_Y_7(Y!0, X!1) = Y!0) <=> (tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4844])).
% 2.47/2.01 tff(4846,plain,
% 2.47/2.01 ((~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) <=> (~(tptp_fun_Y_7(Z!5, X!1) = Y!0))),
% 2.47/2.01 inference(monotonicity,[status(thm)],[4845])).
% 2.47/2.01 tff(4847,plain,
% 2.47/2.01 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[3366, 4840, 4833])).
% 2.47/2.02 tff(4848,plain,
% 2.47/2.02 ((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[1842, 4847])).
% 2.47/2.02 tff(4849,plain,
% 2.47/2.02 (~(tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[3872, 4848, 3678])).
% 2.47/2.02 tff(4850,plain,
% 2.47/2.02 (~(tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[4849, 4846])).
% 2.47/2.02 tff(4851,plain,
% 2.47/2.02 (tptp_fun_Y_7(Z!5, X!1) = X!1),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[3878, 4850])).
% 2.47/2.02 tff(4852,plain,
% 2.47/2.02 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.47/2.02 inference(transitivity,[status(thm)],[4844, 4851, 4807])).
% 2.47/2.02 tff(4853,plain,
% 2.47/2.02 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[1789, 4852])).
% 2.47/2.02 tff(4854,plain,
% 2.47/2.02 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4853])).
% 2.47/2.02 tff(4855,plain,
% 2.47/2.02 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))) <=> (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1)))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4854])).
% 2.47/2.02 tff(4856,plain,
% 2.47/2.02 (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[4809, 4855])).
% 2.47/2.02 tff(4857,plain,
% 2.47/2.02 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[1844, 4849, 4848])).
% 2.47/2.02 tff(4858,plain,
% 2.47/2.02 ($false),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[4857, 4856])).
% 2.47/2.02 tff(4859,plain,(big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.02 tff(4860,plain,
% 2.47/2.02 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[4859, 1672, 3678, 796, 30, 35, 1663])).
% 2.47/2.02 tff(4861,plain,
% 2.47/2.02 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[3679, 3446])).
% 2.47/2.02 tff(4862,plain,
% 2.47/2.02 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[3689, 4861, 1663, 3678])).
% 2.47/2.02 tff(4863,plain,
% 2.47/2.02 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[3694, 4862])).
% 2.47/2.02 tff(4864,plain,
% 2.47/2.02 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[3701, 4861, 4862])).
% 2.47/2.02 tff(4865,assumption,(big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))), introduced(assumption)).
% 2.47/2.02 tff(4866,assumption,(tptp_fun_Y_4(Y!0, X!1) = X!1), introduced(assumption)).
% 2.47/2.02 tff(4867,plain,
% 2.47/2.02 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.47/2.02 inference(symmetry,[status(thm)],[1972])).
% 2.47/2.02 tff(4868,plain,
% 2.47/2.02 (tptp_fun_X_2(X!1) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.47/2.02 inference(transitivity,[status(thm)],[1663, 1789, 4867])).
% 2.47/2.02 tff(4869,plain,
% 2.47/2.02 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4868, 4866])).
% 2.47/2.02 tff(4870,plain,
% 2.47/2.02 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4869])).
% 2.47/2.02 tff(4871,plain,
% 2.47/2.02 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4870])).
% 2.47/2.02 tff(4872,plain,
% 2.47/2.02 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[1970, 4871])).
% 2.47/2.02 tff(4873,plain,
% 2.47/2.02 ($false),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[4865, 4872])).
% 2.47/2.02 tff(4874,plain,(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.02 tff(4875,plain,
% 2.47/2.02 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[4874, 1969, 4866, 1663, 1672, 4865])).
% 2.47/2.02 tff(4876,plain,
% 2.47/2.02 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[1980, 4875, 1969])).
% 2.47/2.02 tff(4877,plain,
% 2.47/2.02 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[1789])).
% 2.47/2.02 tff(4878,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4877])).
% 2.47/2.02 tff(4879,plain,
% 2.47/2.02 (tptp_fun_Z1_12(Y!0) = tptp_fun_X_2(Y!0)),
% 2.47/2.02 inference(transitivity,[status(thm)],[1185, 31])).
% 2.47/2.02 tff(4880,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4879])).
% 2.47/2.02 tff(4881,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4880])).
% 2.47/2.02 tff(4882,plain,
% 2.47/2.02 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X_2(X!1)),
% 2.47/2.02 inference(transitivity,[status(thm)],[1672, 1664])).
% 2.47/2.02 tff(4883,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4882, 30])).
% 2.47/2.02 tff(4884,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4883])).
% 2.47/2.02 tff(4885,plain,
% 2.47/2.02 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(transitivity,[status(thm)],[1671, 4884, 4881, 4878])).
% 2.47/2.02 tff(4886,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4885, 1664])).
% 2.47/2.02 tff(4887,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.47/2.02 inference(symmetry,[status(thm)],[4886])).
% 2.47/2.02 tff(4888,plain,
% 2.47/2.02 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4887, 1789])).
% 2.47/2.02 tff(4889,plain,
% 2.47/2.02 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1)),
% 2.47/2.02 inference(symmetry,[status(thm)],[4888])).
% 2.47/2.02 tff(4890,plain,
% 2.47/2.02 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4889])).
% 2.47/2.02 tff(4891,assumption,(~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))), introduced(assumption)).
% 2.47/2.02 tff(4892,plain,
% 2.47/2.02 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1)),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[4891, 4890])).
% 2.47/2.02 tff(4893,plain,
% 2.47/2.02 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0))),
% 2.47/2.02 inference(rewrite,[status(thm)],[])).
% 2.47/2.02 tff(4894,plain,
% 2.47/2.02 (((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1)) <=> ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0))),
% 2.47/2.02 inference(rewrite,[status(thm)],[])).
% 2.47/2.02 tff(4895,plain,
% 2.47/2.02 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0)))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4894])).
% 2.47/2.02 tff(4896,plain,
% 2.47/2.02 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0))),
% 2.47/2.02 inference(transitivity,[status(thm)],[4895, 4893])).
% 2.47/2.02 tff(4897,plain,
% 2.47/2.02 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1))),
% 2.47/2.02 inference(quant_inst,[status(thm)],[])).
% 2.47/2.02 tff(4898,plain,
% 2.47/2.02 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0)),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[4897, 4896])).
% 2.47/2.02 tff(4899,plain,
% 2.47/2.02 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0)),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[4898, 12])).
% 2.47/2.02 tff(4900,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[4899, 4892])).
% 2.47/2.02 tff(4901,plain,
% 2.47/2.02 (Y!0 = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4900])).
% 2.47/2.02 tff(4902,plain,
% 2.47/2.02 (tptp_fun_X_2(Y!0) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.47/2.02 inference(transitivity,[status(thm)],[30, 4901, 4887])).
% 2.47/2.02 tff(4903,plain,
% 2.47/2.02 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4902, 254])).
% 2.47/2.02 tff(4904,plain,
% 2.47/2.02 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4903])).
% 2.47/2.02 tff(4905,assumption,(big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)), introduced(assumption)).
% 2.47/2.02 tff(4906,plain,
% 2.47/2.02 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[4905, 4904])).
% 2.47/2.02 tff(4907,plain,
% 2.47/2.02 ($false),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[262, 4906])).
% 2.47/2.02 tff(4908,plain,((~(tptp_fun_Z1_12(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) | (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) | (~(tptp_fun_Y_4(X!1, Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.02 tff(4909,plain,
% 2.47/2.02 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[4908, 4875, 262, 254, 30, 1663, 1672, 4876])).
% 2.47/2.02 tff(4910,plain,
% 2.47/2.02 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[594, 4909])).
% 2.47/2.02 tff(4911,plain,
% 2.47/2.02 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.47/2.02 inference(symmetry,[status(thm)],[4910])).
% 2.47/2.02 tff(4912,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4911])).
% 2.47/2.02 tff(4913,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.47/2.02 inference(symmetry,[status(thm)],[4912])).
% 2.47/2.02 tff(4914,plain,
% 2.47/2.02 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[1672])).
% 2.47/2.02 tff(4915,plain,
% 2.47/2.02 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4914])).
% 2.47/2.02 tff(4916,plain,
% 2.47/2.02 ((tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4915, 1789])).
% 2.47/2.02 tff(4917,plain,
% 2.47/2.02 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.47/2.02 inference(symmetry,[status(thm)],[4916])).
% 2.47/2.02 tff(4918,plain,
% 2.47/2.02 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4913])).
% 2.47/2.02 tff(4919,plain,
% 2.47/2.02 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4918])).
% 2.47/2.02 tff(4920,plain,
% 2.47/2.02 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.47/2.02 inference(transitivity,[status(thm)],[4919, 4917])).
% 2.47/2.02 tff(4921,plain,
% 2.47/2.02 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)))) <=> (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1))),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4920])).
% 2.47/2.02 tff(4922,plain,
% 2.47/2.02 (~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[4876, 4921])).
% 2.47/2.02 tff(4923,plain,
% 2.47/2.02 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = Y!0),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[822, 4922])).
% 2.47/2.02 tff(4924,plain,
% 2.47/2.02 (Y!0 = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4923])).
% 2.47/2.02 tff(4925,plain,
% 2.47/2.02 (tptp_fun_X_2(Y!0) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1)),
% 2.47/2.02 inference(transitivity,[status(thm)],[30, 4924, 4915, 4913])).
% 2.47/2.02 tff(4926,plain,
% 2.47/2.02 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)),
% 2.47/2.02 inference(monotonicity,[status(thm)],[4925, 254])).
% 2.47/2.02 tff(4927,plain,
% 2.47/2.02 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.47/2.02 inference(symmetry,[status(thm)],[4926])).
% 2.47/2.02 tff(4928,plain,
% 2.47/2.02 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.47/2.02 inference(modus_ponens,[status(thm)],[4875, 4927])).
% 2.47/2.02 tff(4929,plain,
% 2.47/2.02 ($false),
% 2.47/2.02 inference(unit_resolution,[status(thm)],[262, 4928])).
% 2.47/2.02 tff(4930,plain,((~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))) | big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) | (~(tptp_fun_Y_4(X!1, Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.03 tff(4931,plain,
% 2.47/2.03 (~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4930, 2493, 1445, 30, 1672, 1663, 4863, 4864])).
% 2.47/2.03 tff(4932,plain,
% 2.47/2.03 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[1996, 4931])).
% 2.47/2.03 tff(4933,assumption,(~(tptp_fun_Y_4(Y!0, X!1) = Y!0)), introduced(assumption)).
% 2.47/2.03 tff(4934,plain,
% 2.47/2.03 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[3694, 4933])).
% 2.47/2.03 tff(4935,plain,
% 2.47/2.03 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[3701, 4933, 3685])).
% 2.47/2.03 tff(4936,plain,
% 2.47/2.03 (X!1 = tptp_fun_Y_4(Y!0, X!1)),
% 2.47/2.03 inference(symmetry,[status(thm)],[4866])).
% 2.47/2.03 tff(4937,plain,
% 2.47/2.03 (tptp_fun_Y_4(X!1, X!1) = tptp_fun_Y_4(Y!0, X!1)),
% 2.47/2.03 inference(transitivity,[status(thm)],[2188, 4936])).
% 2.47/2.03 tff(4938,plain,
% 2.47/2.03 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.47/2.03 inference(monotonicity,[status(thm)],[4937])).
% 2.47/2.03 tff(4939,plain,
% 2.47/2.03 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.47/2.03 inference(symmetry,[status(thm)],[4938])).
% 2.47/2.03 tff(4940,plain,
% 2.47/2.03 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.47/2.03 inference(modus_ponens,[status(thm)],[4865, 4939])).
% 2.47/2.03 tff(4941,plain,
% 2.47/2.03 ($false),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[1702, 4940])).
% 2.47/2.03 tff(4942,plain,(big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.03 tff(4943,plain,
% 2.47/2.03 ($false),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4942, 4935, 4934, 1702, 1675])).
% 2.47/2.03 tff(4944,plain,((tptp_fun_Y_4(Y!0, X!1) = Y!0) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1))) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.03 tff(4945,plain,
% 2.47/2.03 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4944, 4861, 4862, 3447])).
% 2.47/2.03 tff(4946,plain,
% 2.47/2.03 (~(tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[1677, 4945, 3447])).
% 2.47/2.03 tff(4947,plain,
% 2.47/2.03 (tptp_fun_Y_4(X!1, X!1) = Y!0),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[1685, 4946])).
% 2.47/2.03 tff(4948,plain,
% 2.47/2.03 (tptp_fun_Y_4(X!1, X!1) = tptp_fun_X_2(Y!0)),
% 2.47/2.03 inference(transitivity,[status(thm)],[4947, 31])).
% 2.47/2.03 tff(4949,plain,
% 2.47/2.03 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.47/2.03 inference(monotonicity,[status(thm)],[4813, 4948])).
% 2.47/2.03 tff(4950,plain,
% 2.47/2.03 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.47/2.03 inference(transitivity,[status(thm)],[4949, 4883])).
% 2.47/2.03 tff(4951,plain,
% 2.47/2.03 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.47/2.03 inference(monotonicity,[status(thm)],[4950, 4947])).
% 2.47/2.03 tff(4952,plain,
% 2.47/2.03 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))),
% 2.47/2.03 inference(symmetry,[status(thm)],[4951])).
% 2.47/2.03 tff(4953,plain,
% 2.47/2.03 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))),
% 2.47/2.03 inference(modus_ponens,[status(thm)],[4795, 4952])).
% 2.47/2.03 tff(4954,plain,
% 2.47/2.03 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.47/2.03 inference(symmetry,[status(thm)],[1671])).
% 2.47/2.03 tff(4955,plain,
% 2.47/2.03 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)),
% 2.47/2.03 inference(transitivity,[status(thm)],[4949, 4883, 4954, 1672, 1664])).
% 2.47/2.03 tff(4956,plain,
% 2.47/2.03 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)))) | (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) | (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)))),
% 2.47/2.03 inference(tautology,[status(thm)],[])).
% 2.47/2.03 tff(4957,plain,
% 2.47/2.03 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4956, 4955, 4953])).
% 2.47/2.03 tff(4958,plain,
% 2.47/2.03 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1))) | ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)))),
% 2.47/2.03 inference(quant_inst,[status(thm)],[])).
% 2.47/2.03 tff(4959,plain,
% 2.47/2.03 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4958, 4957])).
% 2.47/2.03 tff(4960,assumption,(~(tptp_fun_Y_4(X!1, X!1) = X!1)), introduced(assumption)).
% 2.47/2.03 tff(4961,assumption,(~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1))), introduced(assumption)).
% 2.47/2.03 tff(4962,plain,
% 2.47/2.03 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(X!1, X!1))))))))),
% 2.47/2.03 inference(quant_inst,[status(thm)],[])).
% 2.47/2.03 tff(4963,plain,
% 2.47/2.03 (~((~((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(X!1, X!1)))))))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4962, 1268])).
% 2.47/2.03 tff(4964,plain,
% 2.47/2.03 (((~((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(X!1, X!1))))))) | ((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1)))),
% 2.47/2.03 inference(tautology,[status(thm)],[])).
% 2.47/2.03 tff(4965,plain,
% 2.47/2.03 ((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4964, 4963])).
% 2.47/2.03 tff(4966,plain,
% 2.47/2.03 ((~((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1)))) | (tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1))),
% 2.47/2.03 inference(tautology,[status(thm)],[])).
% 2.47/2.03 tff(4967,plain,
% 2.47/2.03 (tptp_fun_Y_4(X!1, X!1) = W1!8),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4966, 4965, 4961])).
% 2.47/2.03 tff(4968,plain,
% 2.47/2.03 ((tptp_fun_Y_4(X!1, X!1) = W1!8) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.47/2.03 inference(monotonicity,[status(thm)],[1289])).
% 2.47/2.03 tff(4969,assumption,(tptp_fun_Y_4(X!1, X!1) = W1!8), introduced(assumption)).
% 2.47/2.03 tff(4970,plain,
% 2.47/2.03 (tptp_fun_Y_4(X!1, X!1) = X!1),
% 2.47/2.03 inference(modus_ponens,[status(thm)],[4969, 4968])).
% 2.47/2.03 tff(4971,plain,
% 2.47/2.03 ($false),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4960, 4970])).
% 2.47/2.03 tff(4972,plain,((~(tptp_fun_Y_4(X!1, X!1) = W1!8)) | (tptp_fun_Y_4(X!1, X!1) = X!1) | (~(W1!8 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.03 tff(4973,plain,
% 2.47/2.03 ($false),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4972, 1275, 4967, 4960])).
% 2.47/2.03 tff(4974,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (tptp_fun_Y_4(X!1, X!1) = X!1) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))), inference(lemma,lemma(discharge,[]))).
% 2.47/2.03 tff(4975,plain,
% 2.47/2.03 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4974, 4946, 4959, 4932])).
% 2.47/2.03 tff(4976,plain,
% 2.47/2.03 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[462, 4975])).
% 2.47/2.03 tff(4977,plain,
% 2.47/2.03 ((tptp_fun_Y_4(X!1, Y!0) = Z!5) <=> (X!1 = Z!5)),
% 2.47/2.03 inference(monotonicity,[status(thm)],[254])).
% 2.47/2.03 tff(4978,plain,
% 2.47/2.03 ((X!1 = Z!5) <=> (tptp_fun_Y_4(X!1, Y!0) = Z!5)),
% 2.47/2.03 inference(symmetry,[status(thm)],[4977])).
% 2.47/2.03 tff(4979,plain,
% 2.47/2.03 (tptp_fun_Y_4(X!1, Y!0) = Z!5),
% 2.47/2.03 inference(modus_ponens,[status(thm)],[3548, 4978])).
% 2.47/2.03 tff(4980,plain,
% 2.47/2.03 ((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~((~((tptp_fun_Y_4(X!1, Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_Y_7(W, tptp_fun_Y_4(X!1, Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y_4(X!1, Y!0)) = W)))) | (~((~(tptp_fun_Y_4(X!1, Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))))))),
% 2.47/2.03 inference(quant_inst,[status(thm)],[])).
% 2.47/2.03 tff(4981,plain,
% 2.47/2.03 (~((~((tptp_fun_Y_4(X!1, Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_Y_7(W, tptp_fun_Y_4(X!1, Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y_4(X!1, Y!0)) = W)))) | (~((~(tptp_fun_Y_4(X!1, Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)))))))),
% 2.47/2.03 inference(unit_resolution,[status(thm)],[4980, 341])).
% 2.47/2.03 tff(4982,plain,
% 2.47/2.03 (((~((tptp_fun_Y_4(X!1, Y!0) = Z!5) | ![W: $i] : ((~big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_Y_7(W, tptp_fun_Y_4(X!1, Y!0)))) <=> (tptp_fun_Y_7(W, tptp_fun_Y_4(X!1, Y!0)) = W)))) | (~((~(tptp_fun_Y_4(X!1, Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))))) | ((~(tptp_fun_Y_4(X!1, Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)))))),
% 2.47/2.03 inference(tautology,[status(thm)],[])).
% 2.47/2.03 tff(4983,plain,
% 2.47/2.03 ((~(tptp_fun_Y_4(X!1, Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[4982, 4981])).
% 2.53/2.04 tff(4984,plain,
% 2.53/2.04 ((~((~(tptp_fun_Y_4(X!1, Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)))))) | (~(tptp_fun_Y_4(X!1, Y!0) = Z!5)) | ![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))),
% 2.53/2.04 inference(tautology,[status(thm)],[])).
% 2.53/2.04 tff(4985,plain,
% 2.53/2.04 (![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[4984, 4983, 4979])).
% 2.53/2.04 tff(4986,plain,
% 2.53/2.04 ((~![Y: $i] : (big_f(tptp_fun_Y_4(X!1, Y!0), Y) <=> (Y = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))) | (big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))),
% 2.53/2.04 inference(quant_inst,[status(thm)],[])).
% 2.53/2.04 tff(4987,plain,
% 2.53/2.04 (big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[4986, 4985])).
% 2.53/2.04 tff(4988,plain,
% 2.53/2.04 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_Y_4(Y!0, X!1)),
% 2.53/2.04 inference(transitivity,[status(thm)],[4954, 1672, 4936])).
% 2.53/2.04 tff(4989,plain,
% 2.53/2.04 (tptp_fun_Y_4(X!1, Y!0) = tptp_fun_X_2(X!1)),
% 2.53/2.04 inference(transitivity,[status(thm)],[254, 1664])).
% 2.53/2.04 tff(4990,plain,
% 2.53/2.04 (big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[4989, 4988])).
% 2.53/2.04 tff(4991,plain,
% 2.53/2.04 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.04 inference(symmetry,[status(thm)],[4990])).
% 2.53/2.04 tff(4992,plain,
% 2.53/2.04 (big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[4865, 4991])).
% 2.53/2.04 tff(4993,plain,
% 2.53/2.04 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[346, 345, 3548])).
% 2.53/2.04 tff(4994,plain,
% 2.53/2.04 (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[321, 4993])).
% 2.53/2.04 tff(4995,plain,
% 2.53/2.04 (Y!0 = tptp_fun_W_6(X!1)),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[3751, 4994, 3678])).
% 2.53/2.04 tff(4996,plain,
% 2.53/2.04 (tptp_fun_W_6(X!1) = Y!0),
% 2.53/2.04 inference(symmetry,[status(thm)],[4995])).
% 2.53/2.04 tff(4997,plain,
% 2.53/2.04 (tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)) = tptp_fun_W_6(X!1)),
% 2.53/2.04 inference(monotonicity,[status(thm)],[254])).
% 2.53/2.04 tff(4998,plain,
% 2.53/2.04 (tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)) = Y!0),
% 2.53/2.04 inference(transitivity,[status(thm)],[4997, 4996])).
% 2.53/2.04 tff(4999,plain,
% 2.53/2.04 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.53/2.04 inference(monotonicity,[status(thm)],[4998])).
% 2.53/2.04 tff(5000,plain,
% 2.53/2.04 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)))),
% 2.53/2.04 inference(symmetry,[status(thm)],[4999])).
% 2.53/2.04 tff(5001,plain,
% 2.53/2.04 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5000])).
% 2.53/2.04 tff(5002,plain,
% 2.53/2.04 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1),
% 2.53/2.04 inference(transitivity,[status(thm)],[4954, 1672])).
% 2.53/2.04 tff(5003,plain,
% 2.53/2.04 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) <=> (X!1 = Y!0)),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5002])).
% 2.53/2.04 tff(5004,plain,
% 2.53/2.04 ((X!1 = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.53/2.04 inference(symmetry,[status(thm)],[5003])).
% 2.53/2.04 tff(5005,plain,
% 2.53/2.04 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5004])).
% 2.53/2.04 tff(5006,plain,
% 2.53/2.04 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[741, 5005])).
% 2.53/2.04 tff(5007,plain,
% 2.53/2.04 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)))),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[5006, 5001])).
% 2.53/2.04 tff(5008,plain,
% 2.53/2.04 ((~(big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0))))) | (~big_f(tptp_fun_Y_4(X!1, Y!0), tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(tptp_fun_Y_4(X!1, Y!0)))),
% 2.53/2.04 inference(tautology,[status(thm)],[])).
% 2.53/2.04 tff(5009,plain,
% 2.53/2.04 ($false),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5008, 5007, 4992, 4987])).
% 2.53/2.04 tff(5010,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_Y_4(X!1, Y!0) = X!1)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(X!1, Y!0)) | (~(X!1 = Z!5))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.04 tff(5011,plain,
% 2.53/2.04 (~(X!1 = Z!5)),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5010, 4976, 4864, 4863, 1672, 30, 1663, 3678, 1445])).
% 2.53/2.04 tff(5012,plain,
% 2.53/2.04 (~(Z!5 = X!1)),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[353, 5011])).
% 2.53/2.04 tff(5013,plain,
% 2.53/2.04 (Z!5 = Y!0),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[361, 5012])).
% 2.53/2.04 tff(5014,plain,
% 2.53/2.04 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5013])).
% 2.53/2.04 tff(5015,plain,
% 2.53/2.04 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5014])).
% 2.53/2.04 tff(5016,plain,
% 2.53/2.04 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.53/2.04 inference(transitivity,[status(thm)],[5015, 339])).
% 2.53/2.04 tff(5017,plain,
% 2.53/2.04 ((~(Y!0 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5016])).
% 2.53/2.04 tff(5018,plain,
% 2.53/2.04 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[385, 4976])).
% 2.53/2.04 tff(5019,plain,
% 2.53/2.04 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[387, 5018])).
% 2.53/2.04 tff(5020,plain,
% 2.53/2.04 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.53/2.04 inference(transitivity,[status(thm)],[5013, 31])).
% 2.53/2.04 tff(5021,plain,
% 2.53/2.04 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5020])).
% 2.53/2.04 tff(5022,plain,
% 2.53/2.04 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.53/2.04 inference(symmetry,[status(thm)],[5021])).
% 2.53/2.04 tff(5023,plain,
% 2.53/2.04 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Z!5, Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5022])).
% 2.53/2.04 tff(5024,plain,
% 2.53/2.04 (~big_f(Z!5, Y!0)),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[35, 5023])).
% 2.53/2.04 tff(5025,plain,
% 2.53/2.04 (~(Y!0 = tptp_fun_W_6(Z!5))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[394, 5024, 5019])).
% 2.53/2.04 tff(5026,plain,
% 2.53/2.04 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[5025, 5017])).
% 2.53/2.04 tff(5027,plain,
% 2.53/2.04 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5002, 5014])).
% 2.53/2.04 tff(5028,plain,
% 2.53/2.04 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.53/2.04 inference(transitivity,[status(thm)],[5027, 1537])).
% 2.53/2.04 tff(5029,plain,
% 2.53/2.04 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5028])).
% 2.53/2.04 tff(5030,plain,
% 2.53/2.04 ((~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))) | (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)))),
% 2.53/2.04 inference(quant_inst,[status(thm)],[])).
% 2.53/2.04 tff(5031,plain,
% 2.53/2.04 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5030, 5018])).
% 2.53/2.04 tff(5032,plain,
% 2.53/2.04 (X!1 = tptp_fun_Y_4(X!1, Y!0)),
% 2.53/2.04 inference(symmetry,[status(thm)],[1445])).
% 2.53/2.04 tff(5033,plain,
% 2.53/2.04 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_Y_4(X!1, Y!0)),
% 2.53/2.04 inference(transitivity,[status(thm)],[4954, 1672, 5032])).
% 2.53/2.04 tff(5034,plain,
% 2.53/2.04 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5020, 5033])).
% 2.53/2.04 tff(5035,plain,
% 2.53/2.04 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.04 inference(symmetry,[status(thm)],[5034])).
% 2.53/2.04 tff(5036,plain,
% 2.53/2.04 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (~big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5035])).
% 2.53/2.04 tff(5037,plain,
% 2.53/2.04 (~big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[2493, 5036])).
% 2.53/2.04 tff(5038,plain,
% 2.53/2.04 ((~(big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)))) | big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) | (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)))),
% 2.53/2.04 inference(tautology,[status(thm)],[])).
% 2.53/2.04 tff(5039,plain,
% 2.53/2.04 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5038, 5037, 5031])).
% 2.53/2.04 tff(5040,plain,
% 2.53/2.04 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[5039, 5029])).
% 2.53/2.04 tff(5041,plain,
% 2.53/2.04 ($false),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[403, 5040, 5026])).
% 2.53/2.04 tff(5042,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~big_f(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.04 tff(5043,plain,
% 2.53/2.04 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5042, 1672, 30, 1663, 35, 3678])).
% 2.53/2.04 tff(5044,plain,
% 2.53/2.04 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[82, 5043])).
% 2.53/2.04 tff(5045,plain,
% 2.53/2.04 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[84, 5044])).
% 2.53/2.04 tff(5046,plain,
% 2.53/2.04 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[561, 5045])).
% 2.53/2.04 tff(5047,plain,
% 2.53/2.04 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[86, 5045])).
% 2.53/2.04 tff(5048,plain,
% 2.53/2.04 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[3717, 5047, 30, 3678, 35])).
% 2.53/2.04 tff(5049,plain,
% 2.53/2.04 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[563, 5048, 5046])).
% 2.53/2.04 tff(5050,plain,
% 2.53/2.04 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[1194, 5049, 4860])).
% 2.53/2.04 tff(5051,plain,
% 2.53/2.04 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[39, 5048])).
% 2.53/2.04 tff(5052,plain,
% 2.53/2.04 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[576, 5049])).
% 2.53/2.04 tff(5053,plain,
% 2.53/2.04 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[751, 5052, 4860])).
% 2.53/2.04 tff(5054,plain,
% 2.53/2.04 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[1191, 5053])).
% 2.53/2.04 tff(5055,plain,
% 2.53/2.04 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[594, 5054])).
% 2.53/2.04 tff(5056,plain,
% 2.53/2.04 (~((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1), X!1)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), X!1) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[1994, 5055, 4860, 1672, 5051, 5050])).
% 2.53/2.04 tff(5057,plain,
% 2.53/2.04 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[1996, 5056])).
% 2.53/2.04 tff(5058,plain,
% 2.53/2.04 (W1!8 = tptp_fun_Y1_11(X!1)),
% 2.53/2.04 inference(symmetry,[status(thm)],[1280])).
% 2.53/2.04 tff(5059,plain,
% 2.53/2.04 (X!1 = W1!8),
% 2.53/2.04 inference(symmetry,[status(thm)],[1275])).
% 2.53/2.04 tff(5060,plain,
% 2.53/2.04 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0),
% 2.53/2.04 inference(transitivity,[status(thm)],[4954, 1672, 5059, 5058, 796])).
% 2.53/2.04 tff(5061,plain,
% 2.53/2.04 ($false),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5006, 5060])).
% 2.53/2.04 tff(5062,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.04 tff(5063,plain,
% 2.53/2.04 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5062, 1672, 796, 30, 1663, 5057, 4794])).
% 2.53/2.04 tff(5064,plain,
% 2.53/2.04 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[462, 5063])).
% 2.53/2.04 tff(5065,plain,
% 2.53/2.04 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[385, 5064])).
% 2.53/2.04 tff(5066,plain,
% 2.53/2.04 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[5030, 5065])).
% 2.53/2.04 tff(5067,plain,
% 2.53/2.04 (X!1 = tptp_fun_Y1_11(Y!0)),
% 2.53/2.04 inference(symmetry,[status(thm)],[5051])).
% 2.53/2.04 tff(5068,plain,
% 2.53/2.04 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.53/2.04 inference(transitivity,[status(thm)],[4954, 1672, 5067])).
% 2.53/2.04 tff(5069,plain,
% 2.53/2.04 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[3829])).
% 2.53/2.04 tff(5070,plain,
% 2.53/2.04 ((Y!0 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.53/2.04 inference(transitivity,[status(thm)],[5069, 339])).
% 2.53/2.04 tff(5071,plain,
% 2.53/2.04 ((~(Y!0 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5070])).
% 2.53/2.04 tff(5072,plain,
% 2.53/2.04 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[387, 982])).
% 2.53/2.04 tff(5073,plain,
% 2.53/2.04 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.53/2.04 inference(transitivity,[status(thm)],[412, 31])).
% 2.53/2.04 tff(5074,plain,
% 2.53/2.04 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5073])).
% 2.53/2.04 tff(5075,plain,
% 2.53/2.04 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.53/2.04 inference(symmetry,[status(thm)],[5074])).
% 2.53/2.04 tff(5076,plain,
% 2.53/2.04 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Z!5, Y!0))),
% 2.53/2.04 inference(monotonicity,[status(thm)],[5075])).
% 2.53/2.04 tff(5077,plain,
% 2.53/2.04 (~big_f(Z!5, Y!0)),
% 2.53/2.04 inference(modus_ponens,[status(thm)],[35, 5076])).
% 2.53/2.04 tff(5078,plain,
% 2.53/2.04 (~(Y!0 = tptp_fun_W_6(Z!5))),
% 2.53/2.04 inference(unit_resolution,[status(thm)],[394, 5077, 5072])).
% 2.53/2.04 tff(5079,plain,
% 2.53/2.04 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[5078, 5071])).
% 2.53/2.05 tff(5080,plain,
% 2.53/2.05 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5002, 3829])).
% 2.53/2.05 tff(5081,plain,
% 2.53/2.05 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.53/2.05 inference(transitivity,[status(thm)],[5080, 1537])).
% 2.53/2.05 tff(5082,plain,
% 2.53/2.05 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5081])).
% 2.53/2.05 tff(5083,plain,
% 2.53/2.05 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5030, 982])).
% 2.53/2.05 tff(5084,plain,
% 2.53/2.05 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.53/2.05 inference(transitivity,[status(thm)],[4954, 1672, 599])).
% 2.53/2.05 tff(5085,plain,
% 2.53/2.05 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[412, 5084])).
% 2.53/2.05 tff(5086,plain,
% 2.53/2.05 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.05 inference(symmetry,[status(thm)],[5085])).
% 2.53/2.05 tff(5087,plain,
% 2.53/2.05 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5086])).
% 2.53/2.05 tff(5088,plain,
% 2.53/2.05 (~big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[41, 5087])).
% 2.53/2.05 tff(5089,plain,
% 2.53/2.05 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5038, 5088, 5083])).
% 2.53/2.05 tff(5090,plain,
% 2.53/2.05 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[5089, 5082])).
% 2.53/2.05 tff(5091,plain,
% 2.53/2.05 ($false),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[403, 5090, 5079])).
% 2.53/2.05 tff(5092,plain,((~(Z!5 = Y!0)) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.05 tff(5093,plain,
% 2.53/2.05 (~(Z!5 = Y!0)),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5092, 1672, 30, 1663, 5050, 5051, 35, 5065])).
% 2.53/2.05 tff(5094,plain,
% 2.53/2.05 (Z!5 = X!1),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[361, 5093])).
% 2.53/2.05 tff(5095,plain,
% 2.53/2.05 (Z!5 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.53/2.05 inference(transitivity,[status(thm)],[5094, 1789])).
% 2.53/2.05 tff(5096,plain,
% 2.53/2.05 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5095, 5068])).
% 2.53/2.05 tff(5097,plain,
% 2.53/2.05 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.05 inference(symmetry,[status(thm)],[5096])).
% 2.53/2.05 tff(5098,plain,
% 2.53/2.05 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[4860, 4796])).
% 2.53/2.05 tff(5099,plain,
% 2.53/2.05 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[5098, 5097])).
% 2.53/2.05 tff(5100,plain,
% 2.53/2.05 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[342, 5064])).
% 2.53/2.05 tff(5101,plain,
% 2.53/2.05 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[344, 5100])).
% 2.53/2.05 tff(5102,plain,
% 2.53/2.05 (X!1 = Z!5),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[353, 5094])).
% 2.53/2.05 tff(5103,plain,
% 2.53/2.05 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[346, 5102, 5101])).
% 2.53/2.05 tff(5104,plain,
% 2.53/2.05 (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[321, 5103])).
% 2.53/2.05 tff(5105,plain,
% 2.53/2.05 (Y!0 = tptp_fun_W_6(X!1)),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[3751, 5104, 3678])).
% 2.53/2.05 tff(5106,plain,
% 2.53/2.05 (tptp_fun_W_6(X!1) = Y!0),
% 2.53/2.05 inference(symmetry,[status(thm)],[5105])).
% 2.53/2.05 tff(5107,plain,
% 2.53/2.05 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(X!1)),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5094])).
% 2.53/2.05 tff(5108,plain,
% 2.53/2.05 (tptp_fun_W_6(Z!5) = Y!0),
% 2.53/2.05 inference(transitivity,[status(thm)],[5107, 5106])).
% 2.53/2.05 tff(5109,plain,
% 2.53/2.05 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5108])).
% 2.53/2.05 tff(5110,plain,
% 2.53/2.05 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.05 inference(symmetry,[status(thm)],[5109])).
% 2.53/2.05 tff(5111,plain,
% 2.53/2.05 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0)) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5110])).
% 2.53/2.05 tff(5112,plain,
% 2.53/2.05 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[5006, 5111])).
% 2.53/2.05 tff(5113,plain,
% 2.53/2.05 ((~(big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)))) | (~big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.53/2.05 inference(tautology,[status(thm)],[])).
% 2.53/2.05 tff(5114,plain,
% 2.53/2.05 ($false),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5113, 5112, 5099, 5066])).
% 2.53/2.05 tff(5115,plain,((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(X!1, Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_Y1_11(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.05 tff(5116,plain,
% 2.53/2.05 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5115, 35, 1663, 30, 3678, 796])).
% 2.53/2.05 tff(5117,plain,
% 2.53/2.05 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[2258, 5116])).
% 2.53/2.05 tff(5118,plain,
% 2.53/2.05 ((~(X!1 = tptp_fun_W_6(Y!0))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[1537])).
% 2.53/2.05 tff(5119,plain,
% 2.53/2.05 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[3701, 4862, 4861])).
% 2.53/2.05 tff(5120,plain,
% 2.53/2.05 (Z!5 = X!1),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[361, 439])).
% 2.53/2.05 tff(5121,plain,
% 2.53/2.05 (Z!5 = tptp_fun_X_2(X!1)),
% 2.53/2.05 inference(transitivity,[status(thm)],[5120, 1664])).
% 2.53/2.05 tff(5122,plain,
% 2.53/2.05 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5121, 4936])).
% 2.53/2.05 tff(5123,plain,
% 2.53/2.05 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(Z!5, X!1)),
% 2.53/2.05 inference(symmetry,[status(thm)],[5122])).
% 2.53/2.05 tff(5124,plain,
% 2.53/2.05 (big_f(Z!5, X!1)),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[4865, 5123])).
% 2.53/2.05 tff(5125,plain,
% 2.53/2.05 (X!1 = Z!5),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[353, 5120])).
% 2.53/2.05 tff(5126,plain,
% 2.53/2.05 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[346, 5125, 345])).
% 2.53/2.05 tff(5127,plain,
% 2.53/2.05 (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[321, 5126])).
% 2.53/2.05 tff(5128,plain,
% 2.53/2.05 (Y!0 = tptp_fun_W_6(X!1)),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[3751, 5127, 3678])).
% 2.53/2.05 tff(5129,plain,
% 2.53/2.05 (tptp_fun_W_6(X!1) = Y!0),
% 2.53/2.05 inference(symmetry,[status(thm)],[5128])).
% 2.53/2.05 tff(5130,plain,
% 2.53/2.05 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(X!1)),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5120])).
% 2.53/2.05 tff(5131,plain,
% 2.53/2.05 (tptp_fun_W_6(Z!5) = Y!0),
% 2.53/2.05 inference(transitivity,[status(thm)],[5130, 5129])).
% 2.53/2.05 tff(5132,plain,
% 2.53/2.05 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = Y!0)),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5131])).
% 2.53/2.05 tff(5133,plain,
% 2.53/2.05 ((X!1 = Y!0) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.53/2.05 inference(symmetry,[status(thm)],[5132])).
% 2.53/2.05 tff(5134,plain,
% 2.53/2.05 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_W_6(Z!5)))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5133])).
% 2.53/2.05 tff(5135,plain,
% 2.53/2.05 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[741, 5134])).
% 2.53/2.05 tff(5136,plain,
% 2.53/2.05 ($false),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[989, 5135, 5124, 1212])).
% 2.53/2.05 tff(5137,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(X!1, Y!0)) | ![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.05 tff(5138,plain,
% 2.53/2.05 (![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5137, 4863, 3678, 1663, 5119, 341])).
% 2.53/2.05 tff(5139,plain,
% 2.53/2.05 ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | (big_f(Y!0, X!1) <=> (X!1 = tptp_fun_W_6(Y!0)))),
% 2.53/2.05 inference(quant_inst,[status(thm)],[])).
% 2.53/2.05 tff(5140,plain,
% 2.53/2.05 (big_f(Y!0, X!1) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5139, 5138])).
% 2.53/2.05 tff(5141,plain,
% 2.53/2.05 (big_f(Y!0, X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[31, 5032])).
% 2.53/2.05 tff(5142,plain,
% 2.53/2.05 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Y!0, X!1)),
% 2.53/2.05 inference(symmetry,[status(thm)],[5141])).
% 2.53/2.05 tff(5143,plain,
% 2.53/2.05 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (~big_f(Y!0, X!1))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5142])).
% 2.53/2.05 tff(5144,plain,
% 2.53/2.05 (~big_f(Y!0, X!1)),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[2493, 5143])).
% 2.53/2.05 tff(5145,plain,
% 2.53/2.05 ((~(big_f(Y!0, X!1) <=> (X!1 = tptp_fun_W_6(Y!0)))) | big_f(Y!0, X!1) | (~(X!1 = tptp_fun_W_6(Y!0)))),
% 2.53/2.05 inference(tautology,[status(thm)],[])).
% 2.53/2.05 tff(5146,plain,
% 2.53/2.05 (~(X!1 = tptp_fun_W_6(Y!0))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5145, 5144, 5140])).
% 2.53/2.05 tff(5147,plain,
% 2.53/2.05 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[5146, 5118])).
% 2.53/2.05 tff(5148,plain,
% 2.53/2.05 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0),
% 2.53/2.05 inference(transitivity,[status(thm)],[4954, 3022])).
% 2.53/2.05 tff(5149,plain,
% 2.53/2.05 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5148])).
% 2.53/2.05 tff(5150,plain,
% 2.53/2.05 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.53/2.05 inference(transitivity,[status(thm)],[5149, 339])).
% 2.53/2.05 tff(5151,plain,
% 2.53/2.05 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5150])).
% 2.53/2.05 tff(5152,plain,
% 2.53/2.05 ((~![Y: $i] : (big_f(Y!0, Y) <=> (Y = tptp_fun_W_6(Y!0)))) | (big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0)))),
% 2.53/2.05 inference(quant_inst,[status(thm)],[])).
% 2.53/2.05 tff(5153,plain,
% 2.53/2.05 (big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5152, 5138])).
% 2.53/2.05 tff(5154,plain,
% 2.53/2.05 (big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.53/2.05 inference(monotonicity,[status(thm)],[31, 5148])).
% 2.53/2.05 tff(5155,plain,
% 2.53/2.05 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.05 inference(symmetry,[status(thm)],[5154])).
% 2.53/2.05 tff(5156,plain,
% 2.53/2.05 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.53/2.05 inference(monotonicity,[status(thm)],[5155])).
% 2.53/2.05 tff(5157,plain,
% 2.53/2.05 (~big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.53/2.05 inference(modus_ponens,[status(thm)],[35, 5156])).
% 2.53/2.05 tff(5158,plain,
% 2.53/2.05 ((~(big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0)))) | big_f(Y!0, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) | (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0)))),
% 2.53/2.05 inference(tautology,[status(thm)],[])).
% 2.53/2.05 tff(5159,plain,
% 2.53/2.05 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Y!0))),
% 2.53/2.05 inference(unit_resolution,[status(thm)],[5158, 5157, 5153])).
% 2.53/2.05 tff(5160,plain,
% 2.54/2.05 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.54/2.05 inference(modus_ponens,[status(thm)],[5159, 5151])).
% 2.54/2.05 tff(5161,plain,
% 2.54/2.05 ($false),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[403, 5160, 5147])).
% 2.54/2.05 tff(5162,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~big_f(X!1, Y!0)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.05 tff(5163,plain,
% 2.54/2.05 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[5162, 341, 30, 1663, 35, 3678, 3022])).
% 2.54/2.05 tff(5164,plain,
% 2.54/2.05 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[82, 5163])).
% 2.54/2.05 tff(5165,plain,
% 2.54/2.05 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[84, 5164])).
% 2.54/2.05 tff(5166,plain,
% 2.54/2.05 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[86, 5165])).
% 2.54/2.05 tff(5167,plain,
% 2.54/2.05 (~(tptp_fun_Y1_11(Y!0) = Y!0)),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[3717, 5166, 30, 3678, 35])).
% 2.54/2.05 tff(5168,plain,
% 2.54/2.05 (tptp_fun_Y1_11(Y!0) = X!1),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[39, 5167])).
% 2.54/2.05 tff(5169,assumption,(~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)), introduced(assumption)).
% 2.54/2.05 tff(5170,plain,
% 2.54/2.05 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[561, 5165])).
% 2.54/2.05 tff(5171,plain,
% 2.54/2.05 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[563, 5167, 5170])).
% 2.54/2.05 tff(5172,plain,
% 2.54/2.05 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[3887, 5168, 3678, 341, 30, 35, 5171])).
% 2.54/2.05 tff(5173,plain,
% 2.54/2.05 (big_f(Z!5, X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.54/2.05 inference(monotonicity,[status(thm)],[349, 599])).
% 2.54/2.05 tff(5174,plain,
% 2.54/2.05 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, X!1)),
% 2.54/2.05 inference(symmetry,[status(thm)],[5173])).
% 2.54/2.05 tff(5175,plain,
% 2.54/2.05 (big_f(Z!5, X!1)),
% 2.54/2.05 inference(modus_ponens,[status(thm)],[622, 5174])).
% 2.54/2.05 tff(5176,plain,
% 2.54/2.05 (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[321, 4294])).
% 2.54/2.05 tff(5177,plain,
% 2.54/2.05 (Y!0 = tptp_fun_W_6(X!1)),
% 2.54/2.05 inference(unit_resolution,[status(thm)],[3751, 5176, 3678])).
% 2.54/2.05 tff(5178,plain,
% 2.54/2.05 (tptp_fun_W_6(X!1) = Y!0),
% 2.54/2.05 inference(symmetry,[status(thm)],[5177])).
% 2.54/2.05 tff(5179,plain,
% 2.54/2.05 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(X!1)),
% 2.54/2.05 inference(monotonicity,[status(thm)],[349])).
% 2.54/2.05 tff(5180,plain,
% 2.54/2.05 (tptp_fun_W_6(Z!5) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.54/2.05 inference(transitivity,[status(thm)],[5179, 5178, 3074, 1671])).
% 2.54/2.05 tff(5181,plain,
% 2.54/2.05 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.54/2.05 inference(monotonicity,[status(thm)],[5180])).
% 2.54/2.05 tff(5182,plain,
% 2.54/2.05 ((X!1 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.54/2.05 inference(transitivity,[status(thm)],[5181, 2270])).
% 2.54/2.06 tff(5183,plain,
% 2.54/2.06 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.54/2.06 inference(symmetry,[status(thm)],[5182])).
% 2.54/2.06 tff(5184,plain,
% 2.54/2.06 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)) <=> (~(X!1 = tptp_fun_W_6(Z!5)))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5183])).
% 2.54/2.06 tff(5185,plain,
% 2.54/2.06 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[5169, 5184])).
% 2.54/2.06 tff(5186,plain,
% 2.54/2.06 ($false),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[989, 5185, 5175, 984])).
% 2.54/2.06 tff(5187,plain,((~(Z!5 = X!1)) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))) | (~big_f(X!1, Y!0)) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.06 tff(5188,plain,
% 2.54/2.06 (~(Z!5 = X!1)),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5187, 5172, 3022, 30, 1663, 5169, 5168, 386, 3678, 345])).
% 2.54/2.06 tff(5189,plain,
% 2.54/2.06 (Z!5 = Y!0),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[361, 5188])).
% 2.54/2.06 tff(5190,plain,
% 2.54/2.06 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(Y!0)),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5189])).
% 2.54/2.06 tff(5191,plain,
% 2.54/2.06 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = tptp_fun_W_6(Y!0))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5190])).
% 2.54/2.06 tff(5192,plain,
% 2.54/2.06 ((X!1 = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = X!1)),
% 2.54/2.06 inference(transitivity,[status(thm)],[5191, 1537])).
% 2.54/2.06 tff(5193,plain,
% 2.54/2.06 ((~(X!1 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5192])).
% 2.54/2.06 tff(5194,plain,
% 2.54/2.06 (X!1 = tptp_fun_Y1_11(Y!0)),
% 2.54/2.06 inference(symmetry,[status(thm)],[5168])).
% 2.54/2.06 tff(5195,plain,
% 2.54/2.06 (Z!5 = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.54/2.06 inference(transitivity,[status(thm)],[5189, 3074])).
% 2.54/2.06 tff(5196,plain,
% 2.54/2.06 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5195, 5194])).
% 2.54/2.06 tff(5197,plain,
% 2.54/2.06 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, X!1)),
% 2.54/2.06 inference(symmetry,[status(thm)],[5196])).
% 2.54/2.06 tff(5198,plain,
% 2.54/2.06 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))) <=> (~big_f(Z!5, X!1))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5197])).
% 2.54/2.06 tff(5199,plain,
% 2.54/2.06 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[3074])).
% 2.54/2.06 tff(5200,plain,
% 2.54/2.06 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0)))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5199])).
% 2.54/2.06 tff(5201,plain,
% 2.54/2.06 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[1194, 5172, 5171])).
% 2.54/2.06 tff(5202,plain,
% 2.54/2.06 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[5201, 5200])).
% 2.54/2.06 tff(5203,plain,
% 2.54/2.06 (~big_f(Z!5, X!1)),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[5202, 5198])).
% 2.54/2.06 tff(5204,plain,
% 2.54/2.06 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[1547, 5203, 1212])).
% 2.54/2.06 tff(5205,plain,
% 2.54/2.06 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[5204, 5193])).
% 2.54/2.06 tff(5206,plain,
% 2.54/2.06 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)) <=> (Y!0 = tptp_fun_W_6(Y!0))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5148, 5190])).
% 2.54/2.06 tff(5207,plain,
% 2.54/2.06 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5)) <=> (tptp_fun_W_6(Y!0) = Y!0)),
% 2.54/2.06 inference(transitivity,[status(thm)],[5206, 339])).
% 2.54/2.06 tff(5208,plain,
% 2.54/2.06 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = Y!0))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5207])).
% 2.54/2.06 tff(5209,plain,
% 2.54/2.06 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5030, 386])).
% 2.54/2.06 tff(5210,plain,
% 2.54/2.06 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.54/2.06 inference(transitivity,[status(thm)],[5189, 31])).
% 2.54/2.06 tff(5211,plain,
% 2.54/2.06 (big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5210, 5148])).
% 2.54/2.06 tff(5212,plain,
% 2.54/2.06 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.54/2.06 inference(symmetry,[status(thm)],[5211])).
% 2.54/2.06 tff(5213,plain,
% 2.54/2.06 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5212])).
% 2.54/2.06 tff(5214,plain,
% 2.54/2.06 (~big_f(Z!5, tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0))),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[35, 5213])).
% 2.54/2.06 tff(5215,plain,
% 2.54/2.06 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_W_6(Z!5))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5038, 5214, 5209])).
% 2.54/2.06 tff(5216,plain,
% 2.54/2.06 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[5215, 5208])).
% 2.54/2.06 tff(5217,plain,
% 2.54/2.06 ($false),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[403, 5216, 5205])).
% 2.54/2.06 tff(5218,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1) | (~big_f(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.06 tff(5219,plain,
% 2.54/2.06 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5218, 5117, 30, 1663, 341, 35, 3678])).
% 2.54/2.06 tff(5220,plain,
% 2.54/2.06 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[5219, 4781])).
% 2.54/2.06 tff(5221,plain,
% 2.54/2.06 ($false),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5116, 5220])).
% 2.54/2.06 tff(5222,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.06 tff(5223,plain,
% 2.54/2.06 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5222, 4771, 30, 3678, 35, 154])).
% 2.54/2.06 tff(5224,plain,
% 2.54/2.06 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[462, 5223])).
% 2.54/2.06 tff(5225,plain,
% 2.54/2.06 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(Y!0, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(Y!0, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(Y!0, X!1))))))))),
% 2.54/2.06 inference(quant_inst,[status(thm)],[])).
% 2.54/2.06 tff(5226,plain,
% 2.54/2.06 (~((~((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(Y!0, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(Y!0, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(Y!0, X!1)))))))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5225, 5224])).
% 2.54/2.06 tff(5227,plain,
% 2.54/2.06 (((~((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(Y!0, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(Y!0, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(Y!0, X!1))))))) | ((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1)))),
% 2.54/2.06 inference(tautology,[status(thm)],[])).
% 2.54/2.06 tff(5228,plain,
% 2.54/2.06 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5227, 5226])).
% 2.54/2.06 tff(5229,plain,
% 2.54/2.06 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) <=> (X!1 = W1!8)),
% 2.54/2.06 inference(monotonicity,[status(thm)],[4775])).
% 2.54/2.06 tff(5230,plain,
% 2.54/2.06 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) <=> (W1!8 = X!1)),
% 2.54/2.06 inference(transitivity,[status(thm)],[5229, 24])).
% 2.54/2.06 tff(5231,plain,
% 2.54/2.06 ((W1!8 = X!1) <=> (tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.06 inference(symmetry,[status(thm)],[5230])).
% 2.54/2.06 tff(5232,plain,
% 2.54/2.06 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[3017, 5224])).
% 2.54/2.06 tff(5233,plain,
% 2.54/2.06 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[3019, 5232])).
% 2.54/2.06 tff(5234,plain,
% 2.54/2.06 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5115, 4771, 30, 3678, 35, 154])).
% 2.54/2.06 tff(5235,plain,
% 2.54/2.06 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[33])).
% 2.54/2.06 tff(5236,plain,
% 2.54/2.06 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[35, 5235])).
% 2.54/2.06 tff(5237,plain,
% 2.54/2.06 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[2258, 5234])).
% 2.54/2.06 tff(5238,plain,
% 2.54/2.06 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[3080, 5237, 5236])).
% 2.54/2.06 tff(5239,plain,
% 2.54/2.06 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[3082, 5238, 5234])).
% 2.54/2.06 tff(5240,plain,
% 2.54/2.06 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[3084, 5239])).
% 2.54/2.06 tff(5241,plain,
% 2.54/2.06 (tptp_fun_X_2(Y!0) = W1!8),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[3086, 5240, 5233])).
% 2.54/2.06 tff(5242,plain,
% 2.54/2.06 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.54/2.06 inference(symmetry,[status(thm)],[5241])).
% 2.54/2.06 tff(5243,plain,
% 2.54/2.06 (W1!8 = Y!0),
% 2.54/2.06 inference(transitivity,[status(thm)],[5242, 30])).
% 2.54/2.06 tff(5244,plain,
% 2.54/2.06 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5243])).
% 2.54/2.06 tff(5245,plain,
% 2.54/2.06 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.54/2.06 inference(transitivity,[status(thm)],[5244, 46])).
% 2.54/2.06 tff(5246,plain,
% 2.54/2.06 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.54/2.06 inference(symmetry,[status(thm)],[5245])).
% 2.54/2.06 tff(5247,plain,
% 2.54/2.06 ((X!1 = Y!0) <=> (tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.06 inference(transitivity,[status(thm)],[5246, 5231])).
% 2.54/2.06 tff(5248,plain,
% 2.54/2.06 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y_4(Y!0, X!1) = W1!8))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5247])).
% 2.54/2.06 tff(5249,plain,
% 2.54/2.06 (~(tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[741, 5248])).
% 2.54/2.06 tff(5250,plain,
% 2.54/2.06 ((~((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1)))) | (tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))),
% 2.54/2.06 inference(tautology,[status(thm)],[])).
% 2.54/2.06 tff(5251,plain,
% 2.54/2.06 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5250, 5249, 5228])).
% 2.54/2.06 tff(5252,plain,
% 2.54/2.06 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))) | ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)))),
% 2.54/2.06 inference(quant_inst,[status(thm)],[])).
% 2.54/2.06 tff(5253,plain,
% 2.54/2.06 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5252, 5251])).
% 2.54/2.06 tff(5254,plain,
% 2.54/2.06 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.54/2.06 inference(monotonicity,[status(thm)],[4771, 599])).
% 2.54/2.06 tff(5255,plain,
% 2.54/2.06 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.06 inference(symmetry,[status(thm)],[5254])).
% 2.54/2.06 tff(5256,plain,
% 2.54/2.06 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[622, 5255])).
% 2.54/2.06 tff(5257,assumption,((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))), introduced(assumption)).
% 2.54/2.06 tff(5258,assumption,(~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))), introduced(assumption)).
% 2.54/2.06 tff(5259,plain,
% 2.54/2.06 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)))) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.06 inference(tautology,[status(thm)],[])).
% 2.54/2.06 tff(5260,plain,
% 2.54/2.06 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5259, 5258, 5257])).
% 2.54/2.06 tff(5261,plain,
% 2.54/2.06 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.06 inference(monotonicity,[status(thm)],[5260, 4866])).
% 2.54/2.06 tff(5262,plain,
% 2.54/2.06 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.06 inference(symmetry,[status(thm)],[5261])).
% 2.54/2.06 tff(5263,plain,
% 2.54/2.06 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.06 inference(modus_ponens,[status(thm)],[862, 5262])).
% 2.54/2.06 tff(5264,plain,
% 2.54/2.06 ($false),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5258, 5263])).
% 2.54/2.06 tff(5265,plain,(big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.06 tff(5266,plain,
% 2.54/2.06 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5265, 5253, 4775, 5256])).
% 2.54/2.06 tff(5267,plain,
% 2.54/2.06 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)))) | (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) | (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)))),
% 2.54/2.06 inference(tautology,[status(thm)],[])).
% 2.54/2.06 tff(5268,plain,
% 2.54/2.06 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.06 inference(unit_resolution,[status(thm)],[5267, 5266, 5253])).
% 2.54/2.07 tff(5269,plain,
% 2.54/2.07 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1)),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[5268, 4778])).
% 2.54/2.07 tff(5270,plain,
% 2.54/2.07 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0))),
% 2.54/2.07 inference(rewrite,[status(thm)],[])).
% 2.54/2.07 tff(5271,plain,
% 2.54/2.07 (((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1)) <=> ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0))),
% 2.54/2.07 inference(rewrite,[status(thm)],[])).
% 2.54/2.07 tff(5272,plain,
% 2.54/2.07 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0)))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5271])).
% 2.54/2.07 tff(5273,plain,
% 2.54/2.07 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0))),
% 2.54/2.07 inference(transitivity,[status(thm)],[5272, 5270])).
% 2.54/2.07 tff(5274,plain,
% 2.54/2.07 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1))),
% 2.54/2.07 inference(quant_inst,[status(thm)],[])).
% 2.54/2.07 tff(5275,plain,
% 2.54/2.07 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0)),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[5274, 5273])).
% 2.54/2.07 tff(5276,plain,
% 2.54/2.07 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0)),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5275, 12])).
% 2.54/2.07 tff(5277,plain,
% 2.54/2.07 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5276, 5269])).
% 2.54/2.07 tff(5278,plain,
% 2.54/2.07 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5277, 4776])).
% 2.54/2.07 tff(5279,plain,
% 2.54/2.07 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.07 inference(symmetry,[status(thm)],[5278])).
% 2.54/2.07 tff(5280,plain,
% 2.54/2.07 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5279])).
% 2.54/2.07 tff(5281,plain,
% 2.54/2.07 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[41, 5280])).
% 2.54/2.07 tff(5282,plain,
% 2.54/2.07 ($false),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5266, 5281])).
% 2.54/2.07 tff(5283,plain,((tptp_fun_Y1_11(X!1) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~big_f(X!1, Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.07 tff(5284,plain,
% 2.54/2.07 (tptp_fun_Y1_11(X!1) = X!1),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5283, 4770, 598, 30, 622, 3678, 41, 2485])).
% 2.54/2.07 tff(5285,plain,
% 2.54/2.07 (tptp_fun_Y1_11(X!1) = tptp_fun_Y1_11(Y!0)),
% 2.54/2.07 inference(transitivity,[status(thm)],[5284, 599])).
% 2.54/2.07 tff(5286,plain,
% 2.54/2.07 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[1599, 106, 30, 35])).
% 2.54/2.07 tff(5287,plain,
% 2.54/2.07 ($false),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[1588, 5286, 3384, 598, 41, 106])).
% 2.54/2.07 tff(5288,plain,((tptp_fun_X_2(X!1) = X!1) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.07 tff(5289,plain,
% 2.54/2.07 (tptp_fun_X_2(X!1) = X!1),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5288, 4770, 41, 30, 598, 1437])).
% 2.54/2.07 tff(5290,plain,
% 2.54/2.07 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1)),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5289])).
% 2.54/2.07 tff(5291,plain,
% 2.54/2.07 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5290])).
% 2.54/2.07 tff(5292,plain,
% 2.54/2.07 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3760, 622, 3678, 598])).
% 2.54/2.07 tff(5293,plain,
% 2.54/2.07 (tptp_fun_Y_4(X!1, Y!0) = tptp_fun_Y1_11(X!1)),
% 2.54/2.07 inference(transitivity,[status(thm)],[859, 889])).
% 2.54/2.07 tff(5294,plain,
% 2.54/2.07 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[30, 5293])).
% 2.54/2.07 tff(5295,plain,
% 2.54/2.07 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.54/2.07 inference(symmetry,[status(thm)],[5294])).
% 2.54/2.07 tff(5296,plain,
% 2.54/2.07 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[2569, 5295])).
% 2.54/2.07 tff(5297,plain,
% 2.54/2.07 ($false),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[2120, 5296])).
% 2.54/2.07 tff(5298,plain,((~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.07 tff(5299,plain,
% 2.54/2.07 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5298, 5284, 30, 4770, 1444])).
% 2.54/2.07 tff(5300,plain,
% 2.54/2.07 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[2506, 5299, 30, 5292, 4770, 5284])).
% 2.54/2.07 tff(5301,plain,
% 2.54/2.07 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[462, 5300])).
% 2.54/2.07 tff(5302,plain,
% 2.54/2.07 (~((~((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(Y!0, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(Y!0, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(Y!0, X!1)))))))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5225, 5301])).
% 2.54/2.07 tff(5303,plain,
% 2.54/2.07 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5227, 5302])).
% 2.54/2.07 tff(5304,plain,
% 2.54/2.07 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[1711, 5289, 2485])).
% 2.54/2.07 tff(5305,plain,
% 2.54/2.07 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3679, 5304])).
% 2.54/2.07 tff(5306,plain,
% 2.54/2.07 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3689, 5305, 3678, 5289])).
% 2.54/2.07 tff(5307,plain,
% 2.54/2.07 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3694, 5306])).
% 2.54/2.07 tff(5308,plain,
% 2.54/2.07 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) <=> (X!1 = W1!8)),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5307])).
% 2.54/2.07 tff(5309,plain,
% 2.54/2.07 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) <=> (W1!8 = X!1)),
% 2.54/2.07 inference(transitivity,[status(thm)],[5308, 24])).
% 2.54/2.07 tff(5310,plain,
% 2.54/2.07 ((W1!8 = X!1) <=> (tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.07 inference(symmetry,[status(thm)],[5309])).
% 2.54/2.07 tff(5311,plain,
% 2.54/2.07 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3017, 5301])).
% 2.54/2.07 tff(5312,plain,
% 2.54/2.07 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3019, 5311])).
% 2.54/2.07 tff(5313,plain,
% 2.54/2.07 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5042, 5289, 30, 3678, 1435, 4770])).
% 2.54/2.07 tff(5314,plain,
% 2.54/2.07 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[4770, 5235])).
% 2.54/2.07 tff(5315,plain,
% 2.54/2.07 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[2258, 5313])).
% 2.54/2.07 tff(5316,plain,
% 2.54/2.07 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3080, 5315, 5314])).
% 2.54/2.07 tff(5317,plain,
% 2.54/2.07 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3082, 5316, 5313])).
% 2.54/2.07 tff(5318,plain,
% 2.54/2.07 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3084, 5317])).
% 2.54/2.07 tff(5319,plain,
% 2.54/2.07 (tptp_fun_X_2(Y!0) = W1!8),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[3086, 5318, 5312])).
% 2.54/2.07 tff(5320,plain,
% 2.54/2.07 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.54/2.07 inference(symmetry,[status(thm)],[5319])).
% 2.54/2.07 tff(5321,plain,
% 2.54/2.07 (W1!8 = Y!0),
% 2.54/2.07 inference(transitivity,[status(thm)],[5320, 30])).
% 2.54/2.07 tff(5322,plain,
% 2.54/2.07 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5321])).
% 2.54/2.07 tff(5323,plain,
% 2.54/2.07 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.54/2.07 inference(transitivity,[status(thm)],[5322, 46])).
% 2.54/2.07 tff(5324,plain,
% 2.54/2.07 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.54/2.07 inference(symmetry,[status(thm)],[5323])).
% 2.54/2.07 tff(5325,plain,
% 2.54/2.07 ((X!1 = Y!0) <=> (tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.07 inference(transitivity,[status(thm)],[5324, 5310])).
% 2.54/2.07 tff(5326,plain,
% 2.54/2.07 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y_4(Y!0, X!1) = W1!8))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5325])).
% 2.54/2.07 tff(5327,plain,
% 2.54/2.07 (~(tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[741, 5326])).
% 2.54/2.07 tff(5328,plain,
% 2.54/2.07 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5250, 5327, 5303])).
% 2.54/2.07 tff(5329,plain,
% 2.54/2.07 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5252, 5328])).
% 2.54/2.07 tff(5330,plain,
% 2.54/2.07 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5289, 599])).
% 2.54/2.07 tff(5331,plain,
% 2.54/2.07 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.07 inference(symmetry,[status(thm)],[5330])).
% 2.54/2.07 tff(5332,plain,
% 2.54/2.07 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[622, 5331])).
% 2.54/2.07 tff(5333,plain,
% 2.54/2.07 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5265, 5329, 5307, 5332])).
% 2.54/2.07 tff(5334,plain,
% 2.54/2.07 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5267, 5333, 5329])).
% 2.54/2.07 tff(5335,plain,
% 2.54/2.07 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1)),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[5334, 5291])).
% 2.54/2.07 tff(5336,plain,
% 2.54/2.07 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5276, 5335])).
% 2.54/2.07 tff(5337,plain,
% 2.54/2.07 (X!1 = tptp_fun_Y_4(Y!0, X!1)),
% 2.54/2.07 inference(symmetry,[status(thm)],[5307])).
% 2.54/2.07 tff(5338,plain,
% 2.54/2.07 (tptp_fun_Y1_11(X!1) = tptp_fun_Y_4(Y!0, X!1)),
% 2.54/2.07 inference(transitivity,[status(thm)],[5284, 5337])).
% 2.54/2.07 tff(5339,plain,
% 2.54/2.07 (X!1 = tptp_fun_X_2(X!1)),
% 2.54/2.07 inference(symmetry,[status(thm)],[5289])).
% 2.54/2.07 tff(5340,plain,
% 2.54/2.07 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5339, 5338])).
% 2.54/2.07 tff(5341,plain,
% 2.54/2.07 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.54/2.07 inference(transitivity,[status(thm)],[5340, 5336])).
% 2.54/2.07 tff(5342,plain,
% 2.54/2.07 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5341, 5285])).
% 2.54/2.07 tff(5343,plain,
% 2.54/2.07 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.54/2.07 inference(symmetry,[status(thm)],[5342])).
% 2.54/2.07 tff(5344,plain,
% 2.54/2.07 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5343])).
% 2.54/2.07 tff(5345,plain,
% 2.54/2.07 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[41, 5344])).
% 2.54/2.07 tff(5346,plain,
% 2.54/2.07 (X!1 = tptp_fun_Y1_11(X!1)),
% 2.54/2.07 inference(symmetry,[status(thm)],[5284])).
% 2.54/2.07 tff(5347,plain,
% 2.54/2.07 (tptp_fun_Y_4(Y!0, X!1) = tptp_fun_Y1_11(X!1)),
% 2.54/2.07 inference(transitivity,[status(thm)],[5307, 5346])).
% 2.54/2.07 tff(5348,plain,
% 2.54/2.07 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.54/2.07 inference(symmetry,[status(thm)],[5340])).
% 2.54/2.07 tff(5349,plain,
% 2.54/2.07 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.54/2.07 inference(monotonicity,[status(thm)],[5348, 5347])).
% 2.54/2.07 tff(5350,plain,
% 2.54/2.07 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.54/2.07 inference(modus_ponens,[status(thm)],[5333, 5349])).
% 2.54/2.07 tff(5351,plain,
% 2.54/2.07 ($false),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5350, 5345])).
% 2.54/2.07 tff(5352,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~big_f(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.07 tff(5353,plain,
% 2.54/2.07 ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5352, 4769])).
% 2.54/2.07 tff(5354,plain,
% 2.54/2.07 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.54/2.07 inference(unit_resolution,[status(thm)],[5353, 41, 30, 40, 4043])).
% 2.54/2.07 tff(5355,plain,
% 2.54/2.07 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[82, 5354])).
% 2.54/2.08 tff(5356,plain,
% 2.54/2.08 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[84, 5355])).
% 2.54/2.08 tff(5357,plain,
% 2.54/2.08 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[561, 5356])).
% 2.54/2.08 tff(5358,plain,
% 2.54/2.08 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[563, 5357, 34])).
% 2.54/2.08 tff(5359,plain,
% 2.54/2.08 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[576, 5358])).
% 2.54/2.08 tff(5360,plain,
% 2.54/2.08 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[751, 5359, 4043])).
% 2.54/2.08 tff(5361,plain,
% 2.54/2.08 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[1191, 5360])).
% 2.54/2.08 tff(5362,plain,
% 2.54/2.08 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[594, 5361])).
% 2.54/2.08 tff(5363,plain,
% 2.54/2.08 ((tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1)),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5362])).
% 2.54/2.08 tff(5364,plain,
% 2.54/2.08 ((~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))) <=> (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5363])).
% 2.54/2.08 tff(5365,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[2392, 5358])).
% 2.54/2.08 tff(5366,plain,
% 2.54/2.08 (tptp_fun_Z1_12(Y!0) = tptp_fun_Y1_11(Y!0)),
% 2.54/2.08 inference(transitivity,[status(thm)],[5362, 2455])).
% 2.54/2.08 tff(5367,plain,
% 2.54/2.08 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.54/2.08 inference(symmetry,[status(thm)],[5362])).
% 2.54/2.08 tff(5368,plain,
% 2.54/2.08 (~(tptp_fun_Y1_11(X!1) = X!1)),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[1562, 5355, 34, 41])).
% 2.54/2.08 tff(5369,plain,
% 2.54/2.08 (tptp_fun_Y1_11(X!1) = Y!0),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[153, 5368])).
% 2.54/2.08 tff(5370,plain,
% 2.54/2.08 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.08 inference(monotonicity,[status(thm)],[31, 5369])).
% 2.54/2.08 tff(5371,plain,
% 2.54/2.08 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X_2(Y!0), Y!0))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5370])).
% 2.54/2.08 tff(5372,plain,
% 2.54/2.08 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[88, 5355])).
% 2.54/2.08 tff(5373,plain,
% 2.54/2.08 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[191, 5372])).
% 2.54/2.08 tff(5374,plain,
% 2.54/2.08 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[161, 5373, 5368])).
% 2.54/2.08 tff(5375,plain,
% 2.54/2.08 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[3195, 5374])).
% 2.54/2.08 tff(5376,plain,
% 2.54/2.08 ((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> (X!1 = tptp_fun_Z1_12(X!1)))),
% 2.54/2.08 inference(quant_inst,[status(thm)],[])).
% 2.54/2.08 tff(5377,plain,
% 2.54/2.08 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> (X!1 = tptp_fun_Z1_12(X!1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5376, 5374])).
% 2.54/2.08 tff(5378,plain,
% 2.54/2.08 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5369])).
% 2.54/2.08 tff(5379,plain,
% 2.54/2.08 (big_f(X!1, Y!0) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.54/2.08 inference(symmetry,[status(thm)],[5378])).
% 2.54/2.08 tff(5380,plain,
% 2.54/2.08 (big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.54/2.08 inference(modus_ponens,[status(thm)],[4769, 5379])).
% 2.54/2.08 tff(5381,plain,
% 2.54/2.08 ((~(big_f(X!1, tptp_fun_Y1_11(X!1)) <=> (X!1 = tptp_fun_Z1_12(X!1)))) | (~big_f(X!1, tptp_fun_Y1_11(X!1))) | (X!1 = tptp_fun_Z1_12(X!1))),
% 2.54/2.08 inference(tautology,[status(thm)],[])).
% 2.54/2.08 tff(5382,plain,
% 2.54/2.08 (X!1 = tptp_fun_Z1_12(X!1)),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5381, 5380, 5377])).
% 2.54/2.08 tff(5383,plain,
% 2.54/2.08 (tptp_fun_Z1_12(X!1) = X!1),
% 2.54/2.08 inference(symmetry,[status(thm)],[5382])).
% 2.54/2.08 tff(5384,plain,
% 2.54/2.08 ((tptp_fun_Z1_12(X!1) = Y!0) <=> (X!1 = Y!0)),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5383])).
% 2.54/2.08 tff(5385,plain,
% 2.54/2.08 ((X!1 = Y!0) <=> (tptp_fun_Z1_12(X!1) = Y!0)),
% 2.54/2.08 inference(symmetry,[status(thm)],[5384])).
% 2.54/2.08 tff(5386,plain,
% 2.54/2.08 ((X!1 = Y!0) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.54/2.08 inference(transitivity,[status(thm)],[5385, 3193])).
% 2.54/2.08 tff(5387,plain,
% 2.54/2.08 ((~(X!1 = Y!0)) <=> (~(Y!0 = tptp_fun_Z1_12(X!1)))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5386])).
% 2.54/2.08 tff(5388,plain,
% 2.54/2.08 (~(Y!0 = tptp_fun_Z1_12(X!1))),
% 2.54/2.08 inference(modus_ponens,[status(thm)],[741, 5387])).
% 2.54/2.08 tff(5389,plain,
% 2.54/2.08 ((~(big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1)))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.54/2.08 inference(tautology,[status(thm)],[])).
% 2.54/2.08 tff(5390,plain,
% 2.54/2.08 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5389, 5388, 5375])).
% 2.54/2.08 tff(5391,plain,
% 2.54/2.08 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.08 inference(modus_ponens,[status(thm)],[5390, 5371])).
% 2.54/2.08 tff(5392,plain,
% 2.54/2.08 (tptp_fun_X_2(X!1) = X!1),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[4026, 5391, 30, 5368])).
% 2.54/2.08 tff(5393,plain,
% 2.54/2.08 (tptp_fun_X_2(X!1) = tptp_fun_Z1_12(Y!0)),
% 2.54/2.08 inference(transitivity,[status(thm)],[5392, 5367])).
% 2.54/2.08 tff(5394,plain,
% 2.54/2.08 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5393])).
% 2.54/2.08 tff(5395,plain,
% 2.54/2.08 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1))),
% 2.54/2.08 inference(symmetry,[status(thm)],[5394])).
% 2.54/2.08 tff(5396,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5395, 5366])).
% 2.54/2.08 tff(5397,plain,
% 2.54/2.08 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0)))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5396])).
% 2.54/2.08 tff(5398,plain,
% 2.54/2.08 (big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_Y1_11(X!1) = Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5222, 4769])).
% 2.54/2.08 tff(5399,plain,
% 2.54/2.08 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5398, 5392, 30, 5391, 5369])).
% 2.54/2.08 tff(5400,plain,
% 2.54/2.08 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[462, 5399])).
% 2.54/2.08 tff(5401,plain,
% 2.54/2.08 (~((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[746, 5400])).
% 2.54/2.08 tff(5402,plain,
% 2.54/2.08 ((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[748, 5401])).
% 2.54/2.08 tff(5403,plain,
% 2.54/2.08 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (X!1 = W1!8)),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5362])).
% 2.54/2.08 tff(5404,plain,
% 2.54/2.08 ((tptp_fun_Z1_12(Y!0) = W1!8) <=> (W1!8 = X!1)),
% 2.54/2.08 inference(transitivity,[status(thm)],[5403, 24])).
% 2.54/2.08 tff(5405,plain,
% 2.54/2.08 ((W1!8 = X!1) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.54/2.08 inference(symmetry,[status(thm)],[5404])).
% 2.54/2.08 tff(5406,plain,
% 2.54/2.08 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.54/2.08 inference(transitivity,[status(thm)],[5370, 33])).
% 2.54/2.08 tff(5407,plain,
% 2.54/2.08 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5406])).
% 2.54/2.08 tff(5408,plain,
% 2.54/2.08 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.54/2.08 inference(modus_ponens,[status(thm)],[5390, 5407])).
% 2.54/2.08 tff(5409,plain,
% 2.54/2.08 ((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_Y1_11(X!1) = Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5115, 4769])).
% 2.54/2.08 tff(5410,plain,
% 2.54/2.08 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5409, 5391, 30, 5369, 5392])).
% 2.54/2.08 tff(5411,assumption,((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)), introduced(assumption)).
% 2.54/2.08 tff(5412,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[3082, 2344, 5411])).
% 2.54/2.08 tff(5413,plain,
% 2.54/2.08 ($false),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[3080, 5412, 2345, 2991])).
% 2.54/2.08 tff(5414,plain,((tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.08 tff(5415,plain,
% 2.54/2.08 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[5414, 5410, 5408])).
% 2.54/2.08 tff(5416,plain,
% 2.54/2.08 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[3084, 5415])).
% 2.54/2.08 tff(5417,plain,
% 2.54/2.08 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[3017, 5400])).
% 2.54/2.08 tff(5418,plain,
% 2.54/2.08 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[3019, 5417])).
% 2.54/2.08 tff(5419,plain,
% 2.54/2.08 (tptp_fun_X_2(Y!0) = W1!8),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[3086, 5418, 5416])).
% 2.54/2.08 tff(5420,plain,
% 2.54/2.08 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.54/2.08 inference(symmetry,[status(thm)],[5419])).
% 2.54/2.08 tff(5421,plain,
% 2.54/2.08 (W1!8 = Y!0),
% 2.54/2.08 inference(transitivity,[status(thm)],[5420, 30])).
% 2.54/2.08 tff(5422,plain,
% 2.54/2.08 ((W1!8 = X!1) <=> (Y!0 = X!1)),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5421])).
% 2.54/2.08 tff(5423,plain,
% 2.54/2.08 ((W1!8 = X!1) <=> (X!1 = Y!0)),
% 2.54/2.08 inference(transitivity,[status(thm)],[5422, 46])).
% 2.54/2.08 tff(5424,plain,
% 2.54/2.08 ((X!1 = Y!0) <=> (W1!8 = X!1)),
% 2.54/2.08 inference(symmetry,[status(thm)],[5423])).
% 2.54/2.08 tff(5425,plain,
% 2.54/2.08 ((X!1 = Y!0) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.54/2.08 inference(transitivity,[status(thm)],[5424, 5405])).
% 2.54/2.08 tff(5426,plain,
% 2.54/2.08 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Z1_12(Y!0) = W1!8))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5425])).
% 2.54/2.08 tff(5427,plain,
% 2.54/2.08 (~(tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.54/2.08 inference(modus_ponens,[status(thm)],[741, 5426])).
% 2.54/2.08 tff(5428,plain,
% 2.54/2.08 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[811, 5427, 5402])).
% 2.54/2.08 tff(5429,plain,
% 2.54/2.08 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[813, 5428])).
% 2.54/2.08 tff(5430,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[2394, 5358])).
% 2.54/2.08 tff(5431,plain,
% 2.54/2.08 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[2390, 5428])).
% 2.54/2.08 tff(5432,plain,
% 2.54/2.08 (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[2434, 5431, 5392, 40, 5430, 5365, 5362, 5429])).
% 2.54/2.08 tff(5433,plain,
% 2.54/2.08 (~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)), tptp_fun_Y1_11(Y!0))),
% 2.54/2.08 inference(modus_ponens,[status(thm)],[5432, 5397])).
% 2.54/2.08 tff(5434,plain,
% 2.54/2.08 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[2452, 5433, 5365])).
% 2.54/2.08 tff(5435,plain,
% 2.54/2.08 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1)),
% 2.54/2.08 inference(modus_ponens,[status(thm)],[5434, 5364])).
% 2.54/2.08 tff(5436,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5366])).
% 2.54/2.08 tff(5437,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(symmetry,[status(thm)],[5436])).
% 2.54/2.08 tff(5438,plain,
% 2.54/2.08 (tptp_fun_Y1_11(Y!0) = tptp_fun_Z1_12(Y!0)),
% 2.54/2.08 inference(transitivity,[status(thm)],[40, 5367])).
% 2.54/2.08 tff(5439,plain,
% 2.54/2.08 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(unit_resolution,[status(thm)],[2436, 5431, 5432])).
% 2.54/2.08 tff(5440,plain,
% 2.54/2.08 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(symmetry,[status(thm)],[5439])).
% 2.54/2.08 tff(5441,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5440, 5438])).
% 2.54/2.08 tff(5442,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Y1_11(Y!0))),
% 2.54/2.08 inference(symmetry,[status(thm)],[5441])).
% 2.54/2.08 tff(5443,plain,
% 2.54/2.08 (big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.54/2.08 inference(transitivity,[status(thm)],[5442, 5437])).
% 2.54/2.08 tff(5444,plain,
% 2.54/2.08 ((~big_f(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0)))),
% 2.54/2.08 inference(monotonicity,[status(thm)],[5443])).
% 2.54/2.09 tff(5445,plain,
% 2.54/2.09 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[5432, 5444])).
% 2.54/2.09 tff(5446,plain,
% 2.54/2.09 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[835, 5445, 5429])).
% 2.54/2.09 tff(5447,assumption,(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0), introduced(assumption)).
% 2.54/2.09 tff(5448,plain,
% 2.54/2.09 (tptp_fun_X_2(X!1) = tptp_fun_Z1_12(Y!0)),
% 2.54/2.09 inference(transitivity,[status(thm)],[1663, 1963])).
% 2.54/2.09 tff(5449,assumption,(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1), introduced(assumption)).
% 2.54/2.09 tff(5450,plain,
% 2.54/2.09 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.54/2.09 inference(monotonicity,[status(thm)],[5449, 5448])).
% 2.54/2.09 tff(5451,plain,
% 2.54/2.09 (tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1))),
% 2.54/2.09 inference(symmetry,[status(thm)],[5450])).
% 2.54/2.09 tff(5452,plain,
% 2.54/2.09 (X!1 = tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0))),
% 2.54/2.09 inference(symmetry,[status(thm)],[5449])).
% 2.54/2.09 tff(5453,plain,
% 2.54/2.09 (X!1 = Y!0),
% 2.54/2.09 inference(transitivity,[status(thm)],[5452, 5451, 5447])).
% 2.54/2.09 tff(5454,plain,
% 2.54/2.09 ($false),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[741, 5453])).
% 2.54/2.09 tff(5455,plain,((~(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)) = X!1)) | (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0)) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.09 tff(5456,plain,
% 2.54/2.09 (~(tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = Y!0)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5455, 5446, 5392, 5362])).
% 2.54/2.09 tff(5457,plain,
% 2.54/2.09 (tptp_fun_X1_10(tptp_fun_X1_10(X!1, tptp_fun_Z1_12(Y!0)), tptp_fun_X_2(X!1)) = X!1),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[4899, 5456])).
% 2.54/2.09 tff(5458,plain,
% 2.54/2.09 ($false),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5457, 5435])).
% 2.54/2.09 tff(5459,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.09 tff(5460,plain,
% 2.54/2.09 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5459, 34, 30])).
% 2.54/2.09 tff(5461,plain,
% 2.54/2.09 (~((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[2122, 35, 30, 40, 5460])).
% 2.54/2.09 tff(5462,plain,
% 2.54/2.09 (~![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[198, 5461])).
% 2.54/2.09 tff(5463,plain,
% 2.54/2.09 (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[52, 5462, 30])).
% 2.54/2.09 tff(5464,plain,
% 2.54/2.09 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[54, 5463])).
% 2.54/2.09 tff(5465,plain,
% 2.54/2.09 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[56, 5464])).
% 2.54/2.09 tff(5466,plain,
% 2.54/2.09 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[82, 5465])).
% 2.54/2.09 tff(5467,plain,
% 2.54/2.09 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[84, 5466])).
% 2.54/2.09 tff(5468,plain,
% 2.54/2.09 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[561, 5467])).
% 2.54/2.09 tff(5469,plain,
% 2.54/2.09 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[563, 5468, 34])).
% 2.54/2.09 tff(5470,plain,
% 2.54/2.09 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1194, 5469, 5460])).
% 2.54/2.09 tff(5471,plain,
% 2.54/2.09 (big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3887, 4769])).
% 2.54/2.09 tff(5472,plain,
% 2.54/2.09 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5471, 5470, 5469, 30, 40, 35])).
% 2.54/2.09 tff(5473,plain,
% 2.54/2.09 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[462, 5472])).
% 2.54/2.09 tff(5474,plain,
% 2.54/2.09 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3017, 5473])).
% 2.54/2.09 tff(5475,plain,
% 2.54/2.09 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3019, 5474])).
% 2.54/2.09 tff(5476,plain,
% 2.54/2.09 ((tptp_fun_X_2(Y!0) = W1!8) <=> (Y!0 = W1!8)),
% 2.54/2.09 inference(monotonicity,[status(thm)],[30])).
% 2.54/2.09 tff(5477,plain,
% 2.54/2.09 ((tptp_fun_X_2(Y!0) = W1!8) <=> (W1!8 = Y!0)),
% 2.54/2.09 inference(transitivity,[status(thm)],[5476, 1])).
% 2.54/2.09 tff(5478,plain,
% 2.54/2.09 ((W1!8 = Y!0) <=> (tptp_fun_X_2(Y!0) = W1!8)),
% 2.54/2.09 inference(symmetry,[status(thm)],[5477])).
% 2.54/2.09 tff(5479,plain,
% 2.54/2.09 ((~(W1!8 = Y!0)) <=> (~(tptp_fun_X_2(Y!0) = W1!8))),
% 2.54/2.09 inference(monotonicity,[status(thm)],[5478])).
% 2.54/2.09 tff(5480,plain,
% 2.54/2.09 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[576, 5469])).
% 2.54/2.09 tff(5481,plain,
% 2.54/2.09 (~(X!1 = tptp_fun_Z1_12(Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[578, 5470, 5480])).
% 2.54/2.09 tff(5482,plain,
% 2.54/2.09 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1264, 5481])).
% 2.54/2.09 tff(5483,plain,
% 2.54/2.09 (tptp_fun_Z1_12(Y!0) = Y!0),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[594, 5482])).
% 2.54/2.09 tff(5484,plain,
% 2.54/2.09 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1254, 5470, 40, 5460])).
% 2.54/2.09 tff(5485,plain,
% 2.54/2.09 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1256, 5484])).
% 2.54/2.09 tff(5486,plain,
% 2.54/2.09 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1269, 5473])).
% 2.54/2.09 tff(5487,plain,
% 2.54/2.09 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1271, 5486])).
% 2.54/2.09 tff(5488,plain,
% 2.54/2.09 (X!1 = W1!8),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1273, 5487, 5485])).
% 2.54/2.09 tff(5489,plain,
% 2.54/2.09 (W1!8 = X!1),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[28, 5488])).
% 2.54/2.09 tff(5490,plain,
% 2.54/2.09 (~(tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1296, 5489, 5482])).
% 2.54/2.09 tff(5491,plain,
% 2.54/2.09 (~(W1!8 = Y!0)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1287, 5490, 5483])).
% 2.54/2.09 tff(5492,plain,
% 2.54/2.09 (~(tptp_fun_X_2(Y!0) = W1!8)),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[5491, 5479])).
% 2.54/2.09 tff(5493,plain,
% 2.54/2.09 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3086, 5492, 5475])).
% 2.54/2.09 tff(5494,plain,
% 2.54/2.09 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3084, 5493])).
% 2.54/2.09 tff(5495,plain,
% 2.54/2.09 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(monotonicity,[status(thm)],[1789, 31])).
% 2.54/2.09 tff(5496,plain,
% 2.54/2.09 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(X!1, Y!0)),
% 2.54/2.09 inference(symmetry,[status(thm)],[5495])).
% 2.54/2.09 tff(5497,plain,
% 2.54/2.09 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (~big_f(X!1, Y!0))),
% 2.54/2.09 inference(monotonicity,[status(thm)],[5496])).
% 2.54/2.09 tff(5498,plain,
% 2.54/2.09 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3480, 1672, 5411])).
% 2.54/2.09 tff(5499,plain,
% 2.54/2.09 (~big_f(X!1, Y!0)),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[5498, 5497])).
% 2.54/2.09 tff(5500,plain,
% 2.54/2.09 ($false),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[4769, 5499])).
% 2.54/2.09 tff(5501,plain,((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.09 tff(5502,plain,
% 2.54/2.09 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5501, 5494, 30])).
% 2.54/2.09 tff(5503,plain,
% 2.54/2.09 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[2258, 5502])).
% 2.54/2.09 tff(5504,plain,
% 2.54/2.09 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X_2(Y!0)),
% 2.54/2.09 inference(transitivity,[status(thm)],[5503, 31])).
% 2.54/2.09 tff(5505,plain,
% 2.54/2.09 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.09 inference(monotonicity,[status(thm)],[5504, 30])).
% 2.54/2.09 tff(5506,plain,
% 2.54/2.09 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(symmetry,[status(thm)],[5505])).
% 2.54/2.09 tff(5507,plain,
% 2.54/2.09 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)))),
% 2.54/2.09 inference(monotonicity,[status(thm)],[5506])).
% 2.54/2.09 tff(5508,plain,
% 2.54/2.09 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[35, 5507])).
% 2.54/2.09 tff(5509,plain,
% 2.54/2.09 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3082, 5502, 5494])).
% 2.54/2.09 tff(5510,plain,
% 2.54/2.09 ($false),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5509, 5508])).
% 2.54/2.09 tff(5511,plain,(big_f(tptp_fun_X_2(Y!0), Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.09 tff(5512,plain,
% 2.54/2.09 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5511, 34, 30])).
% 2.54/2.09 tff(5513,plain,
% 2.54/2.09 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[692, 33])).
% 2.54/2.09 tff(5514,plain,
% 2.54/2.09 ((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3760, 4769])).
% 2.54/2.09 tff(5515,plain,
% 2.54/2.09 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5514, 622, 598])).
% 2.54/2.09 tff(5516,plain,
% 2.54/2.09 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[1219, 5515, 598, 30, 135, 692])).
% 2.54/2.09 tff(5517,plain,
% 2.54/2.09 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[462, 5516])).
% 2.54/2.09 tff(5518,plain,
% 2.54/2.09 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3017, 5517])).
% 2.54/2.09 tff(5519,plain,
% 2.54/2.09 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3266, 5518])).
% 2.54/2.09 tff(5520,plain,
% 2.54/2.09 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[481, 5517])).
% 2.54/2.09 tff(5521,plain,
% 2.54/2.09 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.54/2.09 inference(monotonicity,[status(thm)],[31, 598])).
% 2.54/2.09 tff(5522,plain,
% 2.54/2.09 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[135, 5521])).
% 2.54/2.09 tff(5523,plain,
% 2.54/2.09 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.54/2.09 inference(monotonicity,[status(thm)],[31, 1289])).
% 2.54/2.09 tff(5524,plain,
% 2.54/2.09 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Y!0, W1!8)),
% 2.54/2.09 inference(symmetry,[status(thm)],[5523])).
% 2.54/2.09 tff(5525,assumption,(big_f(tptp_fun_X_2(Y!0), X!1)), introduced(assumption)).
% 2.54/2.09 tff(5526,plain,
% 2.54/2.09 (big_f(Y!0, W1!8)),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[5525, 5524])).
% 2.54/2.09 tff(5527,plain,
% 2.54/2.09 (Y!0 = tptp_fun_Z1_9(W1!8)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[886, 5526, 511])).
% 2.54/2.09 tff(5528,plain,
% 2.54/2.09 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.54/2.09 inference(symmetry,[status(thm)],[5527])).
% 2.54/2.09 tff(5529,plain,
% 2.54/2.09 (big_f(X!1, W1!8)),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[622, 2633])).
% 2.54/2.09 tff(5530,plain,
% 2.54/2.09 (X!1 = tptp_fun_Z1_9(W1!8)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[923, 5529, 497])).
% 2.54/2.09 tff(5531,plain,
% 2.54/2.09 (X!1 = Y!0),
% 2.54/2.09 inference(transitivity,[status(thm)],[5530, 5528])).
% 2.54/2.09 tff(5532,plain,
% 2.54/2.09 ($false),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[741, 5531])).
% 2.54/2.09 tff(5533,plain,((~(W1!8 = X!1)) | (~big_f(tptp_fun_X_2(Y!0), X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.09 tff(5534,plain,
% 2.54/2.09 (~(W1!8 = X!1)),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[5533, 622, 30, 5522, 598, 5520])).
% 2.54/2.09 tff(5535,plain,
% 2.54/2.09 (W1!8 = Y!0),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[19, 5534])).
% 2.54/2.09 tff(5536,plain,
% 2.54/2.09 (tptp_fun_X_2(Y!0) = W1!8),
% 2.54/2.09 inference(modus_ponens,[status(thm)],[5535, 5478])).
% 2.54/2.09 tff(5537,plain,
% 2.54/2.09 (![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3268, 5536, 5519])).
% 2.54/2.09 tff(5538,plain,
% 2.54/2.09 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3235, 5537])).
% 2.54/2.09 tff(5539,plain,
% 2.54/2.09 (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(unit_resolution,[status(thm)],[3237, 5538, 5513])).
% 2.54/2.09 tff(5540,plain,
% 2.54/2.09 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = Y!0),
% 2.54/2.09 inference(symmetry,[status(thm)],[5539])).
% 2.54/2.09 tff(5541,plain,
% 2.54/2.09 (tptp_fun_Z1_9(Y!0) = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.54/2.09 inference(monotonicity,[status(thm)],[31])).
% 2.54/2.09 tff(5542,plain,
% 2.54/2.09 (tptp_fun_Z1_9(Y!0) = Y!0),
% 2.54/2.09 inference(transitivity,[status(thm)],[5541, 5540])).
% 2.54/2.09 tff(5543,plain,
% 2.54/2.09 ((X!1 = tptp_fun_Z1_9(Y!0)) <=> (X!1 = Y!0)),
% 2.54/2.09 inference(monotonicity,[status(thm)],[5542])).
% 2.54/2.09 tff(5544,plain,
% 2.54/2.09 ((X!1 = Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.54/2.09 inference(symmetry,[status(thm)],[5543])).
% 2.54/2.09 tff(5545,plain,
% 2.54/2.09 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_Z1_9(Y!0)))),
% 2.54/2.10 inference(monotonicity,[status(thm)],[5544])).
% 2.54/2.10 tff(5546,plain,
% 2.54/2.10 (~(X!1 = tptp_fun_Z1_9(Y!0))),
% 2.54/2.10 inference(modus_ponens,[status(thm)],[741, 5545])).
% 2.54/2.10 tff(5547,plain,
% 2.54/2.10 ((~(big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0)))) | (~big_f(X!1, Y!0)) | (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.54/2.10 inference(tautology,[status(thm)],[])).
% 2.54/2.10 tff(5548,plain,
% 2.54/2.10 (~(big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5547, 4769, 5546])).
% 2.54/2.10 tff(5549,plain,
% 2.54/2.10 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3003, 5517])).
% 2.54/2.10 tff(5550,plain,
% 2.54/2.10 ((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3286, 5549])).
% 2.54/2.10 tff(5551,plain,
% 2.54/2.10 (Y!0 = W1!8),
% 2.54/2.10 inference(modus_ponens,[status(thm)],[5535, 2])).
% 2.54/2.10 tff(5552,plain,
% 2.54/2.10 (![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3289, 5551, 5550])).
% 2.54/2.10 tff(5553,plain,
% 2.54/2.10 ($false),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3291, 5552, 5548])).
% 2.54/2.10 tff(5554,plain,((~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~big_f(tptp_fun_X_2(Y!0), Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.10 tff(5555,plain,
% 2.54/2.10 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5554, 598, 30, 135, 692])).
% 2.54/2.10 tff(5556,assumption,(~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))), introduced(assumption)).
% 2.54/2.10 tff(5557,plain,
% 2.54/2.10 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1713, 5556])).
% 2.54/2.10 tff(5558,plain,
% 2.54/2.10 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[222, 5556])).
% 2.54/2.10 tff(5559,plain,
% 2.54/2.10 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.54/2.10 inference(modus_ponens,[status(thm)],[692, 1142])).
% 2.54/2.10 tff(5560,plain,
% 2.54/2.10 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1413, 106, 598, 135])).
% 2.54/2.10 tff(5561,plain,
% 2.54/2.10 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1157, 5560, 3384])).
% 2.54/2.10 tff(5562,plain,
% 2.54/2.10 ($false),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5561, 5559])).
% 2.54/2.10 tff(5563,plain,((tptp_fun_X_2(X!1) = X!1) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.10 tff(5564,plain,
% 2.54/2.10 (tptp_fun_X_2(X!1) = X!1),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5563, 5558, 30, 598, 135, 692])).
% 2.54/2.10 tff(5565,plain,
% 2.54/2.10 ((~(tptp_fun_X_2(X!1) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3704, 4769])).
% 2.54/2.10 tff(5566,plain,
% 2.54/2.10 ($false),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5565, 5564, 5557, 598, 5555])).
% 2.54/2.10 tff(5567,plain,(((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~big_f(tptp_fun_X_2(Y!0), Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.10 tff(5568,plain,
% 2.54/2.10 ((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5567, 40, 30, 5460, 5512])).
% 2.54/2.10 tff(5569,plain,
% 2.54/2.10 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[220, 5568])).
% 2.54/2.10 tff(5570,plain,
% 2.54/2.10 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[82, 5569])).
% 2.54/2.10 tff(5571,plain,
% 2.54/2.10 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[88, 5570])).
% 2.54/2.10 tff(5572,plain,
% 2.54/2.10 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[191, 5571])).
% 2.54/2.10 tff(5573,plain,
% 2.54/2.10 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[90, 5571])).
% 2.54/2.10 tff(5574,plain,
% 2.54/2.10 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5554, 40, 30, 5460, 5512])).
% 2.54/2.10 tff(5575,plain,
% 2.54/2.10 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[2791, 277, 598, 135])).
% 2.54/2.10 tff(5576,plain,
% 2.54/2.10 (tptp_fun_X1_13(Y!0, X!1) = Y!0),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1118, 906, 277, 598, 42])).
% 2.54/2.10 tff(5577,plain,
% 2.54/2.10 ($false),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[2572, 5576, 906, 2569])).
% 2.54/2.10 tff(5578,plain,((~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.10 tff(5579,plain,
% 2.54/2.10 (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5578, 277, 598, 5575, 42])).
% 2.54/2.10 tff(5580,plain,
% 2.54/2.10 ($false),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[879, 5579, 631])).
% 2.54/2.10 tff(5581,plain,((~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(X!1, tptp_fun_Y1_11(Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.10 tff(5582,plain,
% 2.54/2.10 (~(tptp_fun_Y1_11(X!1) = X!1)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5581, 40, 5574, 5460, 5573])).
% 2.54/2.10 tff(5583,plain,
% 2.54/2.10 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[161, 5582, 5572])).
% 2.54/2.10 tff(5584,plain,
% 2.54/2.10 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3195, 5583])).
% 2.54/2.10 tff(5585,plain,
% 2.54/2.10 (tptp_fun_Y1_11(X!1) = Y!0),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[153, 5582])).
% 2.54/2.10 tff(5586,plain,
% 2.54/2.10 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.10 inference(monotonicity,[status(thm)],[31, 5585])).
% 2.54/2.10 tff(5587,plain,
% 2.54/2.10 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.54/2.10 inference(symmetry,[status(thm)],[5586])).
% 2.54/2.10 tff(5588,plain,
% 2.54/2.10 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.54/2.10 inference(modus_ponens,[status(thm)],[5512, 5587])).
% 2.54/2.10 tff(5589,plain,
% 2.54/2.10 (Y!0 = tptp_fun_Z1_12(X!1)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5389, 5588, 5584])).
% 2.54/2.10 tff(5590,plain,
% 2.54/2.10 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.54/2.10 inference(symmetry,[status(thm)],[5589])).
% 2.54/2.10 tff(5591,plain,
% 2.54/2.10 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> (X!1 = tptp_fun_Z1_12(X!1))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5376, 5583])).
% 2.54/2.10 tff(5592,plain,
% 2.54/2.10 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 2.54/2.10 inference(monotonicity,[status(thm)],[5585])).
% 2.54/2.10 tff(5593,plain,
% 2.54/2.10 (big_f(X!1, Y!0) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.54/2.10 inference(symmetry,[status(thm)],[5592])).
% 2.54/2.10 tff(5594,plain,
% 2.54/2.10 (big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.54/2.10 inference(modus_ponens,[status(thm)],[4769, 5593])).
% 2.54/2.10 tff(5595,plain,
% 2.54/2.10 (X!1 = tptp_fun_Z1_12(X!1)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5381, 5594, 5591])).
% 2.54/2.10 tff(5596,plain,
% 2.54/2.10 (X!1 = Y!0),
% 2.54/2.10 inference(transitivity,[status(thm)],[5595, 5590])).
% 2.54/2.10 tff(5597,plain,
% 2.54/2.10 ($false),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[741, 5596])).
% 2.54/2.10 tff(5598,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.10 tff(5599,plain,
% 2.54/2.10 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5598, 30])).
% 2.54/2.10 tff(5600,plain,
% 2.54/2.10 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.10 inference(monotonicity,[status(thm)],[31, 5599])).
% 2.54/2.10 tff(5601,plain,
% 2.54/2.10 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.54/2.10 inference(transitivity,[status(thm)],[5600, 33])).
% 2.54/2.10 tff(5602,plain,
% 2.54/2.10 ((~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3714, 4769])).
% 2.54/2.10 tff(5603,plain,
% 2.54/2.10 (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5602, 41, 5599])).
% 2.54/2.10 tff(5604,plain,
% 2.54/2.10 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[958, 5603])).
% 2.54/2.10 tff(5605,plain,
% 2.54/2.10 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[113, 5604, 5599])).
% 2.54/2.10 tff(5606,plain,
% 2.54/2.10 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[86, 5605])).
% 2.54/2.10 tff(5607,plain,
% 2.54/2.10 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[84, 5606])).
% 2.54/2.10 tff(5608,plain,
% 2.54/2.10 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[82, 5607])).
% 2.54/2.10 tff(5609,plain,
% 2.54/2.10 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[56, 5608])).
% 2.54/2.10 tff(5610,plain,
% 2.54/2.10 ((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[54, 5609])).
% 2.54/2.10 tff(5611,plain,
% 2.54/2.10 (![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[52, 5610, 30])).
% 2.54/2.10 tff(5612,plain,
% 2.54/2.10 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) <=> (tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[50, 5611])).
% 2.54/2.10 tff(5613,plain,
% 2.54/2.10 (~big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1139, 5612, 30, 41])).
% 2.54/2.10 tff(5614,plain,
% 2.54/2.10 (tptp_fun_X_2(X!1) = X!1),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1449, 5613, 30, 5599, 5608])).
% 2.54/2.10 tff(5615,plain,
% 2.54/2.10 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[220, 5608])).
% 2.54/2.10 tff(5616,plain,
% 2.54/2.10 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1713, 5615])).
% 2.54/2.10 tff(5617,plain,
% 2.54/2.10 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[1711, 5614, 5616])).
% 2.54/2.10 tff(5618,plain,
% 2.54/2.10 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3679, 5617])).
% 2.54/2.10 tff(5619,plain,
% 2.54/2.10 ((~(tptp_fun_Y_4(Y!0, X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3689, 4769])).
% 2.54/2.10 tff(5620,plain,
% 2.54/2.10 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5619, 5618, 5614])).
% 2.54/2.10 tff(5621,plain,
% 2.54/2.10 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[3694, 5620])).
% 2.54/2.10 tff(5622,plain,
% 2.54/2.10 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1)) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1)),
% 2.54/2.10 inference(monotonicity,[status(thm)],[5614])).
% 2.54/2.10 tff(5623,plain,
% 2.54/2.10 ((~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1))),
% 2.54/2.10 inference(monotonicity,[status(thm)],[5622])).
% 2.54/2.10 tff(5624,plain,
% 2.54/2.10 ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5042, 4769])).
% 2.54/2.10 tff(5625,plain,
% 2.54/2.10 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5624, 5614, 30, 5608, 5613])).
% 2.54/2.10 tff(5626,plain,
% 2.54/2.10 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[2258, 5625])).
% 2.54/2.10 tff(5627,plain,
% 2.54/2.10 ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), Y!0) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5162, 4769])).
% 2.54/2.10 tff(5628,plain,
% 2.54/2.10 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[5627, 5626, 30, 5613, 5608, 5614])).
% 2.54/2.10 tff(5629,plain,
% 2.54/2.10 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.54/2.10 inference(unit_resolution,[status(thm)],[462, 5628])).
% 2.54/2.10 tff(5630,plain,
% 2.54/2.10 (~((~((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(Y!0, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(Y!0, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(Y!0, X!1)))))))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5225, 5629])).
% 2.54/2.11 tff(5631,plain,
% 2.54/2.11 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5227, 5630])).
% 2.54/2.11 tff(5632,plain,
% 2.54/2.11 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) <=> (X!1 = W1!8)),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5621])).
% 2.54/2.11 tff(5633,plain,
% 2.54/2.11 ((tptp_fun_Y_4(Y!0, X!1) = W1!8) <=> (W1!8 = X!1)),
% 2.54/2.11 inference(transitivity,[status(thm)],[5632, 24])).
% 2.54/2.11 tff(5634,plain,
% 2.54/2.11 ((W1!8 = X!1) <=> (tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.11 inference(symmetry,[status(thm)],[5633])).
% 2.54/2.11 tff(5635,plain,
% 2.54/2.11 ((~(W1!8 = X!1)) <=> (~(tptp_fun_Y_4(Y!0, X!1) = W1!8))),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5634])).
% 2.54/2.11 tff(5636,plain,
% 2.54/2.11 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[1709, 5617])).
% 2.54/2.11 tff(5637,plain,
% 2.54/2.11 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[4944, 5620, 5618, 5636])).
% 2.54/2.11 tff(5638,plain,
% 2.54/2.11 (~(tptp_fun_Y_4(X!1, X!1) = X!1)),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[1677, 5637, 5636])).
% 2.54/2.11 tff(5639,plain,
% 2.54/2.11 (~((~((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1)))) | (~((~(tptp_fun_Y_4(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y_4(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y_4(X!1, X!1)))))))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[4962, 5629])).
% 2.54/2.11 tff(5640,plain,
% 2.54/2.11 ((tptp_fun_Y_4(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[4964, 5639])).
% 2.54/2.11 tff(5641,plain,
% 2.54/2.11 (tptp_fun_Y_4(X!1, X!1) = Y!0),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[1685, 5638])).
% 2.54/2.11 tff(5642,plain,
% 2.54/2.11 (tptp_fun_Y_4(X!1, X!1) = tptp_fun_X_2(Y!0)),
% 2.54/2.11 inference(transitivity,[status(thm)],[5641, 31])).
% 2.54/2.11 tff(5643,plain,
% 2.54/2.11 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5614, 5642])).
% 2.54/2.11 tff(5644,plain,
% 2.54/2.11 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = Y!0),
% 2.54/2.11 inference(transitivity,[status(thm)],[5643, 5626])).
% 2.54/2.11 tff(5645,plain,
% 2.54/2.11 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)) <=> (Y!0 = X!1)),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5644, 5614])).
% 2.54/2.11 tff(5646,plain,
% 2.54/2.11 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)) <=> (X!1 = Y!0)),
% 2.54/2.11 inference(transitivity,[status(thm)],[5645, 46])).
% 2.54/2.11 tff(5647,plain,
% 2.54/2.11 ((X!1 = Y!0) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.11 inference(symmetry,[status(thm)],[5646])).
% 2.54/2.11 tff(5648,plain,
% 2.54/2.11 ((~(X!1 = Y!0)) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)))),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5647])).
% 2.54/2.11 tff(5649,plain,
% 2.54/2.11 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.11 inference(modus_ponens,[status(thm)],[741, 5648])).
% 2.54/2.11 tff(5650,plain,
% 2.54/2.11 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(Y!0)),
% 2.54/2.11 inference(transitivity,[status(thm)],[5643, 5626, 31])).
% 2.54/2.11 tff(5651,plain,
% 2.54/2.11 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1)) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5650, 5641])).
% 2.54/2.11 tff(5652,plain,
% 2.54/2.11 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))),
% 2.54/2.11 inference(symmetry,[status(thm)],[5651])).
% 2.54/2.11 tff(5653,plain,
% 2.54/2.11 ((~big_f(tptp_fun_X_2(Y!0), Y!0)) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1)))),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5652])).
% 2.54/2.11 tff(5654,plain,
% 2.54/2.11 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))),
% 2.54/2.11 inference(modus_ponens,[status(thm)],[5613, 5653])).
% 2.54/2.11 tff(5655,plain,
% 2.54/2.11 ((~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)))) | big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1)) | (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.11 inference(tautology,[status(thm)],[])).
% 2.54/2.11 tff(5656,plain,
% 2.54/2.11 (~((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(X!1, X!1)) = tptp_fun_X_2(X!1)))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5655, 5654, 5649])).
% 2.54/2.11 tff(5657,plain,
% 2.54/2.11 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)), tptp_fun_Y_4(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(X!1, X!1)) = Z1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[4958, 5656])).
% 2.54/2.11 tff(5658,plain,
% 2.54/2.11 (tptp_fun_Y_4(X!1, X!1) = W1!8),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[4966, 5657, 5640])).
% 2.54/2.11 tff(5659,plain,
% 2.54/2.11 (~(W1!8 = X!1)),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[4972, 5658, 5638])).
% 2.54/2.11 tff(5660,plain,
% 2.54/2.11 (~(tptp_fun_Y_4(Y!0, X!1) = W1!8)),
% 2.54/2.11 inference(modus_ponens,[status(thm)],[5659, 5635])).
% 2.54/2.11 tff(5661,plain,
% 2.54/2.11 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y_4(Y!0, X!1)) = Z1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5250, 5660, 5631])).
% 2.54/2.11 tff(5662,plain,
% 2.54/2.11 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5252, 5661])).
% 2.54/2.11 tff(5663,plain,
% 2.54/2.11 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5621])).
% 2.54/2.11 tff(5664,plain,
% 2.54/2.11 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[3701, 5620, 5618])).
% 2.54/2.11 tff(5665,plain,
% 2.54/2.11 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.54/2.11 inference(modus_ponens,[status(thm)],[5664, 5663])).
% 2.54/2.11 tff(5666,plain,
% 2.54/2.11 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5265, 5662, 5621, 5665])).
% 2.54/2.11 tff(5667,plain,
% 2.54/2.11 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(X!1))),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5267, 5666, 5662])).
% 2.54/2.11 tff(5668,plain,
% 2.54/2.11 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = X!1)),
% 2.54/2.11 inference(modus_ponens,[status(thm)],[5667, 5623])).
% 2.54/2.11 tff(5669,plain,
% 2.54/2.11 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = Y!0),
% 2.54/2.11 inference(unit_resolution,[status(thm)],[5276, 5668])).
% 2.54/2.11 tff(5670,plain,
% 2.54/2.11 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X_2(Y!0)),
% 2.54/2.11 inference(transitivity,[status(thm)],[5669, 31])).
% 2.54/2.11 tff(5671,plain,
% 2.54/2.11 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5670, 5621])).
% 2.54/2.11 tff(5672,plain,
% 2.54/2.11 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.54/2.11 inference(symmetry,[status(thm)],[5671])).
% 2.54/2.11 tff(5673,plain,
% 2.54/2.11 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)))),
% 2.54/2.11 inference(monotonicity,[status(thm)],[5672])).
% 2.54/2.11 tff(5674,plain,
% 2.54/2.11 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (tptp_fun_Y_4(X!1, Y!0) = X!1)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[198, 5611])).
% 2.60/2.11 tff(5675,plain,
% 2.60/2.11 (tptp_fun_Y_4(X!1, Y!0) = X!1),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[218, 5674, 30, 5599, 41])).
% 2.60/2.11 tff(5676,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5675])).
% 2.60/2.11 tff(5677,plain,
% 2.60/2.11 ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))) <=> (~big_f(tptp_fun_X_2(Y!0), X!1))),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5676])).
% 2.60/2.11 tff(5678,plain,
% 2.60/2.11 (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(X!1, Y!0))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[236, 5675, 5674])).
% 2.60/2.11 tff(5679,plain,
% 2.60/2.11 (~big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5678, 5677])).
% 2.60/2.11 tff(5680,plain,
% 2.60/2.11 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5679, 5673])).
% 2.60/2.11 tff(5681,plain,
% 2.60/2.11 ($false),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[5666, 5680])).
% 2.60/2.11 tff(5682,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.11 tff(5683,plain,
% 2.60/2.11 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[5682, 30])).
% 2.60/2.11 tff(5684,plain,
% 2.60/2.11 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5683, 5601])).
% 2.60/2.11 tff(5685,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5683, 5600])).
% 2.60/2.11 tff(5686,plain,
% 2.60/2.11 (~(tptp_fun_Y_4(Y!0, Y!0) = Y!0)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[1341, 2847, 5685])).
% 2.60/2.11 tff(5687,plain,
% 2.60/2.11 (tptp_fun_Y_4(Y!0, Y!0) = X!1),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[95, 5686])).
% 2.60/2.11 tff(5688,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5687])).
% 2.60/2.11 tff(5689,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[2149, 2847, 30, 5599, 5683])).
% 2.60/2.11 tff(5690,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5689, 5688])).
% 2.60/2.11 tff(5691,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5685, 1142])).
% 2.60/2.11 tff(5692,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[684])).
% 2.60/2.11 tff(5693,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.11 inference(symmetry,[status(thm)],[5692])).
% 2.60/2.11 tff(5694,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5525, 5693])).
% 2.60/2.11 tff(5695,plain,
% 2.60/2.11 ($false),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[1157, 5694, 5691, 3384])).
% 2.60/2.11 tff(5696,plain,((tptp_fun_X_2(X!1) = X!1) | (~big_f(tptp_fun_X_2(Y!0), X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.11 tff(5697,plain,
% 2.60/2.11 (tptp_fun_X_2(X!1) = X!1),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[5696, 5690, 30, 1437])).
% 2.60/2.11 tff(5698,plain,
% 2.60/2.11 (X!1 = tptp_fun_X_2(X!1)),
% 2.60/2.11 inference(symmetry,[status(thm)],[5697])).
% 2.60/2.11 tff(5699,plain,
% 2.60/2.11 ((tptp_fun_Y1_11(Y!0) = Z!5) <=> (Y!0 = Z!5)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5599])).
% 2.60/2.11 tff(5700,plain,
% 2.60/2.11 ((tptp_fun_Y1_11(Y!0) = Z!5) <=> (Z!5 = Y!0)),
% 2.60/2.11 inference(transitivity,[status(thm)],[5699, 4557])).
% 2.60/2.11 tff(5701,plain,
% 2.60/2.11 ((~(tptp_fun_Y1_11(Y!0) = Z!5)) <=> (~(Z!5 = Y!0))),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5700])).
% 2.60/2.11 tff(5702,plain,
% 2.60/2.11 (Z!5 = tptp_fun_Y1_11(Y!0)),
% 2.60/2.11 inference(symmetry,[status(thm)],[1059])).
% 2.60/2.11 tff(5703,plain,
% 2.60/2.11 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.60/2.11 inference(transitivity,[status(thm)],[5702, 109, 31])).
% 2.60/2.11 tff(5704,plain,
% 2.60/2.11 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5703])).
% 2.60/2.11 tff(5705,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.60/2.11 inference(symmetry,[status(thm)],[5704])).
% 2.60/2.11 tff(5706,plain,
% 2.60/2.11 (big_f(Z!5, Y!0)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[692, 5705])).
% 2.60/2.11 tff(5707,plain,
% 2.60/2.11 (Y!0 = tptp_fun_W_6(Z!5)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[1209, 5706, 5072])).
% 2.60/2.11 tff(5708,plain,
% 2.60/2.11 (tptp_fun_W_6(Z!5) = Y!0),
% 2.60/2.11 inference(symmetry,[status(thm)],[5707])).
% 2.60/2.11 tff(5709,plain,
% 2.60/2.11 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5703, 2159])).
% 2.60/2.11 tff(5710,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0)) <=> big_f(Z!5, X!1)),
% 2.60/2.11 inference(symmetry,[status(thm)],[5709])).
% 2.60/2.11 tff(5711,plain,
% 2.60/2.11 (big_f(Z!5, X!1)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[2162, 5710])).
% 2.60/2.11 tff(5712,plain,
% 2.60/2.11 (X!1 = tptp_fun_W_6(Z!5)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[989, 5711, 984])).
% 2.60/2.11 tff(5713,plain,
% 2.60/2.11 (X!1 = Y!0),
% 2.60/2.11 inference(transitivity,[status(thm)],[5712, 5708])).
% 2.60/2.11 tff(5714,plain,
% 2.60/2.11 ($false),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[741, 5713])).
% 2.60/2.11 tff(5715,plain,((~(tptp_fun_Y1_11(Y!0) = Z!5)) | (~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(Y!0, Y!0))) | (~(tptp_fun_Y_4(Y!0, Y!0) = X!1)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.11 tff(5716,plain,
% 2.60/2.11 (~(tptp_fun_Y1_11(Y!0) = Z!5)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[5715, 5687, 30, 5599, 5685, 5689, 386])).
% 2.60/2.11 tff(5717,plain,
% 2.60/2.11 (~(Z!5 = Y!0)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5716, 5701])).
% 2.60/2.11 tff(5718,plain,
% 2.60/2.11 (Z!5 = X!1),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[361, 5717])).
% 2.60/2.11 tff(5719,plain,
% 2.60/2.11 (Z!5 = tptp_fun_X_2(X!1)),
% 2.60/2.11 inference(transitivity,[status(thm)],[5718, 5698])).
% 2.60/2.11 tff(5720,plain,
% 2.60/2.11 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5719])).
% 2.60/2.11 tff(5721,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Z!5, X!1)),
% 2.60/2.11 inference(symmetry,[status(thm)],[5720])).
% 2.60/2.11 tff(5722,plain,
% 2.60/2.11 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[1711, 5697, 2485])).
% 2.60/2.11 tff(5723,plain,
% 2.60/2.11 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[3679, 5722])).
% 2.60/2.11 tff(5724,plain,
% 2.60/2.11 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[5619, 5723, 5697])).
% 2.60/2.11 tff(5725,plain,
% 2.60/2.11 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[3694, 5724])).
% 2.60/2.11 tff(5726,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5725])).
% 2.60/2.11 tff(5727,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[3701, 5724, 5723])).
% 2.60/2.11 tff(5728,plain,
% 2.60/2.11 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5727, 5726])).
% 2.60/2.11 tff(5729,plain,
% 2.60/2.11 (big_f(Z!5, X!1)),
% 2.60/2.11 inference(modus_ponens,[status(thm)],[5728, 5721])).
% 2.60/2.11 tff(5730,plain,
% 2.60/2.11 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[2167, 5687, 30, 341, 5689, 5685])).
% 2.60/2.11 tff(5731,plain,
% 2.60/2.11 (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[321, 5730])).
% 2.60/2.11 tff(5732,plain,
% 2.60/2.11 ((~(big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1)))) | (Y!0 = tptp_fun_W_6(X!1))),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[3751, 4769])).
% 2.60/2.11 tff(5733,plain,
% 2.60/2.11 (Y!0 = tptp_fun_W_6(X!1)),
% 2.60/2.11 inference(unit_resolution,[status(thm)],[5732, 5731])).
% 2.60/2.11 tff(5734,plain,
% 2.60/2.11 (tptp_fun_W_6(X!1) = Y!0),
% 2.60/2.11 inference(symmetry,[status(thm)],[5733])).
% 2.60/2.11 tff(5735,plain,
% 2.60/2.11 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(X!1)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5718])).
% 2.60/2.11 tff(5736,plain,
% 2.60/2.11 (tptp_fun_W_6(Z!5) = Y!0),
% 2.60/2.11 inference(transitivity,[status(thm)],[5735, 5734])).
% 2.60/2.11 tff(5737,plain,
% 2.60/2.11 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = Y!0)),
% 2.60/2.11 inference(monotonicity,[status(thm)],[5736])).
% 2.60/2.11 tff(5738,plain,
% 2.60/2.11 ((X!1 = Y!0) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.60/2.11 inference(symmetry,[status(thm)],[5737])).
% 2.60/2.12 tff(5739,plain,
% 2.60/2.12 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_W_6(Z!5)))),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5738])).
% 2.60/2.12 tff(5740,plain,
% 2.60/2.12 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[741, 5739])).
% 2.60/2.12 tff(5741,plain,
% 2.60/2.12 ((~(big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5)))) | (~big_f(Z!5, X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[989, 5740])).
% 2.60/2.12 tff(5742,plain,
% 2.60/2.12 (~big_f(Z!5, X!1)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5741, 1212])).
% 2.60/2.12 tff(5743,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5742, 5729])).
% 2.60/2.12 tff(5744,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5745,plain,
% 2.60/2.12 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5744, 341, 30])).
% 2.60/2.12 tff(5746,plain,
% 2.60/2.12 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[82, 5745])).
% 2.60/2.12 tff(5747,plain,
% 2.60/2.12 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[88, 5746])).
% 2.60/2.12 tff(5748,plain,
% 2.60/2.12 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[191, 5747])).
% 2.60/2.12 tff(5749,plain,
% 2.60/2.12 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[3195, 162])).
% 2.60/2.12 tff(5750,plain,
% 2.60/2.12 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[5685, 3728])).
% 2.60/2.12 tff(5751,plain,
% 2.60/2.12 (Y!0 = tptp_fun_Z1_12(X!1)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5389, 5750, 5749])).
% 2.60/2.12 tff(5752,plain,
% 2.60/2.12 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.60/2.12 inference(symmetry,[status(thm)],[5751])).
% 2.60/2.12 tff(5753,plain,
% 2.60/2.12 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> (X!1 = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5376, 162])).
% 2.60/2.12 tff(5754,plain,
% 2.60/2.12 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[154])).
% 2.60/2.12 tff(5755,plain,
% 2.60/2.12 (big_f(X!1, Y!0) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(symmetry,[status(thm)],[5754])).
% 2.60/2.12 tff(5756,plain,
% 2.60/2.12 (big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[4769, 5755])).
% 2.60/2.12 tff(5757,plain,
% 2.60/2.12 (X!1 = tptp_fun_Z1_12(X!1)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5381, 5756, 5753])).
% 2.60/2.12 tff(5758,plain,
% 2.60/2.12 (X!1 = Y!0),
% 2.60/2.12 inference(transitivity,[status(thm)],[5757, 5752])).
% 2.60/2.12 tff(5759,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[741, 5758])).
% 2.60/2.12 tff(5760,plain,((tptp_fun_Y1_11(X!1) = X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5761,plain,
% 2.60/2.12 (tptp_fun_Y1_11(X!1) = X!1),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5760, 5748, 30])).
% 2.60/2.12 tff(5762,plain,
% 2.60/2.12 ((X!1 = tptp_fun_Z1_12(X!1)) <=> (tptp_fun_Z1_12(X!1) = X!1)),
% 2.60/2.12 inference(commutativity,[status(thm)],[])).
% 2.60/2.12 tff(5763,plain,
% 2.60/2.12 (tptp_fun_Z1_12(X!1) = X!1),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[5757, 5762])).
% 2.60/2.12 tff(5764,plain,
% 2.60/2.12 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[759, 162])).
% 2.60/2.12 tff(5765,assumption,(![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))), introduced(assumption)).
% 2.60/2.12 tff(5766,plain,
% 2.60/2.12 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[3195, 5765])).
% 2.60/2.12 tff(5767,plain,
% 2.60/2.12 (big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[171, 5765])).
% 2.60/2.12 tff(5768,plain,
% 2.60/2.12 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[759, 5765])).
% 2.60/2.12 tff(5769,assumption,(Y!0 = tptp_fun_Z1_12(X!1)), introduced(assumption)).
% 2.60/2.12 tff(5770,plain,
% 2.60/2.12 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.60/2.12 inference(symmetry,[status(thm)],[5769])).
% 2.60/2.12 tff(5771,plain,
% 2.60/2.12 ((tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5770])).
% 2.60/2.12 tff(5772,plain,
% 2.60/2.12 ((tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(symmetry,[status(thm)],[5771])).
% 2.60/2.12 tff(5773,plain,
% 2.60/2.12 ((~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)) <=> (~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5772])).
% 2.60/2.12 tff(5774,plain,
% 2.60/2.12 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[5769, 3192])).
% 2.60/2.12 tff(5775,plain,
% 2.60/2.12 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[772, 5774, 769, 761])).
% 2.60/2.12 tff(5776,plain,
% 2.60/2.12 (~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[776, 5775, 761])).
% 2.60/2.12 tff(5777,plain,
% 2.60/2.12 (~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[5776, 5773])).
% 2.60/2.12 tff(5778,assumption,(big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))), introduced(assumption)).
% 2.60/2.12 tff(5779,plain,
% 2.60/2.12 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[774, 5775, 5778])).
% 2.60/2.12 tff(5780,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5779, 5777])).
% 2.60/2.12 tff(5781,plain,((~(Y!0 = tptp_fun_Z1_12(X!1))) | (~(big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))) | (~big_f(tptp_fun_Z1_12(X!1), tptp_fun_Y1_11(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5782,plain,
% 2.60/2.12 (~(Y!0 = tptp_fun_Z1_12(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5781, 5768, 761, 5767])).
% 2.60/2.12 tff(5783,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5389, 5782, 5766, 2569])).
% 2.60/2.12 tff(5784,plain,((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5785,plain,
% 2.60/2.12 (~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5784, 5750, 162])).
% 2.60/2.12 tff(5786,assumption,(~((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))), introduced(assumption)).
% 2.60/2.12 tff(5787,plain,
% 2.60/2.12 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(monotonicity,[status(thm)],[240, 1786])).
% 2.60/2.12 tff(5788,plain,
% 2.60/2.12 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.60/2.12 inference(symmetry,[status(thm)],[5787])).
% 2.60/2.12 tff(5789,plain,
% 2.60/2.12 (((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)) | big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.60/2.12 inference(tautology,[status(thm)],[])).
% 2.60/2.12 tff(5790,plain,
% 2.60/2.12 (~(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5789, 763, 5786])).
% 2.60/2.12 tff(5791,plain,
% 2.60/2.12 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = X!1),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[781, 5790])).
% 2.60/2.12 tff(5792,plain,
% 2.60/2.12 (X!1 = tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(symmetry,[status(thm)],[5791])).
% 2.60/2.12 tff(5793,plain,
% 2.60/2.12 (X!1 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.60/2.12 inference(transitivity,[status(thm)],[5792, 5788])).
% 2.60/2.12 tff(5794,plain,
% 2.60/2.12 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5793])).
% 2.60/2.12 tff(5795,plain,
% 2.60/2.12 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.60/2.12 inference(symmetry,[status(thm)],[5794])).
% 2.60/2.12 tff(5796,plain,
% 2.60/2.12 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)) <=> (~big_f(X!1, Y!0))),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5795])).
% 2.60/2.12 tff(5797,plain,
% 2.60/2.12 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5788, 796])).
% 2.60/2.12 tff(5798,plain,
% 2.60/2.12 ((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0))),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5797])).
% 2.60/2.12 tff(5799,plain,
% 2.60/2.12 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[763, 5798])).
% 2.60/2.12 tff(5800,plain,
% 2.60/2.12 (~big_f(X!1, Y!0)),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[5799, 5796])).
% 2.60/2.12 tff(5801,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[3678, 5800])).
% 2.60/2.12 tff(5802,plain,(big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | ((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5803,plain,
% 2.60/2.12 (big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5802, 5786, 3678, 796, 240])).
% 2.60/2.12 tff(5804,plain,
% 2.60/2.12 (((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)) | (~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) | (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.60/2.12 inference(tautology,[status(thm)],[])).
% 2.60/2.12 tff(5805,plain,
% 2.60/2.12 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5804, 5803, 5786])).
% 2.60/2.12 tff(5806,plain,
% 2.60/2.12 (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[774, 5803, 5778])).
% 2.60/2.12 tff(5807,plain,
% 2.60/2.12 (tptp_fun_Z1_12(X!1) = tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(symmetry,[status(thm)],[5806])).
% 2.60/2.12 tff(5808,plain,
% 2.60/2.12 (X!1 = tptp_fun_Z1_12(X!1)),
% 2.60/2.12 inference(symmetry,[status(thm)],[176])).
% 2.60/2.12 tff(5809,plain,
% 2.60/2.12 (X!1 = Y!0),
% 2.60/2.12 inference(transitivity,[status(thm)],[5808, 5807, 5805])).
% 2.60/2.12 tff(5810,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[741, 5809])).
% 2.60/2.12 tff(5811,plain,(((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)) | (~(tptp_fun_Z1_12(X!1) = X!1)) | (~(big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5812,plain,
% 2.60/2.12 (((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)) | (~(tptp_fun_Z1_12(X!1) = X!1)) | (~(big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5811, 4769])).
% 2.60/2.12 tff(5813,plain,
% 2.60/2.12 (~(tptp_fun_Z1_12(X!1) = X!1)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5812, 5785, 240, 154, 5764])).
% 2.60/2.12 tff(5814,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5813, 5763])).
% 2.60/2.12 tff(5815,plain,((tptp_fun_Y1_11(X!1) = X!1) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5816,plain,
% 2.60/2.12 (tptp_fun_Y1_11(X!1) = X!1),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5815, 240, 30, 5748])).
% 2.60/2.12 tff(5817,plain,
% 2.60/2.12 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[90, 5747])).
% 2.60/2.12 tff(5818,plain,
% 2.60/2.12 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[269, 5816, 5817])).
% 2.60/2.12 tff(5819,plain,
% 2.60/2.12 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[879, 5818])).
% 2.60/2.12 tff(5820,plain,
% 2.60/2.12 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[31, 5816])).
% 2.60/2.12 tff(5821,plain,
% 2.60/2.12 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.12 inference(symmetry,[status(thm)],[5820])).
% 2.60/2.12 tff(5822,plain,
% 2.60/2.12 (X!1 = tptp_fun_Y1_11(X!1)),
% 2.60/2.12 inference(symmetry,[status(thm)],[5816])).
% 2.60/2.12 tff(5823,assumption,(~big_f(tptp_fun_X_2(Y!0), X!1)), introduced(assumption)).
% 2.60/2.12 tff(5824,plain,
% 2.60/2.12 (~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[703, 693, 30, 5685])).
% 2.60/2.12 tff(5825,plain,
% 2.60/2.12 (tptp_fun_Y_7(Y!0, Y!0) = X!1),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[708, 5824])).
% 2.60/2.12 tff(5826,plain,
% 2.60/2.12 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[31, 5825])).
% 2.60/2.12 tff(5827,plain,
% 2.60/2.12 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.60/2.12 inference(symmetry,[status(thm)],[5826])).
% 2.60/2.12 tff(5828,plain,
% 2.60/2.12 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)))),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5827])).
% 2.60/2.12 tff(5829,plain,
% 2.60/2.12 (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.60/2.12 inference(modus_ponens,[status(thm)],[5823, 5828])).
% 2.60/2.12 tff(5830,plain,
% 2.60/2.12 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[714, 5824, 693])).
% 2.60/2.12 tff(5831,plain,
% 2.60/2.12 ($false),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5830, 5829])).
% 2.60/2.12 tff(5832,plain,((~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | big_f(tptp_fun_X_2(Y!0), X!1) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.12 tff(5833,plain,
% 2.60/2.12 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[5832, 5823, 30])).
% 2.60/2.12 tff(5834,plain,
% 2.60/2.12 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[720, 5833])).
% 2.60/2.12 tff(5835,plain,
% 2.60/2.12 (Y!0 = Z!5),
% 2.60/2.12 inference(unit_resolution,[status(thm)],[725, 5834, 724])).
% 2.60/2.12 tff(5836,plain,
% 2.60/2.12 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y_7(Z!5, X!1)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5835])).
% 2.60/2.12 tff(5837,plain,
% 2.60/2.12 ((tptp_fun_Y_7(Y!0, X!1) = Y!0) <=> (tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5836])).
% 2.60/2.12 tff(5838,plain,
% 2.60/2.12 ((~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) <=> (~(tptp_fun_Y_7(Z!5, X!1) = Y!0))),
% 2.60/2.12 inference(monotonicity,[status(thm)],[5837])).
% 2.60/2.13 tff(5839,plain,
% 2.60/2.13 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[3366, 5834, 341])).
% 2.60/2.13 tff(5840,plain,
% 2.60/2.13 ((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[1842, 5839])).
% 2.60/2.13 tff(5841,plain,
% 2.60/2.13 ((~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) | (~((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[3872, 4769])).
% 2.60/2.13 tff(5842,plain,
% 2.60/2.13 (~(tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5841, 5840])).
% 2.60/2.13 tff(5843,plain,
% 2.60/2.13 (~(tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5842, 5838])).
% 2.60/2.13 tff(5844,plain,
% 2.60/2.13 (tptp_fun_Y_7(Z!5, X!1) = X!1),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[3878, 5843])).
% 2.60/2.13 tff(5845,plain,
% 2.60/2.13 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y1_11(X!1)),
% 2.60/2.13 inference(transitivity,[status(thm)],[5836, 5844, 5822])).
% 2.60/2.13 tff(5846,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5845])).
% 2.60/2.13 tff(5847,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.60/2.13 inference(symmetry,[status(thm)],[5846])).
% 2.60/2.13 tff(5848,plain,
% 2.60/2.13 ((~big_f(X!1, tptp_fun_Y1_11(X!1))) <=> (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1)))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5847])).
% 2.60/2.13 tff(5849,plain,
% 2.60/2.13 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[271, 5818])).
% 2.60/2.13 tff(5850,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[258])).
% 2.60/2.13 tff(5851,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5850])).
% 2.60/2.13 tff(5852,plain,
% 2.60/2.13 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X_2(X!1), X!1))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5851])).
% 2.60/2.13 tff(5853,plain,
% 2.60/2.13 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5823, 5852])).
% 2.60/2.13 tff(5854,plain,
% 2.60/2.13 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[1518, 5853, 5816, 240, 5849])).
% 2.60/2.13 tff(5855,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5854])).
% 2.60/2.13 tff(5856,plain,
% 2.60/2.13 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (~big_f(X!1, tptp_fun_Y1_11(X!1)))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5855])).
% 2.60/2.13 tff(5857,plain,
% 2.60/2.13 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[316, 5854, 5849])).
% 2.60/2.13 tff(5858,plain,
% 2.60/2.13 (~big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5857, 5856])).
% 2.60/2.13 tff(5859,plain,
% 2.60/2.13 (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5858, 5848])).
% 2.60/2.13 tff(5860,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[1844, 5842, 5840])).
% 2.60/2.13 tff(5861,plain,
% 2.60/2.13 ($false),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5860, 5859])).
% 2.60/2.13 tff(5862,plain,(big_f(tptp_fun_X_2(Y!0), X!1) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.13 tff(5863,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5862, 240, 30, 341])).
% 2.60/2.13 tff(5864,plain,
% 2.60/2.13 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5863, 5821])).
% 2.60/2.13 tff(5865,plain,
% 2.60/2.13 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[2572, 5864, 5819])).
% 2.60/2.13 tff(5866,plain,
% 2.60/2.13 (tptp_fun_X1_13(Y!0, X!1) = X!1),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[915, 5865])).
% 2.60/2.13 tff(5867,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5866])).
% 2.60/2.13 tff(5868,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[920, 5865, 5819])).
% 2.60/2.13 tff(5869,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5868, 5867])).
% 2.60/2.13 tff(5870,plain,
% 2.60/2.13 (big_f(X!1, X!1) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[889])).
% 2.60/2.13 tff(5871,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(X!1, X!1)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5870])).
% 2.60/2.13 tff(5872,assumption,(big_f(X!1, tptp_fun_Y1_11(X!1))), introduced(assumption)).
% 2.60/2.13 tff(5873,plain,
% 2.60/2.13 (big_f(X!1, X!1)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5872, 5871])).
% 2.60/2.13 tff(5874,plain,
% 2.60/2.13 (Y!0 = tptp_fun_W_6(X!1)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5732, 322])).
% 2.60/2.13 tff(5875,plain,
% 2.60/2.13 (tptp_fun_W_6(X!1) = Y!0),
% 2.60/2.13 inference(symmetry,[status(thm)],[5874])).
% 2.60/2.13 tff(5876,plain,
% 2.60/2.13 ((X!1 = tptp_fun_W_6(X!1)) <=> (X!1 = Y!0)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5875])).
% 2.60/2.13 tff(5877,plain,
% 2.60/2.13 ((X!1 = Y!0) <=> (X!1 = tptp_fun_W_6(X!1))),
% 2.60/2.13 inference(symmetry,[status(thm)],[5876])).
% 2.60/2.13 tff(5878,plain,
% 2.60/2.13 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_W_6(X!1)))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5877])).
% 2.60/2.13 tff(5879,plain,
% 2.60/2.13 (~(X!1 = tptp_fun_W_6(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[741, 5878])).
% 2.60/2.13 tff(5880,plain,
% 2.60/2.13 ($false),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[3758, 5879, 5873, 3747])).
% 2.60/2.13 tff(5881,plain,((~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))) | (~big_f(X!1, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.13 tff(5882,plain,
% 2.60/2.13 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5881, 5869, 5816])).
% 2.60/2.13 tff(5883,plain,
% 2.60/2.13 (~(X!1 = Z!5)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[346, 5882, 345])).
% 2.60/2.13 tff(5884,plain,
% 2.60/2.13 (~(Z!5 = X!1)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[353, 5883])).
% 2.60/2.13 tff(5885,plain,
% 2.60/2.13 (Z!5 = Y!0),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[361, 5884])).
% 2.60/2.13 tff(5886,plain,
% 2.60/2.13 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.60/2.13 inference(transitivity,[status(thm)],[5885, 31])).
% 2.60/2.13 tff(5887,plain,
% 2.60/2.13 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5886])).
% 2.60/2.13 tff(5888,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5887])).
% 2.60/2.13 tff(5889,plain,
% 2.60/2.13 (big_f(Z!5, Y!0)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5685, 5888])).
% 2.60/2.13 tff(5890,plain,
% 2.60/2.13 (Y!0 = tptp_fun_W_6(Z!5)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[1209, 5889, 388])).
% 2.60/2.13 tff(5891,plain,
% 2.60/2.13 (tptp_fun_W_6(Z!5) = Y!0),
% 2.60/2.13 inference(symmetry,[status(thm)],[5890])).
% 2.60/2.13 tff(5892,plain,
% 2.60/2.13 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5886])).
% 2.60/2.13 tff(5893,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Z!5, X!1)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5892])).
% 2.60/2.13 tff(5894,plain,
% 2.60/2.13 (big_f(Z!5, X!1)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5863, 5893])).
% 2.60/2.13 tff(5895,plain,
% 2.60/2.13 (X!1 = tptp_fun_W_6(Z!5)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[989, 5894, 1212])).
% 2.60/2.13 tff(5896,plain,
% 2.60/2.13 (X!1 = Y!0),
% 2.60/2.13 inference(transitivity,[status(thm)],[5895, 5891])).
% 2.60/2.13 tff(5897,plain,
% 2.60/2.13 ($false),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[741, 5896])).
% 2.60/2.13 tff(5898,plain,((~(tptp_fun_X_2(X!1) = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.13 tff(5899,plain,
% 2.60/2.13 (~(tptp_fun_X_2(X!1) = Y!0)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5898, 341, 30])).
% 2.60/2.13 tff(5900,plain,
% 2.60/2.13 (tptp_fun_X_2(X!1) = X!1),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[105, 5899])).
% 2.60/2.13 tff(5901,plain,
% 2.60/2.13 (X!1 = tptp_fun_X_2(X!1)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5900])).
% 2.60/2.13 tff(5902,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5901, 5761])).
% 2.60/2.13 tff(5903,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(symmetry,[status(thm)],[5902])).
% 2.60/2.13 tff(5904,plain,
% 2.60/2.13 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[269, 5761, 5817])).
% 2.60/2.13 tff(5905,plain,
% 2.60/2.13 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[879, 5904])).
% 2.60/2.13 tff(5906,plain,
% 2.60/2.13 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[31, 5761])).
% 2.60/2.13 tff(5907,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(symmetry,[status(thm)],[5906])).
% 2.60/2.13 tff(5908,plain,
% 2.60/2.13 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[271, 5904])).
% 2.60/2.13 tff(5909,plain,
% 2.60/2.13 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_X_2(Y!0)),
% 2.60/2.13 inference(transitivity,[status(thm)],[286, 31])).
% 2.60/2.13 tff(5910,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5909, 277])).
% 2.60/2.13 tff(5911,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(symmetry,[status(thm)],[5910])).
% 2.60/2.13 tff(5912,plain,
% 2.60/2.13 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5911])).
% 2.60/2.13 tff(5913,plain,
% 2.60/2.13 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5823, 5912])).
% 2.60/2.13 tff(5914,plain,
% 2.60/2.13 ($false),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[292, 5913])).
% 2.60/2.13 tff(5915,plain,((tptp_fun_X1_13(X!1, X!1) = X!1) | big_f(tptp_fun_X_2(Y!0), X!1) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.13 tff(5916,plain,
% 2.60/2.13 (tptp_fun_X1_13(X!1, X!1) = X!1),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5915, 5823, 5761, 30, 5908])).
% 2.60/2.13 tff(5917,plain,
% 2.60/2.13 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_X_2(X!1)),
% 2.60/2.13 inference(transitivity,[status(thm)],[5916, 5901])).
% 2.60/2.13 tff(5918,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5917, 5761])).
% 2.60/2.13 tff(5919,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(symmetry,[status(thm)],[5918])).
% 2.60/2.13 tff(5920,plain,
% 2.60/2.13 (tptp_fun_Y_7(Z!5, X!1) = tptp_fun_Y_7(Y!0, X!1)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5836])).
% 2.60/2.13 tff(5921,plain,
% 2.60/2.13 ((tptp_fun_Y_7(Z!5, X!1) = Y!0) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5920])).
% 2.60/2.13 tff(5922,plain,
% 2.60/2.13 ((tptp_fun_Y_7(Y!0, X!1) = Y!0) <=> (tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5921])).
% 2.60/2.13 tff(5923,plain,
% 2.60/2.13 ((~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) <=> (~(tptp_fun_Y_7(Z!5, X!1) = Y!0))),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5922])).
% 2.60/2.13 tff(5924,plain,
% 2.60/2.13 (~(tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5842, 5923])).
% 2.60/2.13 tff(5925,plain,
% 2.60/2.13 (tptp_fun_Y_7(Z!5, X!1) = X!1),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[3878, 5924])).
% 2.60/2.13 tff(5926,plain,
% 2.60/2.13 (tptp_fun_Y_7(Y!0, X!1) = X!1),
% 2.60/2.13 inference(transitivity,[status(thm)],[5836, 5925])).
% 2.60/2.13 tff(5927,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5901, 5926])).
% 2.60/2.13 tff(5928,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5860, 5927])).
% 2.60/2.13 tff(5929,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5928, 5919])).
% 2.60/2.13 tff(5930,plain,
% 2.60/2.13 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[316, 5916, 5908])).
% 2.60/2.13 tff(5931,plain,
% 2.60/2.13 ($false),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5930, 5929])).
% 2.60/2.13 tff(5932,plain,(big_f(tptp_fun_X_2(Y!0), X!1) | (~(tptp_fun_X_2(Y!0) = Y!0)) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.13 tff(5933,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5932, 341, 30])).
% 2.60/2.13 tff(5934,plain,
% 2.60/2.13 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5933, 5907])).
% 2.60/2.13 tff(5935,plain,
% 2.60/2.13 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[2572, 5934, 5905])).
% 2.60/2.13 tff(5936,plain,
% 2.60/2.13 (tptp_fun_X1_13(Y!0, X!1) = X!1),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[915, 5935])).
% 2.60/2.13 tff(5937,plain,
% 2.60/2.13 (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_X_2(X!1)),
% 2.60/2.13 inference(transitivity,[status(thm)],[5936, 5901])).
% 2.60/2.13 tff(5938,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5937, 5761])).
% 2.60/2.13 tff(5939,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(transitivity,[status(thm)],[5938, 5903])).
% 2.60/2.13 tff(5940,plain,
% 2.60/2.13 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[920, 5935, 5905])).
% 2.60/2.13 tff(5941,plain,
% 2.60/2.13 (big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5940, 5939])).
% 2.60/2.13 tff(5942,plain,
% 2.60/2.13 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5881, 5941, 5761])).
% 2.60/2.13 tff(5943,plain,
% 2.60/2.13 (~(X!1 = Z!5)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[346, 5942, 345])).
% 2.60/2.13 tff(5944,plain,
% 2.60/2.13 (~(Z!5 = X!1)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[353, 5943])).
% 2.60/2.13 tff(5945,plain,
% 2.60/2.13 (Z!5 = Y!0),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[361, 5944])).
% 2.60/2.13 tff(5946,plain,
% 2.60/2.13 (Z!5 = tptp_fun_X_2(Y!0)),
% 2.60/2.13 inference(transitivity,[status(thm)],[5945, 31])).
% 2.60/2.13 tff(5947,plain,
% 2.60/2.13 (big_f(Z!5, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5946])).
% 2.60/2.13 tff(5948,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(Z!5, Y!0)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5947])).
% 2.60/2.13 tff(5949,plain,
% 2.60/2.13 (big_f(Z!5, Y!0)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5685, 5948])).
% 2.60/2.13 tff(5950,plain,
% 2.60/2.13 (Y!0 = tptp_fun_W_6(Z!5)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[1209, 5949, 388])).
% 2.60/2.13 tff(5951,plain,
% 2.60/2.13 (tptp_fun_W_6(Z!5) = Y!0),
% 2.60/2.13 inference(symmetry,[status(thm)],[5950])).
% 2.60/2.13 tff(5952,plain,
% 2.60/2.13 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.13 inference(monotonicity,[status(thm)],[5946])).
% 2.60/2.13 tff(5953,plain,
% 2.60/2.13 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Z!5, X!1)),
% 2.60/2.13 inference(symmetry,[status(thm)],[5952])).
% 2.60/2.13 tff(5954,plain,
% 2.60/2.13 (big_f(Z!5, X!1)),
% 2.60/2.13 inference(modus_ponens,[status(thm)],[5933, 5953])).
% 2.60/2.13 tff(5955,plain,
% 2.60/2.13 (X!1 = tptp_fun_W_6(Z!5)),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[989, 5954, 1212])).
% 2.60/2.13 tff(5956,plain,
% 2.60/2.13 (X!1 = Y!0),
% 2.60/2.13 inference(transitivity,[status(thm)],[5955, 5951])).
% 2.60/2.13 tff(5957,plain,
% 2.60/2.13 ($false),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[741, 5956])).
% 2.60/2.13 tff(5958,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.13 tff(5959,plain,
% 2.60/2.13 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.60/2.13 inference(unit_resolution,[status(thm)],[5958, 30])).
% 2.60/2.13 tff(5960,plain,
% 2.60/2.13 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[462, 5959])).
% 2.60/2.14 tff(5961,plain,
% 2.60/2.14 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3017, 5960])).
% 2.60/2.14 tff(5962,plain,
% 2.60/2.14 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3266, 5961])).
% 2.60/2.14 tff(5963,plain,
% 2.60/2.14 (tptp_fun_X_2(Y!0) = W1!8),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[486, 5478])).
% 2.60/2.14 tff(5964,plain,
% 2.60/2.14 (![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3268, 5963, 5962])).
% 2.60/2.14 tff(5965,plain,
% 2.60/2.14 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3235, 5964])).
% 2.60/2.14 tff(5966,plain,
% 2.60/2.14 (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3237, 5965, 5684])).
% 2.60/2.14 tff(5967,plain,
% 2.60/2.14 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = Y!0),
% 2.60/2.14 inference(symmetry,[status(thm)],[5966])).
% 2.60/2.14 tff(5968,plain,
% 2.60/2.14 (tptp_fun_Z1_9(Y!0) = Y!0),
% 2.60/2.14 inference(transitivity,[status(thm)],[5541, 5967])).
% 2.60/2.14 tff(5969,plain,
% 2.60/2.14 ((X!1 = tptp_fun_Z1_9(Y!0)) <=> (X!1 = Y!0)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[5968])).
% 2.60/2.14 tff(5970,plain,
% 2.60/2.14 ((X!1 = Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.60/2.14 inference(symmetry,[status(thm)],[5969])).
% 2.60/2.14 tff(5971,plain,
% 2.60/2.14 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_Z1_9(Y!0)))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[5970])).
% 2.60/2.14 tff(5972,plain,
% 2.60/2.14 (~(X!1 = tptp_fun_Z1_9(Y!0))),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[741, 5971])).
% 2.60/2.14 tff(5973,plain,
% 2.60/2.14 (~(big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[5547, 4769, 5972])).
% 2.60/2.14 tff(5974,plain,
% 2.60/2.14 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3003, 5960])).
% 2.60/2.14 tff(5975,plain,
% 2.60/2.14 ((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3286, 5974])).
% 2.60/2.14 tff(5976,plain,
% 2.60/2.14 (Y!0 = W1!8),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[486, 2])).
% 2.60/2.14 tff(5977,plain,
% 2.60/2.14 (![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3289, 5976, 5975])).
% 2.60/2.14 tff(5978,plain,
% 2.60/2.14 ($false),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3291, 5977, 5973])).
% 2.60/2.14 tff(5979,plain,((~(W1!8 = Y!0)) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.14 tff(5980,plain,
% 2.60/2.14 (~(W1!8 = Y!0)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[5979, 30])).
% 2.60/2.14 tff(5981,plain,
% 2.60/2.14 (W1!8 = X!1),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[19, 5980])).
% 2.60/2.14 tff(5982,plain,
% 2.60/2.14 (X!1 = W1!8),
% 2.60/2.14 inference(symmetry,[status(thm)],[5981])).
% 2.60/2.14 tff(5983,plain,
% 2.60/2.14 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[481, 5960])).
% 2.60/2.14 tff(5984,plain,
% 2.60/2.14 (big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[496, 5983])).
% 2.60/2.14 tff(5985,plain,
% 2.60/2.14 (big_f(X!1, W1!8) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[5698, 5981])).
% 2.60/2.14 tff(5986,plain,
% 2.60/2.14 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(X!1, W1!8)),
% 2.60/2.14 inference(symmetry,[status(thm)],[5985])).
% 2.60/2.14 tff(5987,plain,
% 2.60/2.14 (big_f(X!1, W1!8)),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[5728, 5986])).
% 2.60/2.14 tff(5988,plain,
% 2.60/2.14 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.60/2.14 inference(symmetry,[status(thm)],[2056])).
% 2.60/2.14 tff(5989,plain,
% 2.60/2.14 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[483, 5983])).
% 2.60/2.14 tff(5990,plain,
% 2.60/2.14 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[31, 5981])).
% 2.60/2.14 tff(5991,plain,
% 2.60/2.14 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Y!0, W1!8)),
% 2.60/2.14 inference(symmetry,[status(thm)],[5990])).
% 2.60/2.14 tff(5992,plain,
% 2.60/2.14 (big_f(Y!0, W1!8)),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[5690, 5991])).
% 2.60/2.14 tff(5993,plain,
% 2.60/2.14 (Y!0 = tptp_fun_Z1_9(W1!8)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[886, 5992, 5989])).
% 2.60/2.14 tff(5994,plain,
% 2.60/2.14 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.60/2.14 inference(symmetry,[status(thm)],[5993])).
% 2.60/2.14 tff(5995,plain,
% 2.60/2.14 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (Y!0 = X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[5994])).
% 2.60/2.14 tff(5996,plain,
% 2.60/2.14 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = Y!0)),
% 2.60/2.14 inference(transitivity,[status(thm)],[5995, 46])).
% 2.60/2.14 tff(5997,plain,
% 2.60/2.14 ((X!1 = Y!0) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.60/2.14 inference(symmetry,[status(thm)],[5996])).
% 2.60/2.14 tff(5998,plain,
% 2.60/2.14 ((X!1 = Y!0) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.60/2.14 inference(transitivity,[status(thm)],[5997, 5988])).
% 2.60/2.14 tff(5999,plain,
% 2.60/2.14 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_Z1_9(W1!8)))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[5998])).
% 2.60/2.14 tff(6000,plain,
% 2.60/2.14 (~(X!1 = tptp_fun_Z1_9(W1!8))),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[741, 5999])).
% 2.60/2.14 tff(6001,plain,
% 2.60/2.14 ($false),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[923, 6000, 5987, 5984])).
% 2.60/2.14 tff(6002,plain,((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))) | (~(tptp_fun_X_2(Y!0) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.14 tff(6003,plain,
% 2.60/2.14 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6002, 30])).
% 2.60/2.14 tff(6004,plain,
% 2.60/2.14 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[82, 6003])).
% 2.60/2.14 tff(6005,plain,
% 2.60/2.14 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[88, 6004])).
% 2.60/2.14 tff(6006,plain,
% 2.60/2.14 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[191, 6005])).
% 2.60/2.14 tff(6007,plain,
% 2.60/2.14 (tptp_fun_Y1_11(X!1) = X!1),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[5760, 6006, 30])).
% 2.60/2.14 tff(6008,plain,
% 2.60/2.14 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.60/2.14 inference(transitivity,[status(thm)],[6007, 5982])).
% 2.60/2.14 tff(6009,plain,
% 2.60/2.14 (tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_9(W1!8)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6008])).
% 2.60/2.14 tff(6010,plain,
% 2.60/2.14 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(symmetry,[status(thm)],[6009])).
% 2.60/2.14 tff(6011,plain,
% 2.60/2.14 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[90, 6005])).
% 2.60/2.14 tff(6012,plain,
% 2.60/2.14 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[269, 6007, 6011])).
% 2.60/2.14 tff(6013,plain,
% 2.60/2.14 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[271, 6012])).
% 2.60/2.14 tff(6014,plain,
% 2.60/2.14 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[790, 5960])).
% 2.60/2.14 tff(6015,plain,
% 2.60/2.14 ((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[1459, 6014])).
% 2.60/2.14 tff(6016,plain,
% 2.60/2.14 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (tptp_fun_Y1_11(X!1) = X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[5981])).
% 2.60/2.14 tff(6017,plain,
% 2.60/2.14 ((tptp_fun_Y1_11(X!1) = X!1) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.60/2.14 inference(symmetry,[status(thm)],[6016])).
% 2.60/2.14 tff(6018,plain,
% 2.60/2.14 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[6007, 6017])).
% 2.60/2.14 tff(6019,plain,
% 2.60/2.14 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[1465, 6018, 6015])).
% 2.60/2.14 tff(6020,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[1467, 6019])).
% 2.60/2.14 tff(6021,plain,
% 2.60/2.14 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[1490, 6020, 5981, 6007, 6013])).
% 2.60/2.14 tff(6022,plain,
% 2.60/2.14 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[522, 6021])).
% 2.60/2.14 tff(6023,plain,
% 2.60/2.14 (Y!0 = tptp_fun_Z1_9(W1!8)),
% 2.60/2.14 inference(symmetry,[status(thm)],[6022])).
% 2.60/2.14 tff(6024,plain,
% 2.60/2.14 (Y!0 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(transitivity,[status(thm)],[6023, 6010])).
% 2.60/2.14 tff(6025,plain,
% 2.60/2.14 ((tptp_fun_X1_13(Y!0, X!1) = Y!0) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6024])).
% 2.60/2.14 tff(6026,plain,
% 2.60/2.14 ((~(tptp_fun_X1_13(Y!0, X!1) = Y!0)) <=> (~(tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6025])).
% 2.60/2.14 tff(6027,plain,
% 2.60/2.14 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[879, 6012])).
% 2.60/2.14 tff(6028,plain,
% 2.60/2.14 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[31, 6007])).
% 2.60/2.14 tff(6029,plain,
% 2.60/2.14 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(symmetry,[status(thm)],[6028])).
% 2.60/2.14 tff(6030,plain,
% 2.60/2.14 (tptp_fun_Z1_9(W1!8) = tptp_fun_X_2(Y!0)),
% 2.60/2.14 inference(transitivity,[status(thm)],[6022, 31])).
% 2.60/2.14 tff(6031,plain,
% 2.60/2.14 (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6030, 5981])).
% 2.60/2.14 tff(6032,plain,
% 2.60/2.14 (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(transitivity,[status(thm)],[6031, 6029])).
% 2.60/2.14 tff(6033,plain,
% 2.60/2.14 (big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[1506, 5983])).
% 2.60/2.14 tff(6034,plain,
% 2.60/2.14 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[6033, 6032])).
% 2.60/2.14 tff(6035,plain,
% 2.60/2.14 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[2572, 6034, 6027])).
% 2.60/2.14 tff(6036,plain,
% 2.60/2.14 (~(tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[6035, 6026])).
% 2.60/2.14 tff(6037,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[4131, 6019])).
% 2.60/2.14 tff(6038,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[920, 6035, 6027])).
% 2.60/2.14 tff(6039,plain,
% 2.60/2.14 (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[4153, 6038, 6037])).
% 2.60/2.14 tff(6040,plain,
% 2.60/2.14 ($false),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6039, 6036])).
% 2.60/2.14 tff(6041,plain,(~(tptp_fun_X_2(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.60/2.14 tff(6042,plain,
% 2.60/2.14 (tptp_fun_X_2(Y!0) = X!1),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[1877, 6041])).
% 2.60/2.14 tff(6043,plain,
% 2.60/2.14 (X!1 = tptp_fun_X_2(Y!0)),
% 2.60/2.14 inference(symmetry,[status(thm)],[6042])).
% 2.60/2.14 tff(6044,plain,
% 2.60/2.14 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6043, 40])).
% 2.60/2.14 tff(6045,plain,
% 2.60/2.14 ((~big_f(X!1, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X_2(Y!0), X!1))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6044])).
% 2.60/2.14 tff(6046,assumption,(~(Y!0 = tptp_fun_Z1_12(Y!0))), introduced(assumption)).
% 2.60/2.14 tff(6047,plain,
% 2.60/2.14 (~((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[746, 1268])).
% 2.60/2.14 tff(6048,plain,
% 2.60/2.14 (((~((tptp_fun_Z1_12(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)), tptp_fun_Z1_12(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Z1_12(Y!0)) = Z1)))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))))) | ((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))),
% 2.60/2.14 inference(tautology,[status(thm)],[])).
% 2.60/2.14 tff(6049,plain,
% 2.60/2.14 ((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6048, 6047])).
% 2.60/2.14 tff(6050,plain,
% 2.60/2.14 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[6046, 582])).
% 2.60/2.14 tff(6051,plain,
% 2.60/2.14 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[594, 6050])).
% 2.60/2.14 tff(6052,plain,
% 2.60/2.14 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[161, 3151, 144])).
% 2.60/2.14 tff(6053,plain,
% 2.60/2.14 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> (X!1 = tptp_fun_Z1_12(X!1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[5376, 6052])).
% 2.60/2.14 tff(6054,plain,
% 2.60/2.14 (X!1 = tptp_fun_Z1_12(X!1)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[5381, 6053, 5756])).
% 2.60/2.14 tff(6055,plain,
% 2.60/2.14 (tptp_fun_Z1_12(X!1) = X!1),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[6054, 5762])).
% 2.60/2.14 tff(6056,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3910, 6052])).
% 2.60/2.14 tff(6057,assumption,((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))), introduced(assumption)).
% 2.60/2.14 tff(6058,plain,
% 2.60/2.14 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[563, 34, 6057])).
% 2.60/2.14 tff(6059,plain,
% 2.60/2.14 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[596, 6058, 41])).
% 2.60/2.14 tff(6060,plain,
% 2.60/2.14 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3183, 6059, 6042, 41, 796, 1260, 40, 1268])).
% 2.60/2.14 tff(6061,plain,
% 2.60/2.14 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3101, 6060])).
% 2.60/2.14 tff(6062,assumption,((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)), introduced(assumption)).
% 2.60/2.14 tff(6063,assumption,(~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))), introduced(assumption)).
% 2.60/2.14 tff(6064,plain,
% 2.60/2.14 ((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))) | big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.14 inference(tautology,[status(thm)],[])).
% 2.60/2.14 tff(6065,plain,
% 2.60/2.14 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6064, 6063, 6062])).
% 2.60/2.14 tff(6066,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6065, 796])).
% 2.60/2.14 tff(6067,plain,
% 2.60/2.14 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(symmetry,[status(thm)],[6066])).
% 2.60/2.14 tff(6068,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[3678, 6067])).
% 2.60/2.14 tff(6069,plain,
% 2.60/2.14 ($false),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6063, 6068])).
% 2.60/2.14 tff(6070,plain,(big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.14 tff(6071,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6070, 4769])).
% 2.60/2.14 tff(6072,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6071, 6061, 796])).
% 2.60/2.14 tff(6073,plain,
% 2.60/2.14 (tptp_fun_X_2(Y!0) = W1!8),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3179, 6059, 6042, 41, 1260, 1272, 40, 3160])).
% 2.60/2.14 tff(6074,assumption,(tptp_fun_X_2(Y!0) = W1!8), introduced(assumption)).
% 2.60/2.14 tff(6075,plain,
% 2.60/2.14 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.60/2.14 inference(symmetry,[status(thm)],[6074])).
% 2.60/2.14 tff(6076,plain,
% 2.60/2.14 (W1!8 = X!1),
% 2.60/2.14 inference(transitivity,[status(thm)],[6075, 1906])).
% 2.60/2.14 tff(6077,plain,
% 2.60/2.14 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6076])).
% 2.60/2.14 tff(6078,plain,
% 2.60/2.14 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6077, 176])).
% 2.60/2.14 tff(6079,plain,
% 2.60/2.14 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.60/2.14 inference(symmetry,[status(thm)],[6078])).
% 2.60/2.14 tff(6080,plain,
% 2.60/2.14 ((~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)) <=> (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6079])).
% 2.60/2.14 tff(6081,plain,
% 2.60/2.14 (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1))),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[3954, 6080])).
% 2.60/2.14 tff(6082,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(monotonicity,[status(thm)],[6077])).
% 2.60/2.14 tff(6083,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(symmetry,[status(thm)],[6082])).
% 2.60/2.14 tff(6084,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[6064, 3954, 6062])).
% 2.60/2.14 tff(6085,plain,
% 2.60/2.14 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.14 inference(modus_ponens,[status(thm)],[6084, 6083])).
% 2.60/2.14 tff(6086,plain,
% 2.60/2.14 ($false),
% 2.60/2.14 inference(unit_resolution,[status(thm)],[3936, 6085, 6081, 3914])).
% 2.60/2.14 tff(6087,plain,((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) | (~(big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~(tptp_fun_X_2(Y!0) = W1!8)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Z1_12(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.14 tff(6088,plain,
% 2.60/2.14 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6087, 6073, 6042, 3914, 176, 6061])).
% 2.60/2.15 tff(6089,plain,
% 2.60/2.15 ($false),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[3099, 6088, 6061, 6072])).
% 2.60/2.15 tff(6090,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_Z1_12(X!1)))) | (~(tptp_fun_Z1_12(X!1) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.15 tff(6091,plain,
% 2.60/2.15 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6090, 6056, 154, 6055, 41, 1260, 1268, 1559])).
% 2.60/2.15 tff(6092,plain,
% 2.60/2.15 (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[5602, 6091, 41])).
% 2.60/2.15 tff(6093,plain,
% 2.60/2.15 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[113, 6091, 1641])).
% 2.60/2.15 tff(6094,plain,
% 2.60/2.15 ($false),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[958, 6093, 6092])).
% 2.60/2.15 tff(6095,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.60/2.15 tff(6096,plain,
% 2.60/2.15 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6095, 41, 6051, 1268, 144])).
% 2.60/2.15 tff(6097,plain,
% 2.60/2.15 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[82, 6096])).
% 2.60/2.15 tff(6098,plain,
% 2.60/2.15 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[220, 6097])).
% 2.60/2.15 tff(6099,plain,
% 2.60/2.15 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[1713, 6098])).
% 2.60/2.15 tff(6100,plain,
% 2.60/2.15 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[222, 6098])).
% 2.60/2.15 tff(6101,plain,
% 2.60/2.15 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6043, 598])).
% 2.60/2.15 tff(6102,plain,
% 2.60/2.15 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.60/2.15 inference(symmetry,[status(thm)],[6101])).
% 2.60/2.15 tff(6103,plain,
% 2.60/2.15 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6102])).
% 2.60/2.15 tff(6104,plain,
% 2.60/2.15 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[5823, 6103])).
% 2.60/2.15 tff(6105,plain,
% 2.60/2.15 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[5565, 6104, 2620, 598])).
% 2.60/2.15 tff(6106,plain,
% 2.60/2.15 (tptp_fun_X_2(X!1) = Y!0),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[105, 6105])).
% 2.60/2.15 tff(6107,plain,
% 2.60/2.15 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[224, 6105, 3217])).
% 2.60/2.15 tff(6108,plain,
% 2.60/2.15 (~(W1!8 = X!1)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[2645, 6104, 41, 598, 495])).
% 2.60/2.15 tff(6109,plain,
% 2.60/2.15 (W1!8 = Y!0),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[19, 6108])).
% 2.60/2.15 tff(6110,plain,
% 2.60/2.15 (big_f(X!1, W1!8)),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[3678, 499])).
% 2.60/2.15 tff(6111,plain,
% 2.60/2.15 (X!1 = tptp_fun_Z1_9(W1!8)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[923, 6110, 497])).
% 2.60/2.15 tff(6112,plain,
% 2.60/2.15 (tptp_fun_Z1_9(W1!8) = X!1),
% 2.60/2.15 inference(symmetry,[status(thm)],[6111])).
% 2.60/2.15 tff(6113,plain,
% 2.60/2.15 ((tptp_fun_Z1_9(W1!8) = Y!0) <=> (X!1 = Y!0)),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6112])).
% 2.60/2.15 tff(6114,plain,
% 2.60/2.15 ((X!1 = Y!0) <=> (tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.60/2.15 inference(symmetry,[status(thm)],[6113])).
% 2.60/2.15 tff(6115,plain,
% 2.60/2.15 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Z1_9(W1!8) = Y!0))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6114])).
% 2.60/2.15 tff(6116,plain,
% 2.60/2.15 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[741, 6115])).
% 2.60/2.15 tff(6117,plain,
% 2.60/2.15 (big_f(Y!0, W1!8) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.60/2.15 inference(monotonicity,[status(thm)],[273, 486])).
% 2.60/2.15 tff(6118,plain,
% 2.60/2.15 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, W1!8)),
% 2.60/2.15 inference(symmetry,[status(thm)],[6117])).
% 2.60/2.15 tff(6119,plain,
% 2.60/2.15 (big_f(Y!0, W1!8)),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[1144, 6118])).
% 2.60/2.15 tff(6120,plain,
% 2.60/2.15 (Y!0 = tptp_fun_Z1_9(W1!8)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[886, 6119, 511])).
% 2.60/2.15 tff(6121,plain,
% 2.60/2.15 (tptp_fun_Z1_9(W1!8) = Y!0),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[6120, 43])).
% 2.60/2.15 tff(6122,plain,
% 2.60/2.15 ($false),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6121, 6116])).
% 2.60/2.15 tff(6123,plain,((~(W1!8 = Y!0)) | (~big_f(tptp_fun_X_2(X!1), Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~big_f(X!1, Y!0)) | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.15 tff(6124,plain,
% 2.60/2.15 ((~(W1!8 = Y!0)) | (~big_f(tptp_fun_X_2(X!1), Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6123, 4769])).
% 2.60/2.15 tff(6125,plain,
% 2.60/2.15 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6124, 6109, 495, 6106])).
% 2.60/2.15 tff(6126,plain,
% 2.60/2.15 ($false),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[1588, 6125, 6107, 41, 598, 6106])).
% 2.60/2.15 tff(6127,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.60/2.15 tff(6128,plain,
% 2.60/2.15 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6127, 41, 1456, 6100, 6099, 5823])).
% 2.60/2.15 tff(6129,plain,
% 2.60/2.15 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[39, 6128])).
% 2.60/2.15 tff(6130,plain,
% 2.60/2.15 ((W1!8 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.60/2.15 inference(symmetry,[status(thm)],[798])).
% 2.60/2.15 tff(6131,plain,
% 2.60/2.15 ((W1!8 = Y!0) <=> (X!1 = Y!0)),
% 2.60/2.15 inference(monotonicity,[status(thm)],[1275])).
% 2.60/2.15 tff(6132,plain,
% 2.60/2.15 ((X!1 = Y!0) <=> (W1!8 = Y!0)),
% 2.60/2.15 inference(symmetry,[status(thm)],[6131])).
% 2.60/2.15 tff(6133,plain,
% 2.60/2.15 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.60/2.15 inference(transitivity,[status(thm)],[6132, 6130])).
% 2.60/2.15 tff(6134,plain,
% 2.60/2.15 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = W1!8))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6133])).
% 2.60/2.15 tff(6135,plain,
% 2.60/2.15 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[741, 6134])).
% 2.60/2.15 tff(6136,plain,
% 2.60/2.15 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[794, 6135, 1279])).
% 2.60/2.15 tff(6137,plain,
% 2.60/2.15 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[3101, 6136])).
% 2.60/2.15 tff(6138,plain,
% 2.60/2.15 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[5059])).
% 2.60/2.15 tff(6139,plain,
% 2.60/2.15 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6138])).
% 2.60/2.15 tff(6140,plain,
% 2.60/2.15 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.15 inference(symmetry,[status(thm)],[6139])).
% 2.60/2.15 tff(6141,plain,
% 2.60/2.15 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[1469])).
% 2.60/2.15 tff(6142,plain,
% 2.60/2.15 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.60/2.15 inference(symmetry,[status(thm)],[6141])).
% 2.60/2.15 tff(6143,plain,
% 2.60/2.15 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6142])).
% 2.60/2.15 tff(6144,plain,
% 2.60/2.15 ((~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)) <=> (~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6143])).
% 2.60/2.15 tff(6145,plain,
% 2.60/2.15 (~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[3925, 6144])).
% 2.60/2.15 tff(6146,plain,
% 2.60/2.15 (tptp_fun_Y1_11(X!1) = tptp_fun_Y1_11(Y!0)),
% 2.60/2.15 inference(transitivity,[status(thm)],[796, 146])).
% 2.60/2.15 tff(6147,plain,
% 2.60/2.15 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.60/2.15 inference(rewrite,[status(thm)],[])).
% 2.60/2.15 tff(6148,plain,
% 2.60/2.15 (((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)) <=> ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.60/2.15 inference(rewrite,[status(thm)],[])).
% 2.60/2.15 tff(6149,plain,
% 2.60/2.15 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0)))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6148])).
% 2.60/2.15 tff(6150,plain,
% 2.60/2.15 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0))),
% 2.60/2.15 inference(transitivity,[status(thm)],[6149, 6147])).
% 2.60/2.15 tff(6151,plain,
% 2.60/2.15 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1))),
% 2.60/2.15 inference(quant_inst,[status(thm)],[])).
% 2.60/2.15 tff(6152,plain,
% 2.60/2.15 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[6151, 6150])).
% 2.60/2.15 tff(6153,plain,
% 2.60/2.15 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6152, 12])).
% 2.60/2.15 tff(6154,plain,
% 2.60/2.15 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6153, 3925])).
% 2.60/2.15 tff(6155,plain,
% 2.60/2.15 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.60/2.15 inference(transitivity,[status(thm)],[6141, 6154])).
% 2.60/2.15 tff(6156,plain,
% 2.60/2.15 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6155, 6146])).
% 2.60/2.15 tff(6157,plain,
% 2.60/2.15 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.15 inference(symmetry,[status(thm)],[6156])).
% 2.60/2.15 tff(6158,plain,
% 2.60/2.15 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)))),
% 2.60/2.15 inference(monotonicity,[status(thm)],[6157])).
% 2.60/2.15 tff(6159,plain,
% 2.60/2.15 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.15 inference(modus_ponens,[status(thm)],[41, 6158])).
% 2.60/2.15 tff(6160,plain,
% 2.60/2.15 ($false),
% 2.60/2.15 inference(unit_resolution,[status(thm)],[6064, 6159, 6145, 6062])).
% 2.60/2.15 tff(6161,plain,((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(W1!8 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.16 tff(6162,plain,
% 2.60/2.16 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[6161, 6137, 796, 41, 109, 1275])).
% 2.60/2.16 tff(6163,plain,
% 2.60/2.16 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[6162, 6140])).
% 2.60/2.16 tff(6164,plain,
% 2.60/2.16 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.60/2.16 inference(transitivity,[status(thm)],[6138, 6162])).
% 2.60/2.16 tff(6165,plain,
% 2.60/2.16 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6164, 796])).
% 2.60/2.16 tff(6166,plain,
% 2.60/2.16 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.16 inference(symmetry,[status(thm)],[6165])).
% 2.60/2.16 tff(6167,plain,
% 2.60/2.16 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[3678, 6166])).
% 2.60/2.16 tff(6168,plain,
% 2.60/2.16 ($false),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[3099, 6167, 6163, 6137])).
% 2.60/2.16 tff(6169,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.16 tff(6170,plain,
% 2.60/2.16 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[6169, 4769])).
% 2.60/2.16 tff(6171,plain,
% 2.60/2.16 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[6170, 6129, 41, 154, 1268])).
% 2.60/2.16 tff(6172,plain,
% 2.60/2.16 ((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[1256, 6171])).
% 2.60/2.16 tff(6173,plain,
% 2.60/2.16 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.60/2.16 inference(transitivity,[status(thm)],[6129, 3378])).
% 2.60/2.16 tff(6174,plain,
% 2.60/2.16 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6173])).
% 2.60/2.16 tff(6175,plain,
% 2.60/2.16 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_Y1_11(X!1)))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6174])).
% 2.60/2.16 tff(6176,plain,
% 2.60/2.16 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[41, 6175])).
% 2.60/2.16 tff(6177,plain,
% 2.60/2.16 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[596, 1560, 41])).
% 2.60/2.16 tff(6178,plain,
% 2.60/2.16 ((~(X!1 = tptp_fun_W_6(Z!5))) <=> (~(tptp_fun_W_6(Y!0) = X!1))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[3831])).
% 2.60/2.16 tff(6179,plain,
% 2.60/2.16 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[412, 2972])).
% 2.60/2.16 tff(6180,plain,
% 2.60/2.16 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Z!5, X!1)),
% 2.60/2.16 inference(symmetry,[status(thm)],[6179])).
% 2.60/2.16 tff(6181,plain,
% 2.60/2.16 ((~big_f(Y!0, tptp_fun_X_2(Y!0))) <=> (~big_f(Z!5, X!1))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6180])).
% 2.60/2.16 tff(6182,plain,
% 2.60/2.16 (~big_f(Z!5, X!1)),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[2991, 6181])).
% 2.60/2.16 tff(6183,plain,
% 2.60/2.16 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[1547, 6182, 984])).
% 2.60/2.16 tff(6184,plain,
% 2.60/2.16 (~(tptp_fun_W_6(Y!0) = X!1)),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[6183, 6178])).
% 2.60/2.16 tff(6185,plain,
% 2.60/2.16 (big_f(Z!5, Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[412, 1786])).
% 2.60/2.16 tff(6186,plain,
% 2.60/2.16 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Z!5, Y!0)),
% 2.60/2.16 inference(symmetry,[status(thm)],[6185])).
% 2.60/2.16 tff(6187,plain,
% 2.60/2.16 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Z!5, Y!0))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6186])).
% 2.60/2.16 tff(6188,plain,
% 2.60/2.16 (~big_f(Z!5, Y!0)),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[2501, 6187])).
% 2.60/2.16 tff(6189,plain,
% 2.60/2.16 (~(Y!0 = tptp_fun_W_6(Z!5))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[394, 6188, 5072])).
% 2.60/2.16 tff(6190,plain,
% 2.60/2.16 (~(tptp_fun_W_6(Y!0) = Y!0)),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[6189, 5071])).
% 2.60/2.16 tff(6191,plain,
% 2.60/2.16 ($false),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[403, 6190, 6184])).
% 2.60/2.16 tff(6192,plain,((~(Z!5 = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5))))), inference(lemma,lemma(discharge,[]))).
% 2.60/2.16 tff(6193,plain,
% 2.60/2.16 (~(Z!5 = Y!0)),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[6192, 386, 796, 2991, 1906, 2501])).
% 2.60/2.16 tff(6194,plain,
% 2.60/2.16 (Z!5 = X!1),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[361, 6193])).
% 2.60/2.16 tff(6195,plain,
% 2.60/2.16 (big_f(Z!5, X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6194, 599])).
% 2.60/2.16 tff(6196,plain,
% 2.60/2.16 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, X!1)),
% 2.60/2.16 inference(symmetry,[status(thm)],[6195])).
% 2.60/2.16 tff(6197,plain,
% 2.60/2.16 (big_f(Z!5, X!1)),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[622, 6196])).
% 2.60/2.16 tff(6198,plain,
% 2.60/2.16 (X!1 = Z!5),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[353, 6194])).
% 2.60/2.16 tff(6199,plain,
% 2.60/2.16 (![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[346, 6198, 345])).
% 2.60/2.16 tff(6200,plain,
% 2.60/2.16 (big_f(X!1, Y!0) <=> (Y!0 = tptp_fun_W_6(X!1))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[321, 6199])).
% 2.60/2.16 tff(6201,plain,
% 2.60/2.16 (Y!0 = tptp_fun_W_6(X!1)),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[3751, 6200, 3678])).
% 2.60/2.16 tff(6202,plain,
% 2.60/2.16 (tptp_fun_W_6(X!1) = Y!0),
% 2.60/2.16 inference(symmetry,[status(thm)],[6201])).
% 2.60/2.16 tff(6203,plain,
% 2.60/2.16 (tptp_fun_W_6(Z!5) = tptp_fun_W_6(X!1)),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6194])).
% 2.60/2.16 tff(6204,plain,
% 2.60/2.16 (tptp_fun_W_6(Z!5) = Y!0),
% 2.60/2.16 inference(transitivity,[status(thm)],[6203, 6202])).
% 2.60/2.16 tff(6205,plain,
% 2.60/2.16 ((X!1 = tptp_fun_W_6(Z!5)) <=> (X!1 = Y!0)),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6204])).
% 2.60/2.16 tff(6206,plain,
% 2.60/2.16 ((X!1 = Y!0) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.60/2.16 inference(symmetry,[status(thm)],[6205])).
% 2.60/2.16 tff(6207,plain,
% 2.60/2.16 ((~(X!1 = Y!0)) <=> (~(X!1 = tptp_fun_W_6(Z!5)))),
% 2.60/2.16 inference(monotonicity,[status(thm)],[6206])).
% 2.60/2.16 tff(6208,plain,
% 2.60/2.16 (~(X!1 = tptp_fun_W_6(Z!5))),
% 2.60/2.16 inference(modus_ponens,[status(thm)],[741, 6207])).
% 2.60/2.16 tff(6209,plain,
% 2.60/2.16 ((~(big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5)))) | (~big_f(Z!5, X!1))),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[989, 6208])).
% 2.60/2.16 tff(6210,plain,
% 2.60/2.16 (~big_f(Z!5, X!1)),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[6209, 1212])).
% 2.60/2.16 tff(6211,plain,
% 2.60/2.16 ($false),
% 2.60/2.16 inference(unit_resolution,[status(thm)],[6210, 6197])).
% 2.60/2.16 tff(6212,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6213,plain,
% 2.66/2.17 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6212, 6177, 40, 3678, 154, 2991, 1906, 2501])).
% 2.66/2.17 tff(6214,plain,
% 2.66/2.17 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[462, 6213])).
% 2.66/2.17 tff(6215,plain,
% 2.66/2.17 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[790, 6214])).
% 2.66/2.17 tff(6216,plain,
% 2.66/2.17 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[792, 6215])).
% 2.66/2.17 tff(6217,plain,
% 2.66/2.17 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3017, 6214])).
% 2.66/2.17 tff(6218,plain,
% 2.66/2.17 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3019, 6217])).
% 2.66/2.17 tff(6219,plain,
% 2.66/2.17 (X!1 = tptp_fun_Z1_12(Y!0)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[751, 3155, 6177])).
% 2.66/2.17 tff(6220,plain,
% 2.66/2.17 (~(tptp_fun_Z1_12(Y!0) = Y!0)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[1191, 6219])).
% 2.66/2.17 tff(6221,plain,
% 2.66/2.17 (tptp_fun_Z1_12(Y!0) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[594, 6220])).
% 2.66/2.17 tff(6222,plain,
% 2.66/2.17 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[1269, 6214])).
% 2.66/2.17 tff(6223,plain,
% 2.66/2.17 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[1271, 6222])).
% 2.66/2.17 tff(6224,plain,
% 2.66/2.17 (tptp_fun_X_2(Y!0) = W1!8),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3179, 6223, 41, 40, 6177, 6221, 1906, 6218])).
% 2.66/2.17 tff(6225,plain,
% 2.66/2.17 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6224])).
% 2.66/2.17 tff(6226,plain,
% 2.66/2.17 (W1!8 = X!1),
% 2.66/2.17 inference(transitivity,[status(thm)],[6225, 1906])).
% 2.66/2.17 tff(6227,plain,
% 2.66/2.17 ((W1!8 = Y!0) <=> (X!1 = Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6226])).
% 2.66/2.17 tff(6228,plain,
% 2.66/2.17 ((X!1 = Y!0) <=> (W1!8 = Y!0)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6227])).
% 2.66/2.17 tff(6229,plain,
% 2.66/2.17 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.17 inference(transitivity,[status(thm)],[6228, 3764])).
% 2.66/2.17 tff(6230,plain,
% 2.66/2.17 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = W1!8))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6229])).
% 2.66/2.17 tff(6231,plain,
% 2.66/2.17 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[741, 6230])).
% 2.66/2.17 tff(6232,plain,
% 2.66/2.17 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[794, 6231, 6216])).
% 2.66/2.17 tff(6233,plain,
% 2.66/2.17 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3101, 6232])).
% 2.66/2.17 tff(6234,plain,
% 2.66/2.17 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> (Y!0 = tptp_fun_Z1_12(X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3195, 6052])).
% 2.66/2.17 tff(6235,plain,
% 2.66/2.17 (~(Y!0 = tptp_fun_Z1_12(X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3197, 6234, 2501])).
% 2.66/2.17 tff(6236,plain,
% 2.66/2.17 (~(tptp_fun_Z1_12(X!1) = Y!0)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[6235, 3902])).
% 2.66/2.17 tff(6237,plain,
% 2.66/2.17 (tptp_fun_Z1_12(X!1) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[187, 6236])).
% 2.66/2.17 tff(6238,plain,
% 2.66/2.17 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6087, 6056, 6224, 1906, 6237, 6233])).
% 2.66/2.17 tff(6239,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(X!1, Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6238, 154])).
% 2.66/2.17 tff(6240,plain,
% 2.66/2.17 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(symmetry,[status(thm)],[6239])).
% 2.66/2.17 tff(6241,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[3678, 6240])).
% 2.66/2.17 tff(6242,plain,
% 2.66/2.17 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3099, 6238, 6233])).
% 2.66/2.17 tff(6243,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6242, 6241])).
% 2.66/2.17 tff(6244,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~big_f(X!1, Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0)) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (tptp_fun_Y1_11(Y!0) = Y!0) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6245,plain,
% 2.66/2.17 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6244, 34, 1906, 41, 2991, 2501, 3678, 144])).
% 2.66/2.17 tff(6246,plain,
% 2.66/2.17 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[82, 6245])).
% 2.66/2.17 tff(6247,plain,
% 2.66/2.17 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[220, 6246])).
% 2.66/2.17 tff(6248,plain,
% 2.66/2.17 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[222, 6247])).
% 2.66/2.17 tff(6249,plain,
% 2.66/2.17 (tptp_fun_X_2(X!1) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3737, 40, 154, 41, 2501, 6248])).
% 2.66/2.17 tff(6250,plain,
% 2.66/2.17 (X!1 = tptp_fun_X_2(X!1)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6249])).
% 2.66/2.17 tff(6251,plain,
% 2.66/2.17 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6250, 154])).
% 2.66/2.17 tff(6252,plain,
% 2.66/2.17 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6251])).
% 2.66/2.17 tff(6253,plain,
% 2.66/2.17 ((~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)) <=> (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6252])).
% 2.66/2.17 tff(6254,plain,
% 2.66/2.17 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[1713, 6247])).
% 2.66/2.17 tff(6255,plain,
% 2.66/2.17 (big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3704, 6249, 40, 3678, 6254])).
% 2.66/2.17 tff(6256,plain,
% 2.66/2.17 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6212, 6255, 40, 3678, 154, 2991, 1906, 2501])).
% 2.66/2.17 tff(6257,plain,
% 2.66/2.17 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[462, 6256])).
% 2.66/2.17 tff(6258,plain,
% 2.66/2.17 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[790, 6257])).
% 2.66/2.17 tff(6259,plain,
% 2.66/2.17 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[792, 6258])).
% 2.66/2.17 tff(6260,plain,
% 2.66/2.17 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3017, 6257])).
% 2.66/2.17 tff(6261,plain,
% 2.66/2.17 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3019, 6260])).
% 2.66/2.17 tff(6262,assumption,(~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))), introduced(assumption)).
% 2.66/2.17 tff(6263,plain,
% 2.66/2.17 (~((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3689, 3681, 1663, 3678])).
% 2.66/2.17 tff(6264,plain,
% 2.66/2.17 (((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) | (~(tptp_fun_Y_4(Y!0, X!1) = Y!0))),
% 2.66/2.17 inference(tautology,[status(thm)],[])).
% 2.66/2.17 tff(6265,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6264, 6263, 3681, 6262])).
% 2.66/2.17 tff(6266,plain,((~(tptp_fun_Y_4(Y!0, X!1) = Y!0)) | big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6267,plain,
% 2.66/2.17 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6266, 6262, 1663, 3678])).
% 2.66/2.17 tff(6268,plain,
% 2.66/2.17 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3694, 6267])).
% 2.66/2.17 tff(6269,plain,
% 2.66/2.17 (tptp_fun_Y_4(Y!0, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.66/2.17 inference(transitivity,[status(thm)],[6268, 599])).
% 2.66/2.17 tff(6270,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[1663, 6269])).
% 2.66/2.17 tff(6271,plain,
% 2.66/2.17 (big_f(X!1, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(symmetry,[status(thm)],[6270])).
% 2.66/2.17 tff(6272,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[622, 6271])).
% 2.66/2.17 tff(6273,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6262, 6272])).
% 2.66/2.17 tff(6274,plain,(big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) | (~big_f(X!1, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6275,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6274, 6255, 40, 6249, 3678])).
% 2.66/2.17 tff(6276,plain,
% 2.66/2.17 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[1711, 6249, 6254])).
% 2.66/2.17 tff(6277,plain,
% 2.66/2.17 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3679, 6276])).
% 2.66/2.17 tff(6278,plain,
% 2.66/2.17 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3689, 6277, 3678, 6249])).
% 2.66/2.17 tff(6279,plain,
% 2.66/2.17 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3694, 6278])).
% 2.66/2.17 tff(6280,plain,
% 2.66/2.17 (tptp_fun_Y_4(Y!0, X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.17 inference(transitivity,[status(thm)],[4866, 2972])).
% 2.66/2.17 tff(6281,plain,
% 2.66/2.17 (tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) = tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[1663, 6280])).
% 2.66/2.17 tff(6282,plain,
% 2.66/2.17 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(symmetry,[status(thm)],[6281])).
% 2.66/2.17 tff(6283,plain,
% 2.66/2.17 (tptp_fun_X_2(X!1) = tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(transitivity,[status(thm)],[1663, 1789, 6282])).
% 2.66/2.17 tff(6284,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6283])).
% 2.66/2.17 tff(6285,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(symmetry,[status(thm)],[6284])).
% 2.66/2.17 tff(6286,plain,
% 2.66/2.17 ((~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6285])).
% 2.66/2.17 tff(6287,plain,
% 2.66/2.17 (tptp_fun_X_2(Y!0) = tptp_fun_Y_4(Y!0, X!1)),
% 2.66/2.17 inference(transitivity,[status(thm)],[1906, 4936])).
% 2.66/2.17 tff(6288,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6282, 6287])).
% 2.66/2.17 tff(6289,plain,
% 2.66/2.17 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1)))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6288])).
% 2.66/2.17 tff(6290,plain,
% 2.66/2.17 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[5498, 6289])).
% 2.66/2.17 tff(6291,plain,
% 2.66/2.17 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[6290, 6286])).
% 2.66/2.17 tff(6292,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[4865, 6291])).
% 2.66/2.17 tff(6293,plain,((~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6294,plain,
% 2.66/2.17 (~(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6293, 5411, 1906, 1663, 4866, 4865])).
% 2.66/2.17 tff(6295,plain,
% 2.66/2.17 (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = Y!0),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[2258, 6294])).
% 2.66/2.17 tff(6296,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3082, 6294, 5411])).
% 2.66/2.17 tff(6297,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3080, 6296, 6295, 2991])).
% 2.66/2.17 tff(6298,plain,((~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~(tptp_fun_Y_4(Y!0, X!1) = X!1)) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6299,plain,
% 2.66/2.17 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6298, 6249, 1906, 2991, 6279, 6275])).
% 2.66/2.17 tff(6300,plain,
% 2.66/2.17 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3084, 6299])).
% 2.66/2.17 tff(6301,plain,
% 2.66/2.17 (tptp_fun_X_2(Y!0) = W1!8),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3086, 6300, 6261])).
% 2.66/2.17 tff(6302,plain,
% 2.66/2.17 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6301])).
% 2.66/2.17 tff(6303,plain,
% 2.66/2.17 (W1!8 = X!1),
% 2.66/2.17 inference(transitivity,[status(thm)],[6302, 1906])).
% 2.66/2.17 tff(6304,plain,
% 2.66/2.17 ((W1!8 = Y!0) <=> (X!1 = Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6303])).
% 2.66/2.17 tff(6305,plain,
% 2.66/2.17 ((X!1 = Y!0) <=> (W1!8 = Y!0)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6304])).
% 2.66/2.17 tff(6306,plain,
% 2.66/2.17 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.17 inference(transitivity,[status(thm)],[6305, 3764])).
% 2.66/2.17 tff(6307,plain,
% 2.66/2.17 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = W1!8))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6306])).
% 2.66/2.17 tff(6308,plain,
% 2.66/2.17 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[741, 6307])).
% 2.66/2.17 tff(6309,plain,
% 2.66/2.17 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[794, 6308, 6259])).
% 2.66/2.17 tff(6310,plain,
% 2.66/2.17 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3101, 6309])).
% 2.66/2.17 tff(6311,assumption,(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1), introduced(assumption)).
% 2.66/2.17 tff(6312,plain,
% 2.66/2.17 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[1663, 1786])).
% 2.66/2.17 tff(6313,plain,
% 2.66/2.17 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1),
% 2.66/2.17 inference(transitivity,[status(thm)],[6312, 6311])).
% 2.66/2.17 tff(6314,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6313])).
% 2.66/2.17 tff(6315,plain,
% 2.66/2.17 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6314])).
% 2.66/2.17 tff(6316,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[3678, 6315])).
% 2.66/2.17 tff(6317,plain,
% 2.66/2.17 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6312])).
% 2.66/2.17 tff(6318,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6317, 796])).
% 2.66/2.17 tff(6319,plain,
% 2.66/2.17 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0))),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6318])).
% 2.66/2.17 tff(6320,plain,
% 2.66/2.17 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3099, 6311, 6062])).
% 2.66/2.17 tff(6321,plain,
% 2.66/2.17 (~big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[6320, 6319])).
% 2.66/2.17 tff(6322,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6321, 6316])).
% 2.66/2.17 tff(6323,plain,((~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6324,plain,
% 2.66/2.17 (~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6323, 6249, 154, 3678, 6310])).
% 2.66/2.17 tff(6325,plain,
% 2.66/2.17 (~(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[6324, 6253])).
% 2.66/2.17 tff(6326,plain,
% 2.66/2.17 (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = Y!0),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3059, 6325])).
% 2.66/2.17 tff(6327,plain,
% 2.66/2.17 (Y!0 = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6326])).
% 2.66/2.17 tff(6328,plain,
% 2.66/2.17 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6327, 154])).
% 2.66/2.17 tff(6329,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(symmetry,[status(thm)],[6328])).
% 2.66/2.17 tff(6330,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6251, 154])).
% 2.66/2.17 tff(6331,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6064, 6324, 6310])).
% 2.66/2.17 tff(6332,plain,
% 2.66/2.17 (big_f(tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0), Y!0)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[6331, 6330])).
% 2.66/2.17 tff(6333,plain,
% 2.66/2.17 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[6332, 6329])).
% 2.66/2.17 tff(6334,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[2501, 6333])).
% 2.66/2.17 tff(6335,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(Y!0, tptp_fun_X_2(Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6336,plain,
% 2.66/2.17 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6335, 2991, 3678, 1906, 2501, 41, 144])).
% 2.66/2.17 tff(6337,plain,
% 2.66/2.17 (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3714, 6336, 3678, 41])).
% 2.66/2.17 tff(6338,plain,
% 2.66/2.17 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[958, 6337])).
% 2.66/2.17 tff(6339,plain,
% 2.66/2.17 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[113, 6338, 6336])).
% 2.66/2.17 tff(6340,plain,
% 2.66/2.17 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[86, 6339])).
% 2.66/2.17 tff(6341,plain,
% 2.66/2.17 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[84, 6340])).
% 2.66/2.17 tff(6342,plain,
% 2.66/2.17 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[82, 6341])).
% 2.66/2.17 tff(6343,plain,
% 2.66/2.17 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[220, 6342])).
% 2.66/2.17 tff(6344,plain,
% 2.66/2.17 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[222, 6343])).
% 2.66/2.17 tff(6345,plain,
% 2.66/2.17 (tptp_fun_X_2(X!1) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3396, 6344, 1906, 41, 2991, 6336])).
% 2.66/2.17 tff(6346,plain,
% 2.66/2.17 (X!1 = tptp_fun_X_2(X!1)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6345])).
% 2.66/2.17 tff(6347,plain,
% 2.66/2.17 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6346, 154])).
% 2.66/2.17 tff(6348,plain,
% 2.66/2.17 ((tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6347])).
% 2.66/2.17 tff(6349,plain,
% 2.66/2.17 ((tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6348])).
% 2.66/2.17 tff(6350,plain,
% 2.66/2.17 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[1713, 6343])).
% 2.66/2.17 tff(6351,plain,
% 2.66/2.17 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[1711, 6345, 6350])).
% 2.66/2.17 tff(6352,plain,
% 2.66/2.17 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3679, 6351])).
% 2.66/2.17 tff(6353,plain,
% 2.66/2.17 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3689, 6352, 3678, 6345])).
% 2.66/2.17 tff(6354,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3701, 6353, 6352])).
% 2.66/2.17 tff(6355,plain,
% 2.66/2.17 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3694, 6353])).
% 2.66/2.17 tff(6356,plain,
% 2.66/2.17 (~((~big_f(tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(X!1, tptp_fun_X_2(Y!0)) = X!1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6298, 6355, 1906, 2991, 6345, 6354])).
% 2.66/2.17 tff(6357,plain,
% 2.66/2.17 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3084, 6356])).
% 2.66/2.17 tff(6358,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6355])).
% 2.66/2.17 tff(6359,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[6354, 6358])).
% 2.66/2.17 tff(6360,plain,
% 2.66/2.17 (Z!5 = tptp_fun_X_2(X!1)),
% 2.66/2.17 inference(transitivity,[status(thm)],[6194, 1664])).
% 2.66/2.17 tff(6361,plain,
% 2.66/2.17 (big_f(Z!5, X!1) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.17 inference(monotonicity,[status(thm)],[6360])).
% 2.66/2.17 tff(6362,plain,
% 2.66/2.17 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Z!5, X!1)),
% 2.66/2.17 inference(symmetry,[status(thm)],[6361])).
% 2.66/2.17 tff(6363,plain,
% 2.66/2.17 (big_f(Z!5, X!1)),
% 2.66/2.17 inference(modus_ponens,[status(thm)],[862, 6362])).
% 2.66/2.17 tff(6364,plain,
% 2.66/2.17 ($false),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6210, 6363])).
% 2.66/2.17 tff(6365,plain,((~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))) | (~big_f(tptp_fun_X_2(X!1), X!1)) | (~(tptp_fun_X_2(X!1) = X!1)) | (~big_f(X!1, Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.17 tff(6366,plain,
% 2.66/2.17 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[6365, 6359, 6345, 3678, 154, 2991, 1906, 2501])).
% 2.66/2.17 tff(6367,plain,
% 2.66/2.17 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[462, 6366])).
% 2.66/2.17 tff(6368,plain,
% 2.66/2.17 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.66/2.17 inference(unit_resolution,[status(thm)],[3017, 6367])).
% 2.66/2.18 tff(6369,plain,
% 2.66/2.18 ((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[3019, 6368])).
% 2.66/2.18 tff(6370,plain,
% 2.66/2.18 (tptp_fun_X_2(Y!0) = W1!8),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[3086, 6369, 6357])).
% 2.66/2.18 tff(6371,plain,
% 2.66/2.18 (W1!8 = tptp_fun_X_2(Y!0)),
% 2.66/2.18 inference(symmetry,[status(thm)],[6370])).
% 2.66/2.18 tff(6372,plain,
% 2.66/2.18 (W1!8 = X!1),
% 2.66/2.18 inference(transitivity,[status(thm)],[6371, 1906])).
% 2.66/2.18 tff(6373,plain,
% 2.66/2.18 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6372])).
% 2.66/2.18 tff(6374,plain,
% 2.66/2.18 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.18 inference(transitivity,[status(thm)],[6373, 6347])).
% 2.66/2.18 tff(6375,plain,
% 2.66/2.18 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(tptp_fun_X_2(X!1), Y!0) = X!1)),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6374])).
% 2.66/2.18 tff(6376,plain,
% 2.66/2.18 ((tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.18 inference(transitivity,[status(thm)],[6375, 6349])).
% 2.66/2.18 tff(6377,plain,
% 2.66/2.18 (W1!8 = X!1),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[6370, 3166])).
% 2.66/2.18 tff(6378,plain,
% 2.66/2.18 (~((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[790, 6367])).
% 2.66/2.18 tff(6379,plain,
% 2.66/2.18 ((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[792, 6378])).
% 2.66/2.18 tff(6380,plain,
% 2.66/2.18 ((W1!8 = Y!0) <=> (X!1 = Y!0)),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6372])).
% 2.66/2.18 tff(6381,plain,
% 2.66/2.18 ((X!1 = Y!0) <=> (W1!8 = Y!0)),
% 2.66/2.18 inference(symmetry,[status(thm)],[6380])).
% 2.66/2.18 tff(6382,plain,
% 2.66/2.18 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.18 inference(transitivity,[status(thm)],[6381, 3764])).
% 2.66/2.18 tff(6383,plain,
% 2.66/2.18 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = W1!8))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6382])).
% 2.66/2.18 tff(6384,plain,
% 2.66/2.18 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[741, 6383])).
% 2.66/2.18 tff(6385,plain,
% 2.66/2.18 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[794, 6384, 6379])).
% 2.66/2.18 tff(6386,plain,
% 2.66/2.18 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[3101, 6385])).
% 2.66/2.18 tff(6387,plain,
% 2.66/2.18 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6161, 6386, 154, 41, 6336, 6377])).
% 2.66/2.18 tff(6388,plain,
% 2.66/2.18 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[6387, 6376])).
% 2.66/2.18 tff(6389,plain,
% 2.66/2.18 (~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6323, 6386, 154, 3678, 6345])).
% 2.66/2.18 tff(6390,plain,
% 2.66/2.18 ($false),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6389, 6388])).
% 2.66/2.18 tff(6391,plain,(big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~big_f(X!1, Y!0)) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.18 tff(6392,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (tptp_fun_Y1_11(X!1) = X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6391, 4769])).
% 2.66/2.18 tff(6393,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6392, 6176, 6042, 41, 144])).
% 2.66/2.18 tff(6394,assumption,(~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)), introduced(assumption)).
% 2.66/2.18 tff(6395,plain,
% 2.66/2.18 (tptp_fun_X1_10(Y!0, X!1) = Y!0),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1249, 6394, 1224])).
% 2.66/2.18 tff(6396,plain,
% 2.66/2.18 (Y!0 = tptp_fun_X1_10(Y!0, X!1)),
% 2.66/2.18 inference(symmetry,[status(thm)],[6395])).
% 2.66/2.18 tff(6397,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6396, 1906])).
% 2.66/2.18 tff(6398,plain,
% 2.66/2.18 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.18 inference(symmetry,[status(thm)],[6397])).
% 2.66/2.18 tff(6399,plain,
% 2.66/2.18 ((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6398])).
% 2.66/2.18 tff(6400,plain,
% 2.66/2.18 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[6394, 6399])).
% 2.66/2.18 tff(6401,plain,
% 2.66/2.18 ($false),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[3230, 6400])).
% 2.66/2.18 tff(6402,plain,(big_f(tptp_fun_X1_10(Y!0, X!1), X!1) | (~big_f(Y!0, tptp_fun_X_2(Y!0))) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.18 tff(6403,plain,
% 2.66/2.18 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6402, 6393, 6042, 6172])).
% 2.66/2.18 tff(6404,plain,
% 2.66/2.18 (~(tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1230, 6403, 6172])).
% 2.66/2.18 tff(6405,plain,
% 2.66/2.18 (tptp_fun_X1_10(Y!0, X!1) = X!1),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1243, 6404])).
% 2.66/2.18 tff(6406,plain,
% 2.66/2.18 (tptp_fun_X1_10(Y!0, X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.18 inference(transitivity,[status(thm)],[6405, 6043])).
% 2.66/2.18 tff(6407,plain,
% 2.66/2.18 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6406])).
% 2.66/2.18 tff(6408,plain,
% 2.66/2.18 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.66/2.18 inference(symmetry,[status(thm)],[6407])).
% 2.66/2.18 tff(6409,plain,
% 2.66/2.18 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6408])).
% 2.66/2.18 tff(6410,plain,
% 2.66/2.18 (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[5823, 6409])).
% 2.66/2.18 tff(6411,plain,
% 2.66/2.18 ($false),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6403, 6410])).
% 2.66/2.18 tff(6412,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(tptp_fun_X_2(Y!0), X!1) | (tptp_fun_Y1_11(X!1) = X!1) | (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (Y!0 = tptp_fun_Z1_12(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.18 tff(6413,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6412, 1268, 144, 5823, 6046])).
% 2.66/2.18 tff(6414,plain,
% 2.66/2.18 (~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1181, 6413, 6046])).
% 2.66/2.18 tff(6415,plain,
% 2.66/2.18 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[583, 6414])).
% 2.66/2.18 tff(6416,plain,
% 2.66/2.18 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.66/2.18 inference(symmetry,[status(thm)],[6044])).
% 2.66/2.18 tff(6417,plain,
% 2.66/2.18 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(X!1, tptp_fun_Y1_11(Y!0)))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6416])).
% 2.66/2.18 tff(6418,plain,
% 2.66/2.18 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[5823, 6417])).
% 2.66/2.18 tff(6419,plain,
% 2.66/2.18 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1254, 6418, 135, 40])).
% 2.66/2.18 tff(6420,plain,
% 2.66/2.18 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1256, 6419])).
% 2.66/2.18 tff(6421,plain,
% 2.66/2.18 (X!1 = W1!8),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1273, 6420, 1954])).
% 2.66/2.18 tff(6422,plain,
% 2.66/2.18 (W1!8 = X!1),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[28, 6421])).
% 2.66/2.18 tff(6423,plain,
% 2.66/2.18 (W1!8 = X!1),
% 2.66/2.18 inference(symmetry,[status(thm)],[6421])).
% 2.66/2.18 tff(6424,plain,
% 2.66/2.18 ((W1!8 = Y!0) <=> (X!1 = Y!0)),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6423])).
% 2.66/2.18 tff(6425,plain,
% 2.66/2.18 ((X!1 = Y!0) <=> (W1!8 = Y!0)),
% 2.66/2.18 inference(symmetry,[status(thm)],[6424])).
% 2.66/2.18 tff(6426,plain,
% 2.66/2.18 ((X!1 = Y!0) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.18 inference(transitivity,[status(thm)],[6425, 6130])).
% 2.66/2.18 tff(6427,plain,
% 2.66/2.18 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Y1_11(X!1) = W1!8))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6426])).
% 2.66/2.18 tff(6428,plain,
% 2.66/2.18 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[741, 6427])).
% 2.66/2.18 tff(6429,plain,
% 2.66/2.18 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[794, 6428, 1941])).
% 2.66/2.18 tff(6430,plain,
% 2.66/2.18 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[3101, 6429])).
% 2.66/2.18 tff(6431,plain,
% 2.66/2.18 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6071, 6430, 796])).
% 2.66/2.18 tff(6432,plain,
% 2.66/2.18 (~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[3099, 6430, 6431])).
% 2.66/2.18 tff(6433,plain,
% 2.66/2.18 (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[3956, 6432, 6422])).
% 2.66/2.18 tff(6434,plain,
% 2.66/2.18 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6153, 6433])).
% 2.66/2.18 tff(6435,plain,
% 2.66/2.18 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6421])).
% 2.66/2.18 tff(6436,plain,
% 2.66/2.18 (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.66/2.18 inference(transitivity,[status(thm)],[6435, 6434])).
% 2.66/2.18 tff(6437,plain,
% 2.66/2.18 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6436])).
% 2.66/2.18 tff(6438,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(symmetry,[status(thm)],[6437])).
% 2.66/2.18 tff(6439,plain,
% 2.66/2.18 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6438])).
% 2.66/2.18 tff(6440,assumption,(~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))), introduced(assumption)).
% 2.66/2.18 tff(6441,plain,
% 2.66/2.18 (~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[563, 34, 6440])).
% 2.66/2.18 tff(6442,plain,
% 2.66/2.18 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[561, 6441])).
% 2.66/2.18 tff(6443,plain,
% 2.66/2.18 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[84, 6442])).
% 2.66/2.18 tff(6444,plain,
% 2.66/2.18 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[82, 6443])).
% 2.66/2.18 tff(6445,plain,
% 2.66/2.18 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[220, 6444])).
% 2.66/2.18 tff(6446,plain,
% 2.66/2.18 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1713, 6445])).
% 2.66/2.18 tff(6447,plain,
% 2.66/2.18 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[5565, 6418, 6446, 40])).
% 2.66/2.18 tff(6448,plain,
% 2.66/2.18 (tptp_fun_X_2(X!1) = Y!0),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[105, 6447])).
% 2.66/2.18 tff(6449,plain,
% 2.66/2.18 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6448, 1786])).
% 2.66/2.18 tff(6450,plain,
% 2.66/2.18 ((~big_f(tptp_fun_X_2(X!1), Y!0)) <=> (~big_f(Y!0, tptp_fun_Y1_11(X!1)))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6449])).
% 2.66/2.18 tff(6451,plain,
% 2.66/2.18 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[222, 6445])).
% 2.66/2.18 tff(6452,plain,
% 2.66/2.18 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[224, 6447, 6451])).
% 2.66/2.18 tff(6453,plain,
% 2.66/2.18 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1413, 6448, 135, 40])).
% 2.66/2.18 tff(6454,plain,
% 2.66/2.18 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[1157, 6453, 6452])).
% 2.66/2.18 tff(6455,plain,
% 2.66/2.18 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[6454, 6450])).
% 2.66/2.18 tff(6456,plain,
% 2.66/2.18 (~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[6455, 6439])).
% 2.66/2.18 tff(6457,plain,
% 2.66/2.18 ($false),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6431, 6456])).
% 2.66/2.18 tff(6458,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | big_f(tptp_fun_X_2(Y!0), X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.18 tff(6459,plain,
% 2.66/2.18 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6458, 1279, 154, 1272, 6413, 5823, 6415])).
% 2.66/2.18 tff(6460,plain,
% 2.66/2.18 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.66/2.18 inference(transitivity,[status(thm)],[6459, 3378])).
% 2.66/2.18 tff(6461,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6460])).
% 2.66/2.18 tff(6462,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[6413, 6461])).
% 2.66/2.18 tff(6463,plain,
% 2.66/2.18 (big_f(X!1, tptp_fun_Z1_12(Y!0)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6043, 1260])).
% 2.66/2.18 tff(6464,plain,
% 2.66/2.18 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(X!1, tptp_fun_Z1_12(Y!0))),
% 2.66/2.18 inference(symmetry,[status(thm)],[6463])).
% 2.66/2.18 tff(6465,plain,
% 2.66/2.18 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(X!1, tptp_fun_Z1_12(Y!0)))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[6464])).
% 2.66/2.18 tff(6466,plain,
% 2.66/2.18 (~big_f(X!1, tptp_fun_Z1_12(Y!0))),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[5823, 6465])).
% 2.66/2.18 tff(6467,assumption,(big_f(X!1, tptp_fun_Z1_12(Y!0))), introduced(assumption)).
% 2.66/2.18 tff(6468,plain,
% 2.66/2.18 ($false),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6467, 6466])).
% 2.66/2.18 tff(6469,plain,((~big_f(X!1, tptp_fun_Z1_12(Y!0))) | big_f(tptp_fun_X_2(Y!0), X!1) | (~(tptp_fun_Z1_12(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.18 tff(6470,plain,
% 2.66/2.18 (~big_f(X!1, tptp_fun_Z1_12(Y!0))),
% 2.66/2.18 inference(unit_resolution,[status(thm)],[6469, 6051, 5823])).
% 2.66/2.18 tff(6471,plain,
% 2.66/2.18 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.18 inference(monotonicity,[status(thm)],[106, 3378])).
% 2.66/2.18 tff(6472,plain,
% 2.66/2.18 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.18 inference(symmetry,[status(thm)],[6471])).
% 2.66/2.18 tff(6473,plain,
% 2.66/2.18 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.18 inference(modus_ponens,[status(thm)],[2569, 6472])).
% 2.66/2.19 tff(6474,plain,
% 2.66/2.19 (~(W1!8 = Y!0)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6124, 6473, 495, 106])).
% 2.66/2.19 tff(6475,plain,
% 2.66/2.19 (W1!8 = X!1),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[19, 6474])).
% 2.66/2.19 tff(6476,assumption,((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))), introduced(assumption)).
% 2.66/2.19 tff(6477,plain,
% 2.66/2.19 (tptp_fun_X_2(Y!0) = W1!8),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[3648, 6475, 6042])).
% 2.66/2.19 tff(6478,plain,
% 2.66/2.19 (![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[3268, 6477, 6476])).
% 2.66/2.19 tff(6479,plain,
% 2.66/2.19 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[3235, 6478])).
% 2.66/2.19 tff(6480,plain,
% 2.66/2.19 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.19 inference(monotonicity,[status(thm)],[106, 6043])).
% 2.66/2.19 tff(6481,plain,
% 2.66/2.19 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6480])).
% 2.66/2.19 tff(6482,plain,
% 2.66/2.19 (~(tptp_fun_Y1_11(X!1) = W1!8)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[803, 6474, 154])).
% 2.66/2.19 tff(6483,plain,
% 2.66/2.19 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[794, 6482, 1941])).
% 2.66/2.19 tff(6484,plain,
% 2.66/2.19 ((~big_f(tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Y!0, tptp_fun_Y1_11(X!1)) = Y!0)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[788, 6483])).
% 2.66/2.19 tff(6485,plain,
% 2.66/2.19 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[5784, 6484, 2569])).
% 2.66/2.19 tff(6486,plain,
% 2.66/2.19 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[161, 6485, 144])).
% 2.66/2.19 tff(6487,plain,
% 2.66/2.19 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[191, 6486])).
% 2.66/2.19 tff(6488,plain,
% 2.66/2.19 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[88, 6487])).
% 2.66/2.19 tff(6489,plain,
% 2.66/2.19 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[82, 6488])).
% 2.66/2.19 tff(6490,plain,
% 2.66/2.19 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[220, 6489])).
% 2.66/2.19 tff(6491,plain,
% 2.66/2.19 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[222, 6490])).
% 2.66/2.19 tff(6492,plain,
% 2.66/2.19 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[224, 6491, 47])).
% 2.66/2.19 tff(6493,plain,
% 2.66/2.19 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[1157, 6492, 6473])).
% 2.66/2.19 tff(6494,plain,
% 2.66/2.19 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.19 inference(modus_ponens,[status(thm)],[6493, 6481])).
% 2.66/2.19 tff(6495,plain,
% 2.66/2.19 ((~(big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.66/2.19 inference(tautology,[status(thm)],[])).
% 2.66/2.19 tff(6496,plain,
% 2.66/2.19 (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6495, 6494, 6479])).
% 2.66/2.19 tff(6497,plain,
% 2.66/2.19 (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.66/2.19 inference(modus_ponens,[status(thm)],[4067, 4135])).
% 2.66/2.19 tff(6498,assumption,(~(Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))), introduced(assumption)).
% 2.66/2.19 tff(6499,plain,
% 2.66/2.19 ($false),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6498, 6497])).
% 2.66/2.19 tff(6500,plain,((~(tptp_fun_Z1_9(W1!8) = Y!0)) | (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) | (~(W1!8 = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.19 tff(6501,plain,
% 2.66/2.19 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6500, 6496, 6042, 6475])).
% 2.66/2.19 tff(6502,assumption,((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))), introduced(assumption)).
% 2.66/2.19 tff(6503,plain,
% 2.66/2.19 ((X!1 = tptp_fun_Z1_12(Y!0)) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.66/2.19 inference(symmetry,[status(thm)],[1291])).
% 2.66/2.19 tff(6504,plain,
% 2.66/2.19 ((tptp_fun_Z1_12(Y!0) = X!1) <=> (tptp_fun_Z1_12(Y!0) = W1!8)),
% 2.66/2.19 inference(transitivity,[status(thm)],[572, 6503])).
% 2.66/2.19 tff(6505,plain,
% 2.66/2.19 (tptp_fun_Z1_12(Y!0) = W1!8),
% 2.66/2.19 inference(modus_ponens,[status(thm)],[1260, 6504])).
% 2.66/2.19 tff(6506,plain,
% 2.66/2.19 ($false),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[1285, 6505])).
% 2.66/2.19 tff(6507,plain,((~(tptp_fun_Z1_12(Y!0) = X!1)) | (tptp_fun_Z1_12(Y!0) = W1!8) | (~(W1!8 = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.19 tff(6508,plain,
% 2.66/2.19 (tptp_fun_Z1_12(Y!0) = W1!8),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6507, 6475, 1260])).
% 2.66/2.19 tff(6509,plain,
% 2.66/2.19 ((~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))) | (~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))),
% 2.66/2.19 inference(tautology,[status(thm)],[])).
% 2.66/2.19 tff(6510,plain,
% 2.66/2.19 (![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6509, 6508, 6502])).
% 2.66/2.19 tff(6511,plain,
% 2.66/2.19 ((~![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))) | (big_f(X!1, tptp_fun_Z1_12(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))),
% 2.66/2.19 inference(quant_inst,[status(thm)],[])).
% 2.66/2.19 tff(6512,plain,
% 2.66/2.19 (big_f(X!1, tptp_fun_Z1_12(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6511, 6510])).
% 2.66/2.19 tff(6513,assumption,(~big_f(X!1, tptp_fun_Z1_12(Y!0))), introduced(assumption)).
% 2.66/2.19 tff(6514,plain,
% 2.66/2.19 ((~(big_f(X!1, tptp_fun_Z1_12(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))) | big_f(X!1, tptp_fun_Z1_12(Y!0)) | (~(X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))),
% 2.66/2.19 inference(tautology,[status(thm)],[])).
% 2.66/2.19 tff(6515,plain,
% 2.66/2.19 ((~(big_f(X!1, tptp_fun_Z1_12(Y!0)) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))) | (~(X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6514, 6513])).
% 2.66/2.19 tff(6516,plain,
% 2.66/2.19 (~(X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6515, 6512])).
% 2.66/2.19 tff(6517,plain,
% 2.66/2.19 (tptp_fun_Z1_12(Y!0) = tptp_fun_X_2(Y!0)),
% 2.66/2.19 inference(transitivity,[status(thm)],[1260, 2972])).
% 2.66/2.19 tff(6518,plain,
% 2.66/2.19 (tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)) = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6517])).
% 2.66/2.19 tff(6519,plain,
% 2.66/2.19 ((X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6518])).
% 2.66/2.19 tff(6520,plain,
% 2.66/2.19 ((X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))),
% 2.66/2.19 inference(symmetry,[status(thm)],[6519])).
% 2.66/2.19 tff(6521,plain,
% 2.66/2.19 (tptp_fun_Z1_9(tptp_fun_X_2(Y!0)) = tptp_fun_Z1_9(W1!8)),
% 2.66/2.19 inference(symmetry,[status(thm)],[4093])).
% 2.66/2.19 tff(6522,plain,
% 2.66/2.19 ((X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6521])).
% 2.66/2.19 tff(6523,plain,
% 2.66/2.19 ((X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) <=> (tptp_fun_Z1_9(W1!8) = X!1)),
% 2.66/2.19 inference(transitivity,[status(thm)],[6522, 2056])).
% 2.66/2.19 tff(6524,plain,
% 2.66/2.19 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.66/2.19 inference(symmetry,[status(thm)],[6523])).
% 2.66/2.19 tff(6525,plain,
% 2.66/2.19 ((tptp_fun_Z1_9(W1!8) = X!1) <=> (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))),
% 2.66/2.19 inference(transitivity,[status(thm)],[6524, 6520])).
% 2.66/2.19 tff(6526,plain,
% 2.66/2.19 (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))),
% 2.66/2.19 inference(modus_ponens,[status(thm)],[1473, 6525])).
% 2.66/2.19 tff(6527,assumption,(~(X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))), introduced(assumption)).
% 2.66/2.19 tff(6528,plain,
% 2.66/2.19 ($false),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6527, 6526])).
% 2.66/2.19 tff(6529,plain,((~(tptp_fun_Z1_9(W1!8) = X!1)) | (X!1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0))) | (~(W1!8 = X!1)) | (~(tptp_fun_X_2(Y!0) = X!1)) | (~(tptp_fun_Z1_12(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.19 tff(6530,plain,
% 2.66/2.19 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6529, 6516, 6042, 1260, 6475])).
% 2.66/2.19 tff(6531,plain,
% 2.66/2.19 ($false),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[522, 6530, 6501])).
% 2.66/2.19 tff(6532,plain,((tptp_fun_X_2(X!1) = X!1) | (~(tptp_fun_Z1_12(Y!0) = X!1)) | big_f(X!1, tptp_fun_Z1_12(Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~((~(tptp_fun_Z1_12(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Z1_12(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Z1_12(Y!0)))))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))) | (~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8))))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.19 tff(6533,plain,
% 2.66/2.19 (tptp_fun_X_2(X!1) = X!1),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6532, 6051, 6470, 144, 6462, 6049, 3267, 1279, 1456])).
% 2.66/2.19 tff(6534,plain,
% 2.66/2.19 (Y!0 = tptp_fun_Z1_12(X!1)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[5389, 5766, 2569])).
% 2.66/2.19 tff(6535,plain,
% 2.66/2.19 (tptp_fun_Z1_12(X!1) = Y!0),
% 2.66/2.19 inference(symmetry,[status(thm)],[6534])).
% 2.66/2.19 tff(6536,plain,
% 2.66/2.19 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> (X!1 = tptp_fun_Z1_12(X!1))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[5376, 5765])).
% 2.66/2.19 tff(6537,plain,
% 2.66/2.19 (X!1 = tptp_fun_Z1_12(X!1)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[5381, 6536, 5872])).
% 2.66/2.19 tff(6538,plain,
% 2.66/2.19 (X!1 = Y!0),
% 2.66/2.19 inference(transitivity,[status(thm)],[6537, 6535])).
% 2.66/2.19 tff(6539,plain,
% 2.66/2.19 ($false),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[741, 6538])).
% 2.66/2.19 tff(6540,plain,((~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))) | (~big_f(X!1, tptp_fun_Y1_11(X!1))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.19 tff(6541,plain,
% 2.66/2.19 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6540, 6462, 5756])).
% 2.66/2.19 tff(6542,plain,
% 2.66/2.19 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[161, 6541, 144])).
% 2.66/2.19 tff(6543,plain,
% 2.66/2.19 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[191, 6542])).
% 2.66/2.19 tff(6544,plain,
% 2.66/2.19 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[88, 6543])).
% 2.66/2.19 tff(6545,plain,
% 2.66/2.19 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[82, 6544])).
% 2.66/2.19 tff(6546,plain,
% 2.66/2.19 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[220, 6545])).
% 2.66/2.19 tff(6547,plain,
% 2.66/2.19 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[1713, 6546])).
% 2.66/2.19 tff(6548,plain,
% 2.66/2.19 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[1711, 6547, 6533])).
% 2.66/2.19 tff(6549,plain,
% 2.66/2.19 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[3679, 6548])).
% 2.66/2.19 tff(6550,plain,
% 2.66/2.19 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[5619, 6549, 6533])).
% 2.66/2.19 tff(6551,plain,
% 2.66/2.19 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[3694, 6550])).
% 2.66/2.19 tff(6552,plain,
% 2.66/2.19 (tptp_fun_X_2(X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.19 inference(transitivity,[status(thm)],[6533, 6043])).
% 2.66/2.19 tff(6553,plain,
% 2.66/2.19 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6552, 6551])).
% 2.66/2.19 tff(6554,plain,
% 2.66/2.19 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.19 inference(symmetry,[status(thm)],[6553])).
% 2.66/2.19 tff(6555,plain,
% 2.66/2.19 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6554])).
% 2.66/2.19 tff(6556,plain,
% 2.66/2.19 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.19 inference(modus_ponens,[status(thm)],[5823, 6555])).
% 2.66/2.19 tff(6557,plain,
% 2.66/2.19 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[3701, 6550, 6549])).
% 2.66/2.19 tff(6558,plain,
% 2.66/2.19 ($false),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6557, 6556])).
% 2.66/2.19 tff(6559,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | big_f(tptp_fun_X_2(Y!0), X!1) | (tptp_fun_Y1_11(X!1) = X!1) | (Y!0 = tptp_fun_Z1_12(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.19 tff(6560,plain,
% 2.66/2.19 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[6559, 5823, 144, 6046])).
% 2.66/2.19 tff(6561,plain,
% 2.66/2.19 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[462, 6560])).
% 2.66/2.19 tff(6562,plain,
% 2.66/2.19 (Y!0 = Z!5),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[725, 722, 724])).
% 2.66/2.19 tff(6563,plain,
% 2.66/2.19 (tptp_fun_Y_7(Y!0, X!1) = tptp_fun_Y_7(Z!5, X!1)),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6562])).
% 2.66/2.19 tff(6564,plain,
% 2.66/2.19 ((tptp_fun_Y_7(Y!0, X!1) = Y!0) <=> (tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6563])).
% 2.66/2.19 tff(6565,plain,
% 2.66/2.19 ((~(tptp_fun_Y_7(Y!0, X!1) = Y!0)) <=> (~(tptp_fun_Y_7(Z!5, X!1) = Y!0))),
% 2.66/2.19 inference(monotonicity,[status(thm)],[6564])).
% 2.66/2.19 tff(6566,plain,
% 2.66/2.19 (![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W))),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[3366, 722, 341])).
% 2.66/2.19 tff(6567,plain,
% 2.66/2.19 ((~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))) <=> (tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[1842, 6566])).
% 2.66/2.19 tff(6568,plain,
% 2.66/2.19 (~(tptp_fun_Y_7(Y!0, X!1) = Y!0)),
% 2.66/2.19 inference(unit_resolution,[status(thm)],[5841, 6567])).
% 2.66/2.19 tff(6569,plain,
% 2.66/2.20 (~(tptp_fun_Y_7(Z!5, X!1) = Y!0)),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[6568, 6565])).
% 2.66/2.20 tff(6570,plain,
% 2.66/2.20 (tptp_fun_Y_7(Z!5, X!1) = X!1),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[3878, 6569])).
% 2.66/2.20 tff(6571,plain,
% 2.66/2.20 (tptp_fun_Y_7(Y!0, X!1) = X!1),
% 2.66/2.20 inference(transitivity,[status(thm)],[6563, 6570])).
% 2.66/2.20 tff(6572,plain,
% 2.66/2.20 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6043, 6571])).
% 2.66/2.20 tff(6573,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.66/2.20 inference(symmetry,[status(thm)],[6572])).
% 2.66/2.20 tff(6574,plain,
% 2.66/2.20 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1)))),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6573])).
% 2.66/2.20 tff(6575,plain,
% 2.66/2.20 (~big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[5823, 6574])).
% 2.66/2.20 tff(6576,plain,
% 2.66/2.20 (big_f(X!1, tptp_fun_Y_7(Y!0, X!1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1844, 6568, 6567])).
% 2.66/2.20 tff(6577,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6576, 6575])).
% 2.66/2.20 tff(6578,plain,(![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W)) | big_f(tptp_fun_X_2(Y!0), X!1) | (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X))))))))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6579,plain,
% 2.66/2.20 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6578, 5823, 6561])).
% 2.66/2.20 tff(6580,plain,
% 2.66/2.20 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[720, 6579])).
% 2.66/2.20 tff(6581,plain,
% 2.66/2.20 ((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1110, 6579])).
% 2.66/2.20 tff(6582,assumption,(~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))), introduced(assumption)).
% 2.66/2.20 tff(6583,plain,
% 2.66/2.20 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[561, 6582])).
% 2.66/2.20 tff(6584,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6059, 6418])).
% 2.66/2.20 tff(6585,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | big_f(tptp_fun_X_2(Y!0), X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6586,plain,
% 2.66/2.20 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6585, 6583, 41, 5823])).
% 2.66/2.20 tff(6587,plain,
% 2.66/2.20 (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[5602, 6586, 41])).
% 2.66/2.20 tff(6588,plain,
% 2.66/2.20 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[86, 6582])).
% 2.66/2.20 tff(6589,plain,
% 2.66/2.20 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[113, 6586, 6588])).
% 2.66/2.20 tff(6590,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[958, 6589, 6587])).
% 2.66/2.20 tff(6591,plain,(((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6592,plain,
% 2.66/2.20 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6591, 41, 5823])).
% 2.66/2.20 tff(6593,plain,
% 2.66/2.20 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[84, 6592])).
% 2.66/2.20 tff(6594,plain,
% 2.66/2.20 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[82, 6593])).
% 2.66/2.20 tff(6595,plain,
% 2.66/2.20 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[220, 6594])).
% 2.66/2.20 tff(6596,plain,
% 2.66/2.20 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1713, 6595])).
% 2.66/2.20 tff(6597,plain,
% 2.66/2.20 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[5565, 6104, 6596, 598])).
% 2.66/2.20 tff(6598,plain,
% 2.66/2.20 (tptp_fun_X_2(X!1) = Y!0),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[105, 6597])).
% 2.66/2.20 tff(6599,plain,
% 2.66/2.20 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[222, 6595])).
% 2.66/2.20 tff(6600,plain,
% 2.66/2.20 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[224, 6597, 6599])).
% 2.66/2.20 tff(6601,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[234, 6600])).
% 2.66/2.20 tff(6602,plain,
% 2.66/2.20 (~(tptp_fun_W_3(X!1) = X!1)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1578, 6601, 41, 598, 6598])).
% 2.66/2.20 tff(6603,plain,
% 2.66/2.20 (tptp_fun_Y1_11(Y!0) = tptp_fun_X_2(Y!0)),
% 2.66/2.20 inference(transitivity,[status(thm)],[598, 6043])).
% 2.66/2.20 tff(6604,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6603])).
% 2.66/2.20 tff(6605,plain,
% 2.66/2.20 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6604])).
% 2.66/2.20 tff(6606,plain,
% 2.66/2.20 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[41, 6605])).
% 2.66/2.20 tff(6607,plain,
% 2.66/2.20 (~(tptp_fun_W_3(X!1) = Y!0)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[2996, 6601, 693, 6606, 6042, 6598])).
% 2.66/2.20 tff(6608,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[252, 6607, 6602])).
% 2.66/2.20 tff(6609,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6610,plain,
% 2.66/2.20 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6609, 41, 693, 5823])).
% 2.66/2.20 tff(6611,plain,
% 2.66/2.20 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[39, 6610])).
% 2.66/2.20 tff(6612,plain,
% 2.66/2.20 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.66/2.20 inference(transitivity,[status(thm)],[6611, 3378])).
% 2.66/2.20 tff(6613,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6612])).
% 2.66/2.20 tff(6614,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.20 inference(symmetry,[status(thm)],[6613])).
% 2.66/2.20 tff(6615,plain,
% 2.66/2.20 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[3350, 6611, 6042, 1079, 41])).
% 2.66/2.20 tff(6616,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6392, 6615, 6042, 41, 144])).
% 2.66/2.20 tff(6617,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[6616, 6614])).
% 2.66/2.20 tff(6618,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[41, 6617])).
% 2.66/2.20 tff(6619,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (tptp_fun_Y1_11(X!1) = X!1) | (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6620,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6619, 6581, 144, 6580, 5823])).
% 2.66/2.20 tff(6621,plain,
% 2.66/2.20 (~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1181, 6620, 6046])).
% 2.66/2.20 tff(6622,plain,
% 2.66/2.20 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[583, 6621])).
% 2.66/2.20 tff(6623,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[3631, 6448, 1079, 135, 40])).
% 2.66/2.20 tff(6624,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1157, 6453, 6623, 6452])).
% 2.66/2.20 tff(6625,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | big_f(tptp_fun_X_2(Y!0), X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6626,plain,
% 2.66/2.20 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6625, 6620, 6581, 5823, 6622])).
% 2.66/2.20 tff(6627,plain,
% 2.66/2.20 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.66/2.20 inference(transitivity,[status(thm)],[6626, 3378])).
% 2.66/2.20 tff(6628,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6627])).
% 2.66/2.20 tff(6629,plain,
% 2.66/2.20 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[6620, 6628])).
% 2.66/2.20 tff(6630,plain,
% 2.66/2.20 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6540, 6629, 5756])).
% 2.66/2.20 tff(6631,plain,
% 2.66/2.20 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[161, 6630, 144])).
% 2.66/2.20 tff(6632,plain,
% 2.66/2.20 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[191, 6631])).
% 2.66/2.20 tff(6633,plain,
% 2.66/2.20 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[88, 6632])).
% 2.66/2.20 tff(6634,plain,
% 2.66/2.20 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[82, 6633])).
% 2.66/2.20 tff(6635,plain,
% 2.66/2.20 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[220, 6634])).
% 2.66/2.20 tff(6636,plain,
% 2.66/2.20 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[222, 6635])).
% 2.66/2.20 tff(6637,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[234, 3384])).
% 2.66/2.20 tff(6638,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[2569, 3732])).
% 2.66/2.20 tff(6639,plain,
% 2.66/2.20 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1157, 6638, 3384])).
% 2.66/2.20 tff(6640,plain,
% 2.66/2.20 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[6639, 6481])).
% 2.66/2.20 tff(6641,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(X!1), Y!0) <=> (Y!0 = tptp_fun_W_3(X!1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1146, 3384])).
% 2.66/2.20 tff(6642,plain,
% 2.66/2.20 (Y!0 = tptp_fun_W_3(X!1)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1148, 6638, 6641])).
% 2.66/2.20 tff(6643,plain,
% 2.66/2.20 (tptp_fun_W_3(X!1) = Y!0),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[6642, 1581])).
% 2.66/2.20 tff(6644,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[2996, 6643, 6640, 693, 106, 6042, 6637])).
% 2.66/2.20 tff(6645,plain,((tptp_fun_X_2(X!1) = X!1) | (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | (~big_f(Y!0, tptp_fun_Y1_11(X!1))) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6646,plain,
% 2.66/2.20 (tptp_fun_X_2(X!1) = X!1),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6645, 6580, 6629, 154, 6636])).
% 2.66/2.20 tff(6647,plain,
% 2.66/2.20 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1713, 6635])).
% 2.66/2.20 tff(6648,plain,
% 2.66/2.20 (![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[1711, 6646, 6647])).
% 2.66/2.20 tff(6649,plain,
% 2.66/2.20 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))) <=> (tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[3679, 6648])).
% 2.66/2.20 tff(6650,plain,
% 2.66/2.20 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[5619, 6649, 6646])).
% 2.66/2.20 tff(6651,plain,
% 2.66/2.20 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[3694, 6650])).
% 2.66/2.20 tff(6652,plain,
% 2.66/2.20 (tptp_fun_X_2(X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.20 inference(transitivity,[status(thm)],[6646, 6043])).
% 2.66/2.20 tff(6653,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6652, 6651])).
% 2.66/2.20 tff(6654,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.20 inference(symmetry,[status(thm)],[6653])).
% 2.66/2.20 tff(6655,plain,
% 2.66/2.20 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6654])).
% 2.66/2.20 tff(6656,plain,
% 2.66/2.20 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[5823, 6655])).
% 2.66/2.20 tff(6657,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[3701, 6650, 6649])).
% 2.66/2.20 tff(6658,plain,
% 2.66/2.20 ($false),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6657, 6656])).
% 2.66/2.20 tff(6659,plain,(big_f(tptp_fun_X_2(Y!0), X!1) | (tptp_fun_Y1_11(X!1) = X!1) | (Y!0 = tptp_fun_Z1_12(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.20 tff(6660,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6659, 144, 6046])).
% 2.66/2.20 tff(6661,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.66/2.20 inference(monotonicity,[status(thm)],[6042])).
% 2.66/2.20 tff(6662,plain,
% 2.66/2.20 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.66/2.20 inference(symmetry,[status(thm)],[6661])).
% 2.66/2.20 tff(6663,plain,
% 2.66/2.20 (big_f(tptp_fun_X_2(Y!0), Y!0)),
% 2.66/2.20 inference(modus_ponens,[status(thm)],[4769, 6662])).
% 2.66/2.20 tff(6664,plain,
% 2.66/2.20 ((~(big_f(tptp_fun_X_2(Y!0), Y!0) <=> (Y!0 = tptp_fun_W_3(Y!0)))) | (~big_f(tptp_fun_X_2(Y!0), Y!0)) | (Y!0 = tptp_fun_W_3(Y!0))),
% 2.66/2.20 inference(tautology,[status(thm)],[])).
% 2.66/2.20 tff(6665,plain,
% 2.66/2.20 (Y!0 = tptp_fun_W_3(Y!0)),
% 2.66/2.20 inference(unit_resolution,[status(thm)],[6664, 3241, 6663])).
% 2.66/2.20 tff(6666,plain,
% 2.66/2.20 (tptp_fun_W_3(Y!0) = Y!0),
% 2.66/2.20 inference(symmetry,[status(thm)],[6665])).
% 2.66/2.20 tff(6667,plain,
% 2.66/2.20 ((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (big_f(tptp_fun_X_2(Y!0), X!1) <=> (X!1 = tptp_fun_W_3(Y!0)))),
% 2.66/2.20 inference(quant_inst,[status(thm)],[])).
% 2.66/2.21 tff(6668,plain,
% 2.66/2.21 (big_f(tptp_fun_X_2(Y!0), X!1) <=> (X!1 = tptp_fun_W_3(Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6667, 3240])).
% 2.66/2.21 tff(6669,plain,
% 2.66/2.21 ((~(big_f(tptp_fun_X_2(Y!0), X!1) <=> (X!1 = tptp_fun_W_3(Y!0)))) | (~big_f(tptp_fun_X_2(Y!0), X!1)) | (X!1 = tptp_fun_W_3(Y!0))),
% 2.66/2.21 inference(tautology,[status(thm)],[])).
% 2.66/2.21 tff(6670,plain,
% 2.66/2.21 (X!1 = tptp_fun_W_3(Y!0)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6669, 6668, 5525])).
% 2.66/2.21 tff(6671,plain,
% 2.66/2.21 (X!1 = Y!0),
% 2.66/2.21 inference(transitivity,[status(thm)],[6670, 6666])).
% 2.66/2.21 tff(6672,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[741, 6671])).
% 2.66/2.21 tff(6673,plain,((~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))) | (~big_f(tptp_fun_X_2(Y!0), X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6674,plain,
% 2.66/2.21 (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6673, 6660])).
% 2.66/2.21 tff(6675,plain,
% 2.66/2.21 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1858, 6674, 6041])).
% 2.66/2.21 tff(6676,plain,
% 2.66/2.21 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[2663, 6675])).
% 2.66/2.21 tff(6677,plain,
% 2.66/2.21 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[56, 6676])).
% 2.66/2.21 tff(6678,plain,
% 2.66/2.21 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[82, 6677])).
% 2.66/2.21 tff(6679,plain,
% 2.66/2.21 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[84, 6678])).
% 2.66/2.21 tff(6680,plain,
% 2.66/2.21 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[561, 6679])).
% 2.66/2.21 tff(6681,plain,
% 2.66/2.21 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[88, 6678])).
% 2.66/2.21 tff(6682,plain,
% 2.66/2.21 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[191, 6681])).
% 2.66/2.21 tff(6683,plain,
% 2.66/2.21 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[161, 6682, 144])).
% 2.66/2.21 tff(6684,plain,
% 2.66/2.21 (~big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6540, 6683, 5756])).
% 2.66/2.21 tff(6685,plain,
% 2.66/2.21 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[86, 6679])).
% 2.66/2.21 tff(6686,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6392, 41, 6042, 2501, 144])).
% 2.66/2.21 tff(6687,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.21 inference(symmetry,[status(thm)],[6604])).
% 2.66/2.21 tff(6688,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.21 inference(modus_ponens,[status(thm)],[3230, 6687])).
% 2.66/2.21 tff(6689,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[41, 6688])).
% 2.66/2.21 tff(6690,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~big_f(Y!0, tptp_fun_X_2(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6691,plain,
% 2.66/2.21 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6690, 41, 6686])).
% 2.66/2.21 tff(6692,plain,
% 2.66/2.21 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[39, 6691])).
% 2.66/2.21 tff(6693,plain,
% 2.66/2.21 (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[5602, 6692, 41])).
% 2.66/2.21 tff(6694,plain,
% 2.66/2.21 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[113, 6692, 112])).
% 2.66/2.21 tff(6695,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[958, 6694, 6693])).
% 2.66/2.21 tff(6696,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6697,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6696, 6685, 6684, 144])).
% 2.66/2.21 tff(6698,plain,
% 2.66/2.21 (~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1181, 6697, 6046])).
% 2.66/2.21 tff(6699,plain,
% 2.66/2.21 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[583, 6698])).
% 2.66/2.21 tff(6700,plain,
% 2.66/2.21 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[563, 6699, 6680])).
% 2.66/2.21 tff(6701,plain,
% 2.66/2.21 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.66/2.21 inference(transitivity,[status(thm)],[6700, 3378])).
% 2.66/2.21 tff(6702,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6701])).
% 2.66/2.21 tff(6703,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.21 inference(symmetry,[status(thm)],[6702])).
% 2.66/2.21 tff(6704,plain,
% 2.66/2.21 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6703])).
% 2.66/2.21 tff(6705,plain,
% 2.66/2.21 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.21 inference(modus_ponens,[status(thm)],[6684, 6704])).
% 2.66/2.21 tff(6706,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6697, 6705])).
% 2.66/2.21 tff(6707,plain,((tptp_fun_Y1_11(X!1) = X!1) | (Y!0 = tptp_fun_Z1_12(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6708,plain,
% 2.66/2.21 (Y!0 = tptp_fun_Z1_12(Y!0)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6707, 144])).
% 2.66/2.21 tff(6709,plain,
% 2.66/2.21 (~(big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> (Y!0 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[585, 6708, 41])).
% 2.66/2.21 tff(6710,plain,
% 2.66/2.21 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[583, 6709])).
% 2.66/2.21 tff(6711,plain,
% 2.66/2.21 (Y!0 = tptp_fun_Z1_12(Y!0)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6659, 144, 5823])).
% 2.66/2.21 tff(6712,plain,
% 2.66/2.21 (tptp_fun_Z1_12(Y!0) = Y!0),
% 2.66/2.21 inference(symmetry,[status(thm)],[6711])).
% 2.66/2.21 tff(6713,plain,
% 2.66/2.21 ((X!1 = tptp_fun_Z1_12(Y!0)) <=> (X!1 = Y!0)),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6712])).
% 2.66/2.21 tff(6714,plain,
% 2.66/2.21 ((X!1 = Y!0) <=> (X!1 = tptp_fun_Z1_12(Y!0))),
% 2.66/2.21 inference(symmetry,[status(thm)],[6713])).
% 2.66/2.21 tff(6715,plain,
% 2.66/2.21 ((X!1 = Y!0) <=> (tptp_fun_Z1_12(Y!0) = X!1)),
% 2.66/2.21 inference(transitivity,[status(thm)],[6714, 573])).
% 2.66/2.21 tff(6716,plain,
% 2.66/2.21 ((~(X!1 = Y!0)) <=> (~(tptp_fun_Z1_12(Y!0) = X!1))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6715])).
% 2.66/2.21 tff(6717,plain,
% 2.66/2.21 (~(tptp_fun_Z1_12(Y!0) = X!1)),
% 2.66/2.21 inference(modus_ponens,[status(thm)],[741, 6716])).
% 2.66/2.21 tff(6718,plain,
% 2.66/2.21 (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6127, 598, 5823, 41, 6596, 6599])).
% 2.66/2.21 tff(6719,plain,
% 2.66/2.21 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[481, 6718])).
% 2.66/2.21 tff(6720,plain,
% 2.66/2.21 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6609, 598, 5823, 41])).
% 2.66/2.21 tff(6721,plain,
% 2.66/2.21 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[720, 6720])).
% 2.66/2.21 tff(6722,plain,
% 2.66/2.21 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6578, 6721, 5823])).
% 2.66/2.21 tff(6723,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[462, 6722, 6719])).
% 2.66/2.21 tff(6724,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(tptp_fun_X_2(Y!0), X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6725,plain,
% 2.66/2.21 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6724, 41, 5823])).
% 2.66/2.21 tff(6726,plain,
% 2.66/2.21 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[39, 6725])).
% 2.66/2.21 tff(6727,plain,
% 2.66/2.21 (~(tptp_fun_Y_4(Y!0, X!1) = Y!0)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[5619, 3680, 1663])).
% 2.66/2.21 tff(6728,plain,
% 2.66/2.21 (tptp_fun_Y_4(Y!0, X!1) = X!1),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3694, 6727])).
% 2.66/2.21 tff(6729,plain,
% 2.66/2.21 (tptp_fun_X_2(X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.21 inference(transitivity,[status(thm)],[1663, 6043])).
% 2.66/2.21 tff(6730,plain,
% 2.66/2.21 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6729, 6728])).
% 2.66/2.21 tff(6731,plain,
% 2.66/2.21 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.21 inference(symmetry,[status(thm)],[6730])).
% 2.66/2.21 tff(6732,plain,
% 2.66/2.21 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1)))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6731])).
% 2.66/2.21 tff(6733,plain,
% 2.66/2.21 (~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.21 inference(modus_ponens,[status(thm)],[5823, 6732])).
% 2.66/2.21 tff(6734,plain,
% 2.66/2.21 (big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(Y!0, X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3701, 6727, 3680])).
% 2.66/2.21 tff(6735,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6734, 6733])).
% 2.66/2.21 tff(6736,plain,((~(tptp_fun_X_2(X!1) = X!1)) | big_f(tptp_fun_X_2(Y!0), X!1) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6737,plain,
% 2.66/2.21 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6736, 6596, 5823])).
% 2.66/2.21 tff(6738,plain,
% 2.66/2.21 ((tptp_fun_X_2(X!1) = X!1) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3396, 6042])).
% 2.66/2.21 tff(6739,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6738, 6737, 41, 6726, 6599])).
% 2.66/2.21 tff(6740,plain,
% 2.66/2.21 ((~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | (~big_f(Y!0, tptp_fun_X_2(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3350, 6042])).
% 2.66/2.21 tff(6741,plain,
% 2.66/2.21 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6740, 6739, 41, 6726])).
% 2.66/2.21 tff(6742,plain,
% 2.66/2.21 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1110, 6741])).
% 2.66/2.21 tff(6743,plain,
% 2.66/2.21 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6578, 6742, 5823])).
% 2.66/2.21 tff(6744,plain,
% 2.66/2.21 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6402, 1224, 6042, 3230])).
% 2.66/2.21 tff(6745,plain,
% 2.66/2.21 (~(tptp_fun_X1_10(Y!0, X!1) = Y!0)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1230, 6744, 1224])).
% 2.66/2.21 tff(6746,plain,
% 2.66/2.21 (tptp_fun_X1_10(Y!0, X!1) = X!1),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1243, 6745])).
% 2.66/2.21 tff(6747,plain,
% 2.66/2.21 (tptp_fun_X1_10(Y!0, X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.21 inference(transitivity,[status(thm)],[6746, 6043])).
% 2.66/2.21 tff(6748,plain,
% 2.66/2.21 (big_f(tptp_fun_X1_10(Y!0, X!1), X!1) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6747])).
% 2.66/2.21 tff(6749,plain,
% 2.66/2.21 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.66/2.21 inference(symmetry,[status(thm)],[6748])).
% 2.66/2.21 tff(6750,plain,
% 2.66/2.21 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6749])).
% 2.66/2.21 tff(6751,plain,
% 2.66/2.21 (~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)),
% 2.66/2.21 inference(modus_ponens,[status(thm)],[5823, 6750])).
% 2.66/2.21 tff(6752,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6744, 6751])).
% 2.66/2.21 tff(6753,plain,((~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))) | big_f(tptp_fun_X_2(Y!0), X!1) | (~big_f(Y!0, tptp_fun_X_2(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6754,plain,
% 2.66/2.21 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6753, 6739, 5823])).
% 2.66/2.21 tff(6755,plain,
% 2.66/2.21 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1256, 6754])).
% 2.66/2.21 tff(6756,plain,
% 2.66/2.21 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6170, 6755, 796, 41, 6726])).
% 2.66/2.21 tff(6757,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[462, 6756, 6743])).
% 2.66/2.21 tff(6758,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6759,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6758, 796, 5823])).
% 2.66/2.21 tff(6760,plain,
% 2.66/2.21 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1254, 6104, 6759, 598])).
% 2.66/2.21 tff(6761,plain,
% 2.66/2.21 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1256, 6760])).
% 2.66/2.21 tff(6762,plain,
% 2.66/2.21 (tptp_fun_Y_7(X!1, Y!0) = tptp_fun_Y1_11(X!1)),
% 2.66/2.21 inference(transitivity,[status(thm)],[1102, 1786])).
% 2.66/2.21 tff(6763,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6762])).
% 2.66/2.21 tff(6764,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.66/2.21 inference(symmetry,[status(thm)],[6763])).
% 2.66/2.21 tff(6765,plain,
% 2.66/2.21 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0)))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6764])).
% 2.66/2.21 tff(6766,plain,
% 2.66/2.21 (~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))),
% 2.66/2.21 inference(modus_ponens,[status(thm)],[2501, 6765])).
% 2.66/2.21 tff(6767,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1092, 6766])).
% 2.66/2.21 tff(6768,plain,((~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))) | big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6769,plain,
% 2.66/2.21 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6768, 2501, 796, 6759, 598])).
% 2.66/2.21 tff(6770,plain,
% 2.66/2.21 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1110, 6769])).
% 2.66/2.21 tff(6771,plain,
% 2.66/2.21 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6578, 6770, 5823])).
% 2.66/2.21 tff(6772,plain,
% 2.66/2.21 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[462, 6771])).
% 2.66/2.21 tff(6773,plain,
% 2.66/2.21 (~((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1))))))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1269, 6772])).
% 2.66/2.21 tff(6774,plain,
% 2.66/2.21 ((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1271, 6773])).
% 2.66/2.21 tff(6775,plain,
% 2.66/2.21 (X!1 = W1!8),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1273, 6774, 6761])).
% 2.66/2.21 tff(6776,plain,
% 2.66/2.21 (W1!8 = X!1),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[28, 6775])).
% 2.66/2.21 tff(6777,plain,
% 2.66/2.21 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[1298, 6772, 1266, 6761, 796])).
% 2.66/2.21 tff(6778,plain,
% 2.66/2.21 ((~big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3101, 6777])).
% 2.66/2.21 tff(6779,plain,
% 2.66/2.21 (big_f(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6071, 6778, 796])).
% 2.66/2.21 tff(6780,plain,
% 2.66/2.21 (~(tptp_fun_X1_10(X!1, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3099, 6779, 6778])).
% 2.66/2.21 tff(6781,plain,
% 2.66/2.21 (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = X!1)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3956, 6780, 6776])).
% 2.66/2.21 tff(6782,plain,
% 2.66/2.21 (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = Y!0),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6153, 6781])).
% 2.66/2.21 tff(6783,plain,
% 2.66/2.21 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6782])).
% 2.66/2.21 tff(6784,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(symmetry,[status(thm)],[6783])).
% 2.66/2.21 tff(6785,plain,
% 2.66/2.21 ((~big_f(Y!0, tptp_fun_Y1_11(X!1))) <=> (~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1)))),
% 2.66/2.21 inference(monotonicity,[status(thm)],[6784])).
% 2.66/2.21 tff(6786,plain,
% 2.66/2.21 (~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(modus_ponens,[status(thm)],[2501, 6785])).
% 2.66/2.21 tff(6787,plain,
% 2.66/2.21 ((~big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3916, 6777])).
% 2.66/2.21 tff(6788,plain,
% 2.66/2.21 (~(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)) = W1!8)),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3932, 6781, 6776])).
% 2.66/2.21 tff(6789,plain,
% 2.66/2.21 (big_f(tptp_fun_X1_10(W1!8, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[3934, 6788, 6787])).
% 2.66/2.21 tff(6790,plain,
% 2.66/2.21 ($false),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6789, 6786])).
% 2.66/2.21 tff(6791,plain,(big_f(Y!0, tptp_fun_Y1_11(X!1)) | (~(tptp_fun_Y1_11(X!1) = Y!0)) | (tptp_fun_Z1_12(Y!0) = X!1) | big_f(tptp_fun_X_2(Y!0), X!1) | (~(tptp_fun_Y1_11(Y!0) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.21 tff(6792,plain,
% 2.66/2.21 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6791, 598, 6717, 5823, 154])).
% 2.66/2.21 tff(6793,plain,
% 2.66/2.21 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.21 inference(unit_resolution,[status(thm)],[6540, 6792, 5756])).
% 2.66/2.21 tff(6794,plain,
% 2.66/2.21 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[161, 6793, 144])).
% 2.66/2.22 tff(6795,plain,
% 2.66/2.22 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[191, 6794])).
% 2.66/2.22 tff(6796,plain,
% 2.66/2.22 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[88, 6795])).
% 2.66/2.22 tff(6797,plain,
% 2.66/2.22 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[82, 6796])).
% 2.66/2.22 tff(6798,plain,
% 2.66/2.22 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[220, 6797])).
% 2.66/2.22 tff(6799,plain,
% 2.66/2.22 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[1713, 6798])).
% 2.66/2.22 tff(6800,plain,
% 2.66/2.22 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6736, 6799, 5823])).
% 2.66/2.22 tff(6801,plain,
% 2.66/2.22 (tptp_fun_X_2(X!1) = Y!0),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[105, 6800])).
% 2.66/2.22 tff(6802,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6801, 3378])).
% 2.66/2.22 tff(6803,plain,
% 2.66/2.22 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.22 inference(symmetry,[status(thm)],[6802])).
% 2.66/2.22 tff(6804,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.22 inference(modus_ponens,[status(thm)],[6792, 6803])).
% 2.66/2.22 tff(6805,plain,
% 2.66/2.22 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[222, 6798])).
% 2.66/2.22 tff(6806,plain,
% 2.66/2.22 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[224, 6800, 6805])).
% 2.66/2.22 tff(6807,plain,
% 2.66/2.22 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6758, 154, 5823])).
% 2.66/2.22 tff(6808,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[1413, 6801, 6807, 598])).
% 2.66/2.22 tff(6809,plain,
% 2.66/2.22 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[1157, 6808, 6806])).
% 2.66/2.22 tff(6810,plain,
% 2.66/2.22 ($false),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6809, 6804])).
% 2.66/2.22 tff(6811,plain,((~(tptp_fun_Y1_11(Y!0) = X!1)) | big_f(tptp_fun_X_2(Y!0), X!1) | (tptp_fun_Y1_11(X!1) = X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.22 tff(6812,plain,
% 2.66/2.22 (~(tptp_fun_Y1_11(Y!0) = X!1)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6811, 144, 5823])).
% 2.66/2.22 tff(6813,plain,
% 2.66/2.22 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[39, 6812])).
% 2.66/2.22 tff(6814,plain,
% 2.66/2.22 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.66/2.22 inference(transitivity,[status(thm)],[6813, 3378])).
% 2.66/2.22 tff(6815,plain,
% 2.66/2.22 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6814])).
% 2.66/2.22 tff(6816,plain,
% 2.66/2.22 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.22 inference(modus_ponens,[status(thm)],[6807, 6815])).
% 2.66/2.22 tff(6817,plain,
% 2.66/2.22 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6540, 6816, 5756])).
% 2.66/2.22 tff(6818,plain,
% 2.66/2.22 (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[161, 6817, 144])).
% 2.66/2.22 tff(6819,plain,
% 2.66/2.22 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[191, 6818])).
% 2.66/2.22 tff(6820,plain,
% 2.66/2.22 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[88, 6819])).
% 2.66/2.22 tff(6821,plain,
% 2.66/2.22 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[82, 6820])).
% 2.66/2.22 tff(6822,plain,
% 2.66/2.22 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[220, 6821])).
% 2.66/2.22 tff(6823,plain,
% 2.66/2.22 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[222, 6822])).
% 2.66/2.22 tff(6824,plain,
% 2.66/2.22 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[1713, 6822])).
% 2.66/2.22 tff(6825,plain,
% 2.66/2.22 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6736, 6824, 5823])).
% 2.66/2.22 tff(6826,plain,
% 2.66/2.22 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6645, 6825, 154, 6816, 6823])).
% 2.66/2.22 tff(6827,plain,
% 2.66/2.22 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[720, 6826])).
% 2.66/2.22 tff(6828,plain,
% 2.66/2.22 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6578, 6827, 5823])).
% 2.66/2.22 tff(6829,plain,
% 2.66/2.22 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[462, 6828])).
% 2.66/2.22 tff(6830,plain,
% 2.66/2.22 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[481, 6829])).
% 2.66/2.22 tff(6831,plain,
% 2.66/2.22 (big_f(X!1, W1!8) <=> (X!1 = tptp_fun_Z1_9(W1!8))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[496, 6830])).
% 2.66/2.22 tff(6832,plain,
% 2.66/2.22 (big_f(X!1, W1!8) <=> big_f(tptp_fun_X_2(Y!0), W1!8)),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6043])).
% 2.66/2.22 tff(6833,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(Y!0), W1!8) <=> big_f(X!1, W1!8)),
% 2.66/2.22 inference(symmetry,[status(thm)],[6832])).
% 2.66/2.22 tff(6834,plain,
% 2.66/2.22 (tptp_fun_X_2(X!1) = Y!0),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[105, 6825])).
% 2.66/2.22 tff(6835,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6834, 3378])).
% 2.66/2.22 tff(6836,plain,
% 2.66/2.22 (big_f(Y!0, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.22 inference(symmetry,[status(thm)],[6835])).
% 2.66/2.22 tff(6837,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.22 inference(modus_ponens,[status(thm)],[6816, 6836])).
% 2.66/2.22 tff(6838,plain,
% 2.66/2.22 (~(W1!8 = Y!0)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6124, 6837, 6834, 6830])).
% 2.66/2.22 tff(6839,plain,
% 2.66/2.22 (W1!8 = X!1),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[19, 6838])).
% 2.66/2.22 tff(6840,plain,
% 2.66/2.22 (X!1 = W1!8),
% 2.66/2.22 inference(symmetry,[status(thm)],[6839])).
% 2.66/2.22 tff(6841,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X_2(Y!0), W1!8)),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6840])).
% 2.66/2.22 tff(6842,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(X!1, W1!8)),
% 2.66/2.22 inference(transitivity,[status(thm)],[6841, 6833])).
% 2.66/2.22 tff(6843,plain,
% 2.66/2.22 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(X!1, W1!8))),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6842])).
% 2.66/2.22 tff(6844,plain,
% 2.66/2.22 (~big_f(X!1, W1!8)),
% 2.66/2.22 inference(modus_ponens,[status(thm)],[5823, 6843])).
% 2.66/2.22 tff(6845,plain,
% 2.66/2.22 (~(X!1 = tptp_fun_Z1_9(W1!8))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[502, 6844, 6831])).
% 2.66/2.22 tff(6846,plain,
% 2.66/2.22 (~(tptp_fun_Z1_9(W1!8) = X!1)),
% 2.66/2.22 inference(modus_ponens,[status(thm)],[6845, 2484])).
% 2.66/2.22 tff(6847,plain,
% 2.66/2.22 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[3017, 6829])).
% 2.66/2.22 tff(6848,plain,
% 2.66/2.22 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[3266, 6847])).
% 2.66/2.22 tff(6849,plain,
% 2.66/2.22 ((~(W1!8 = X!1)) | (tptp_fun_X_2(Y!0) = W1!8)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[3648, 6042])).
% 2.66/2.22 tff(6850,plain,
% 2.66/2.22 (tptp_fun_X_2(Y!0) = W1!8),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6849, 6839])).
% 2.66/2.22 tff(6851,plain,
% 2.66/2.22 (![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[3268, 6850, 6848])).
% 2.66/2.22 tff(6852,plain,
% 2.66/2.22 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[3235, 6851])).
% 2.66/2.22 tff(6853,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6834, 6043])).
% 2.66/2.22 tff(6854,plain,
% 2.66/2.22 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.66/2.22 inference(monotonicity,[status(thm)],[6853])).
% 2.66/2.22 tff(6855,plain,
% 2.66/2.22 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[224, 6825, 6823])).
% 2.66/2.22 tff(6856,plain,
% 2.66/2.22 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[1157, 6837, 6855])).
% 2.66/2.22 tff(6857,plain,
% 2.66/2.22 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.22 inference(modus_ponens,[status(thm)],[6856, 6854])).
% 2.66/2.22 tff(6858,plain,
% 2.66/2.22 (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6495, 6857, 6852])).
% 2.66/2.22 tff(6859,plain,
% 2.66/2.22 ((~(tptp_fun_Z1_9(W1!8) = Y!0)) | (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))) | (~(W1!8 = X!1))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6500, 6042])).
% 2.66/2.22 tff(6860,plain,
% 2.66/2.22 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6859, 6858, 6839])).
% 2.66/2.22 tff(6861,plain,
% 2.66/2.22 (tptp_fun_Z1_9(W1!8) = X!1),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[522, 6860])).
% 2.66/2.22 tff(6862,plain,
% 2.66/2.22 ($false),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6861, 6846])).
% 2.66/2.22 tff(6863,plain,((tptp_fun_Y1_11(X!1) = X!1) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.22 tff(6864,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6863, 144])).
% 2.66/2.22 tff(6865,plain,
% 2.66/2.22 (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6673, 6864])).
% 2.66/2.22 tff(6866,plain,
% 2.66/2.22 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[1858, 6041])).
% 2.66/2.22 tff(6867,plain,
% 2.66/2.22 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6866, 6865])).
% 2.66/2.22 tff(6868,plain,
% 2.66/2.22 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[2663, 6867])).
% 2.66/2.22 tff(6869,plain,
% 2.66/2.22 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[56, 6868])).
% 2.66/2.22 tff(6870,plain,
% 2.66/2.22 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[82, 6869])).
% 2.66/2.22 tff(6871,plain,
% 2.66/2.22 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[84, 6870])).
% 2.66/2.22 tff(6872,plain,
% 2.66/2.22 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[561, 6871])).
% 2.66/2.22 tff(6873,plain,
% 2.66/2.22 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[563, 6872, 6710])).
% 2.66/2.22 tff(6874,plain,
% 2.66/2.22 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[86, 6871])).
% 2.66/2.22 tff(6875,plain,
% 2.66/2.22 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[113, 6874, 6873])).
% 2.66/2.22 tff(6876,plain,
% 2.66/2.22 (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[5602, 6873, 41])).
% 2.66/2.22 tff(6877,plain,
% 2.66/2.22 ($false),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[958, 6876, 6875])).
% 2.66/2.22 tff(6878,plain,((tptp_fun_Y1_11(X!1) = X!1) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.22 tff(6879,plain,
% 2.66/2.22 (tptp_fun_Y1_11(X!1) = X!1),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6878, 41])).
% 2.66/2.22 tff(6880,plain,
% 2.66/2.22 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[1562, 34, 6879, 41])).
% 2.66/2.22 tff(6881,plain,
% 2.66/2.22 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[82, 6880])).
% 2.66/2.22 tff(6882,plain,
% 2.66/2.22 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[56, 6881])).
% 2.66/2.22 tff(6883,plain,
% 2.66/2.22 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6724, 40, 41])).
% 2.66/2.22 tff(6884,plain,
% 2.66/2.22 (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6673, 6883])).
% 2.66/2.22 tff(6885,plain,
% 2.66/2.22 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[6866, 6884])).
% 2.66/2.22 tff(6886,plain,
% 2.66/2.22 ($false),
% 2.66/2.22 inference(unit_resolution,[status(thm)],[2663, 6885, 6882])).
% 2.66/2.22 tff(6887,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.22 tff(6888,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6887, 34])).
% 2.66/2.23 tff(6889,plain,
% 2.66/2.23 (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6673, 5525])).
% 2.66/2.23 tff(6890,plain,
% 2.66/2.23 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6866, 6889])).
% 2.66/2.23 tff(6891,plain,
% 2.66/2.23 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[2663, 6890])).
% 2.66/2.23 tff(6892,plain,
% 2.66/2.23 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[56, 6891])).
% 2.66/2.23 tff(6893,plain,
% 2.66/2.23 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[82, 6892])).
% 2.66/2.23 tff(6894,plain,
% 2.66/2.23 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[84, 6893])).
% 2.66/2.23 tff(6895,plain,
% 2.66/2.23 ((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[561, 6894])).
% 2.66/2.23 tff(6896,plain,
% 2.66/2.23 (![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[563, 6895, 34])).
% 2.66/2.23 tff(6897,plain,
% 2.66/2.23 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1194, 6896, 6888])).
% 2.66/2.23 tff(6898,plain,
% 2.66/2.23 (~big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.23 inference(modus_ponens,[status(thm)],[6897, 6045])).
% 2.66/2.23 tff(6899,plain,
% 2.66/2.23 ($false),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[5525, 6898])).
% 2.66/2.23 tff(6900,plain,((~big_f(tptp_fun_X_2(Y!0), X!1)) | (tptp_fun_Y1_11(Y!0) = Y!0)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.23 tff(6901,plain,
% 2.66/2.23 (~big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6900, 34])).
% 2.66/2.23 tff(6902,plain,
% 2.66/2.23 (tptp_fun_Y1_11(X!1) = X!1),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6863, 6901])).
% 2.66/2.23 tff(6903,plain,
% 2.66/2.23 (~big_f(X!1, tptp_fun_Y1_11(Y!0))),
% 2.66/2.23 inference(modus_ponens,[status(thm)],[6901, 6417])).
% 2.66/2.23 tff(6904,plain,
% 2.66/2.23 (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[5581, 6903, 6888, 40, 6902])).
% 2.66/2.23 tff(6905,plain,
% 2.66/2.23 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[90, 6904])).
% 2.66/2.23 tff(6906,plain,
% 2.66/2.23 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[88, 6905])).
% 2.66/2.23 tff(6907,plain,
% 2.66/2.23 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[82, 6906])).
% 2.66/2.23 tff(6908,plain,
% 2.66/2.23 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[220, 6907])).
% 2.66/2.23 tff(6909,plain,
% 2.66/2.23 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[222, 6908])).
% 2.66/2.23 tff(6910,plain,
% 2.66/2.23 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1713, 6908])).
% 2.66/2.23 tff(6911,plain,
% 2.66/2.23 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6736, 6910, 6901])).
% 2.66/2.23 tff(6912,plain,
% 2.66/2.23 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[224, 6911, 6909])).
% 2.66/2.23 tff(6913,plain,
% 2.66/2.23 (tptp_fun_X_2(X!1) = Y!0),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[105, 6911])).
% 2.66/2.23 tff(6914,plain,
% 2.66/2.23 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1254, 6903, 6888, 40])).
% 2.66/2.23 tff(6915,plain,
% 2.66/2.23 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1256, 6914])).
% 2.66/2.23 tff(6916,plain,
% 2.66/2.23 (~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1273, 6915, 2835])).
% 2.66/2.23 tff(6917,plain,
% 2.66/2.23 ((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1)))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1271, 6916])).
% 2.66/2.23 tff(6918,plain,
% 2.66/2.23 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1269, 6917])).
% 2.66/2.23 tff(6919,plain,
% 2.66/2.23 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[462, 6918])).
% 2.66/2.23 tff(6920,plain,
% 2.66/2.23 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6578, 6919, 6901])).
% 2.66/2.23 tff(6921,plain,
% 2.66/2.23 ((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1110, 6920])).
% 2.66/2.23 tff(6922,plain,
% 2.66/2.23 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[3631, 6921, 40, 6888, 6913])).
% 2.66/2.23 tff(6923,plain,
% 2.66/2.23 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1413, 6913, 40, 6888])).
% 2.66/2.23 tff(6924,plain,
% 2.66/2.23 ($false),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[1157, 6923, 6922, 6912])).
% 2.66/2.23 tff(6925,plain,((tptp_fun_Y1_11(Y!0) = Y!0) | (X!1 = W1!8)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.23 tff(6926,plain,
% 2.66/2.23 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6925, 2835])).
% 2.66/2.23 tff(6927,plain,
% 2.66/2.23 (tptp_fun_Y1_11(X!1) = X!1),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6863, 5823])).
% 2.66/2.23 tff(6928,plain,
% 2.66/2.23 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[269, 1556, 6927])).
% 2.66/2.23 tff(6929,plain,
% 2.66/2.23 ((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[879, 6928])).
% 2.66/2.23 tff(6930,plain,
% 2.66/2.23 (~(tptp_fun_X1_13(Y!0, X!1) = Y!0)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[4576, 906, 6042, 277, 3230])).
% 2.66/2.23 tff(6931,plain,
% 2.66/2.23 (tptp_fun_X1_13(Y!0, X!1) = X!1),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[915, 6930])).
% 2.66/2.23 tff(6932,plain,
% 2.66/2.23 (tptp_fun_X1_13(Y!0, X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.23 inference(transitivity,[status(thm)],[6931, 6043])).
% 2.66/2.23 tff(6933,plain,
% 2.66/2.23 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6932, 277])).
% 2.66/2.23 tff(6934,plain,
% 2.66/2.23 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.66/2.23 inference(symmetry,[status(thm)],[6933])).
% 2.66/2.23 tff(6935,plain,
% 2.66/2.23 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1)))),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6934])).
% 2.66/2.23 tff(6936,plain,
% 2.66/2.23 (~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.66/2.23 inference(modus_ponens,[status(thm)],[5823, 6935])).
% 2.66/2.23 tff(6937,plain,
% 2.66/2.23 (big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[920, 6930, 906])).
% 2.66/2.23 tff(6938,plain,
% 2.66/2.23 ($false),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6937, 6936])).
% 2.66/2.23 tff(6939,plain,((~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))) | big_f(tptp_fun_X_2(Y!0), X!1) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~big_f(Y!0, tptp_fun_X_2(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.23 tff(6940,plain,
% 2.66/2.23 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6939, 6929, 6927, 5823])).
% 2.66/2.23 tff(6941,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6591, 1558, 5823])).
% 2.66/2.23 tff(6942,assumption,(~(tptp_fun_Y_7(Y!0, Y!0) = Y!0)), introduced(assumption)).
% 2.66/2.23 tff(6943,plain,
% 2.66/2.23 (tptp_fun_Y_7(Y!0, Y!0) = X!1),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[708, 6942])).
% 2.66/2.23 tff(6944,plain,
% 2.66/2.23 (tptp_fun_Y_7(Y!0, Y!0) = tptp_fun_X_2(Y!0)),
% 2.66/2.23 inference(transitivity,[status(thm)],[6943, 6043])).
% 2.66/2.23 tff(6945,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6944])).
% 2.66/2.23 tff(6946,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.66/2.23 inference(symmetry,[status(thm)],[6945])).
% 2.66/2.23 tff(6947,plain,
% 2.66/2.23 ((~big_f(Y!0, tptp_fun_X_2(Y!0))) <=> (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)))),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6946])).
% 2.66/2.23 tff(6948,plain,
% 2.66/2.23 (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.66/2.23 inference(modus_ponens,[status(thm)],[2991, 6947])).
% 2.66/2.23 tff(6949,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[714, 6942, 693])).
% 2.66/2.23 tff(6950,plain,
% 2.66/2.23 ($false),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6949, 6948])).
% 2.66/2.23 tff(6951,plain,((tptp_fun_Y_7(Y!0, Y!0) = Y!0) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.23 tff(6952,plain,
% 2.66/2.23 (tptp_fun_Y_7(Y!0, Y!0) = Y!0),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6951, 693, 2991])).
% 2.66/2.23 tff(6953,plain,
% 2.66/2.23 (Y!0 = tptp_fun_Y_7(Y!0, Y!0)),
% 2.66/2.23 inference(symmetry,[status(thm)],[6952])).
% 2.66/2.23 tff(6954,plain,
% 2.66/2.23 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y_7(Y!0, Y!0)),
% 2.66/2.23 inference(transitivity,[status(thm)],[109, 6953])).
% 2.66/2.23 tff(6955,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6954])).
% 2.66/2.23 tff(6956,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.23 inference(symmetry,[status(thm)],[6955])).
% 2.66/2.23 tff(6957,plain,
% 2.66/2.23 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (~big_f(Y!0, tptp_fun_Y1_11(Y!0)))),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6956])).
% 2.66/2.23 tff(6958,plain,
% 2.66/2.23 (~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[699, 6952, 693])).
% 2.66/2.23 tff(6959,plain,
% 2.66/2.23 (~big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.23 inference(modus_ponens,[status(thm)],[6958, 6957])).
% 2.66/2.23 tff(6960,plain,
% 2.66/2.23 ($false),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[135, 6959])).
% 2.66/2.23 tff(6961,plain,((~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(Y!0, tptp_fun_X_2(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.23 tff(6962,plain,
% 2.66/2.23 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6961, 6941, 109, 6940])).
% 2.66/2.23 tff(6963,plain,
% 2.66/2.23 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[720, 6962])).
% 2.66/2.23 tff(6964,plain,
% 2.66/2.23 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6578, 6963, 5823])).
% 2.66/2.23 tff(6965,plain,
% 2.66/2.23 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[462, 6964])).
% 2.66/2.23 tff(6966,plain,
% 2.66/2.23 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[481, 6965])).
% 2.66/2.23 tff(6967,plain,
% 2.66/2.23 (big_f(Y!0, W1!8) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[483, 6966])).
% 2.66/2.23 tff(6968,plain,
% 2.66/2.23 (big_f(Y!0, W1!8) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.23 inference(monotonicity,[status(thm)],[4066])).
% 2.66/2.23 tff(6969,plain,
% 2.66/2.23 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, W1!8)),
% 2.66/2.23 inference(symmetry,[status(thm)],[6968])).
% 2.66/2.23 tff(6970,plain,
% 2.66/2.23 (big_f(Y!0, W1!8)),
% 2.66/2.23 inference(modus_ponens,[status(thm)],[6941, 6969])).
% 2.66/2.23 tff(6971,plain,
% 2.66/2.23 ((tptp_fun_Z1_9(W1!8) = Y!0) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.66/2.23 inference(symmetry,[status(thm)],[43])).
% 2.66/2.23 tff(6972,plain,
% 2.66/2.23 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[3003, 6965])).
% 2.66/2.23 tff(6973,plain,
% 2.66/2.23 ((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[3286, 6972])).
% 2.66/2.23 tff(6974,plain,
% 2.66/2.23 (![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[3289, 6973, 5976])).
% 2.66/2.23 tff(6975,plain,
% 2.66/2.23 (big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[3291, 6974])).
% 2.66/2.23 tff(6976,plain,
% 2.66/2.23 ((~(big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0)))) | (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[5547, 4769])).
% 2.66/2.23 tff(6977,plain,
% 2.66/2.23 (X!1 = tptp_fun_Z1_9(Y!0)),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[6976, 6975])).
% 2.66/2.23 tff(6978,plain,
% 2.66/2.23 (tptp_fun_Z1_9(Y!0) = X!1),
% 2.66/2.23 inference(symmetry,[status(thm)],[6977])).
% 2.66/2.23 tff(6979,plain,
% 2.66/2.23 (tptp_fun_Z1_9(W1!8) = tptp_fun_Z1_9(Y!0)),
% 2.66/2.23 inference(monotonicity,[status(thm)],[486])).
% 2.66/2.23 tff(6980,plain,
% 2.66/2.23 (tptp_fun_Z1_9(W1!8) = X!1),
% 2.66/2.23 inference(transitivity,[status(thm)],[6979, 6978])).
% 2.66/2.23 tff(6981,plain,
% 2.66/2.23 ((tptp_fun_Z1_9(W1!8) = Y!0) <=> (X!1 = Y!0)),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6980])).
% 2.66/2.23 tff(6982,plain,
% 2.66/2.23 ((X!1 = Y!0) <=> (tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.66/2.23 inference(symmetry,[status(thm)],[6981])).
% 2.66/2.23 tff(6983,plain,
% 2.66/2.23 ((X!1 = Y!0) <=> (Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.66/2.23 inference(transitivity,[status(thm)],[6982, 6971])).
% 2.66/2.23 tff(6984,plain,
% 2.66/2.23 ((~(X!1 = Y!0)) <=> (~(Y!0 = tptp_fun_Z1_9(W1!8)))),
% 2.66/2.23 inference(monotonicity,[status(thm)],[6983])).
% 2.66/2.23 tff(6985,plain,
% 2.66/2.23 (~(Y!0 = tptp_fun_Z1_9(W1!8))),
% 2.66/2.23 inference(modus_ponens,[status(thm)],[741, 6984])).
% 2.66/2.23 tff(6986,plain,
% 2.66/2.23 ($false),
% 2.66/2.23 inference(unit_resolution,[status(thm)],[886, 6985, 6970, 6967])).
% 2.66/2.23 tff(6987,plain,((~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))) | (~(W1!8 = Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.23 tff(6988,plain,
% 2.66/2.23 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6987, 5823, 6926, 486])).
% 2.66/2.24 tff(6989,plain,
% 2.66/2.24 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[82, 6988])).
% 2.66/2.24 tff(6990,plain,
% 2.66/2.24 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[220, 6989])).
% 2.66/2.24 tff(6991,plain,
% 2.66/2.24 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[1713, 6990])).
% 2.66/2.24 tff(6992,plain,
% 2.66/2.24 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6736, 6991, 5823])).
% 2.66/2.24 tff(6993,plain,
% 2.66/2.24 (tptp_fun_X_2(X!1) = Y!0),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[105, 6992])).
% 2.66/2.24 tff(6994,plain,
% 2.66/2.24 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.24 inference(monotonicity,[status(thm)],[6993, 6043])).
% 2.66/2.24 tff(6995,plain,
% 2.66/2.24 ((~big_f(tptp_fun_X_2(X!1), X!1)) <=> (~big_f(Y!0, tptp_fun_X_2(Y!0)))),
% 2.66/2.24 inference(monotonicity,[status(thm)],[6994])).
% 2.66/2.24 tff(6996,plain,
% 2.66/2.24 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[222, 6990])).
% 2.66/2.24 tff(6997,plain,
% 2.66/2.24 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[224, 6992, 6996])).
% 2.66/2.24 tff(6998,plain,
% 2.66/2.24 (Y!0 = tptp_fun_Y1_11(Y!0)),
% 2.66/2.24 inference(symmetry,[status(thm)],[6926])).
% 2.66/2.24 tff(6999,plain,
% 2.66/2.24 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.24 inference(monotonicity,[status(thm)],[6993, 6998])).
% 2.66/2.24 tff(7000,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.24 inference(symmetry,[status(thm)],[6999])).
% 2.66/2.24 tff(7001,plain,
% 2.66/2.24 (big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[234, 6997])).
% 2.66/2.24 tff(7002,plain,
% 2.66/2.24 ((~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | big_f(Y!0, tptp_fun_X_2(Y!0)) | (~(tptp_fun_X_2(X!1) = Y!0)) | big_f(Y!0, tptp_fun_Y1_11(Y!0)) | (~(tptp_fun_Y1_11(Y!0) = Y!0))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[3393, 6042])).
% 2.66/2.24 tff(7003,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7002, 41, 245, 240, 6926])).
% 2.66/2.24 tff(7004,plain,
% 2.66/2.24 (~((~big_f(tptp_fun_X1_10(Y!0, X!1), X!1)) <=> (tptp_fun_X1_10(Y!0, X!1) = Y!0))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6753, 7003, 5823])).
% 2.66/2.24 tff(7005,plain,
% 2.66/2.24 (~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[1256, 7004])).
% 2.66/2.24 tff(7006,plain,
% 2.66/2.24 (~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[1273, 7005, 2835])).
% 2.66/2.24 tff(7007,plain,
% 2.66/2.24 ((~((X!1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, X!1), X!1)) <=> (tptp_fun_X1_10(Z1, X!1) = Z1)))) | (~((~(X!1 = W1!8)) | ![X1: $i] : (big_f(X1, X!1) <=> (X1 = tptp_fun_Z1_9(X!1)))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[1271, 7006])).
% 2.66/2.24 tff(7008,plain,
% 2.66/2.24 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6740, 7003, 41, 6926])).
% 2.66/2.24 tff(7009,plain,
% 2.66/2.24 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[1110, 7008])).
% 2.66/2.24 tff(7010,plain,
% 2.66/2.24 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6578, 7009, 5823])).
% 2.66/2.24 tff(7011,plain,
% 2.66/2.24 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[462, 7010])).
% 2.66/2.24 tff(7012,plain,
% 2.66/2.24 ($false),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[1269, 7011, 7007])).
% 2.66/2.24 tff(7013,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0)) | big_f(tptp_fun_X_2(Y!0), X!1) | (X!1 = W1!8) | (~big_f(tptp_fun_X_2(X!1), tptp_fun_W_3(X!1))) | (~(tptp_fun_X_2(X!1) = Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.24 tff(7014,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7013, 5823, 2835, 7001, 6993])).
% 2.66/2.24 tff(7015,plain,
% 2.66/2.24 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.24 inference(modus_ponens,[status(thm)],[7014, 7000])).
% 2.66/2.24 tff(7016,plain,
% 2.66/2.24 (~big_f(tptp_fun_X_2(X!1), X!1)),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[1157, 7015, 6997])).
% 2.66/2.24 tff(7017,plain,
% 2.66/2.24 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.24 inference(modus_ponens,[status(thm)],[7016, 6995])).
% 2.66/2.24 tff(7018,plain,
% 2.66/2.24 (~![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6124, 7015, 486, 6993])).
% 2.66/2.24 tff(7019,plain,
% 2.66/2.24 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[481, 7018])).
% 2.66/2.24 tff(7020,plain,
% 2.66/2.24 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[462, 7019])).
% 2.66/2.24 tff(7021,plain,
% 2.66/2.24 (![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6578, 7020, 5823])).
% 2.66/2.24 tff(7022,plain,
% 2.66/2.24 ((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0)),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[720, 7021])).
% 2.66/2.24 tff(7023,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6961, 7022, 6926, 7014])).
% 2.66/2.24 tff(7024,plain,
% 2.66/2.24 ($false),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7023, 7017])).
% 2.66/2.24 tff(7025,plain,(big_f(tptp_fun_X_2(Y!0), X!1) | (~(W1!8 = Y!0)) | (X!1 = W1!8)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.24 tff(7026,plain,
% 2.66/2.24 (big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7025, 20, 29])).
% 2.66/2.24 tff(7027,plain,
% 2.66/2.24 (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6673, 7026])).
% 2.66/2.24 tff(7028,plain,
% 2.66/2.24 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6866, 7027])).
% 2.66/2.24 tff(7029,plain,
% 2.66/2.24 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[2663, 7028])).
% 2.66/2.24 tff(7030,plain,
% 2.66/2.24 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[56, 7029])).
% 2.66/2.24 tff(7031,plain,
% 2.66/2.24 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[82, 7030])).
% 2.66/2.24 tff(7032,plain,
% 2.66/2.24 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[88, 7031])).
% 2.66/2.24 tff(7033,plain,
% 2.66/2.24 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[191, 7032])).
% 2.66/2.24 tff(7034,plain,
% 2.66/2.24 (tptp_fun_Y1_11(Y!0) = Y!0),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6925, 29])).
% 2.66/2.24 tff(7035,plain,
% 2.66/2.24 (~((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[84, 7031])).
% 2.66/2.24 tff(7036,plain,
% 2.66/2.24 ((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[86, 7035])).
% 2.66/2.24 tff(7037,plain,
% 2.66/2.24 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[113, 7036, 7034])).
% 2.66/2.24 tff(7038,plain,
% 2.66/2.24 ((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1)),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[958, 7037])).
% 2.66/2.24 tff(7039,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[5602, 7038, 7034])).
% 2.66/2.24 tff(7040,plain,
% 2.66/2.24 (tptp_fun_Y1_11(Y!0) = tptp_fun_Y1_11(X!1)),
% 2.66/2.24 inference(transitivity,[status(thm)],[109, 3378])).
% 2.66/2.24 tff(7041,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.24 inference(monotonicity,[status(thm)],[7040])).
% 2.66/2.24 tff(7042,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_Y1_11(X!1))),
% 2.66/2.24 inference(modus_ponens,[status(thm)],[135, 7041])).
% 2.66/2.24 tff(7043,plain,
% 2.66/2.24 ($false),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[6540, 5756, 7042, 162])).
% 2.66/2.24 tff(7044,plain,((tptp_fun_Y1_11(X!1) = X!1) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.24 tff(7045,plain,
% 2.66/2.24 (tptp_fun_Y1_11(X!1) = X!1),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7044, 7039, 7034, 7033])).
% 2.66/2.24 tff(7046,plain,
% 2.66/2.24 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.24 inference(transitivity,[status(thm)],[297, 6043])).
% 2.66/2.24 tff(7047,plain,
% 2.66/2.24 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.24 inference(monotonicity,[status(thm)],[7046, 277])).
% 2.66/2.24 tff(7048,plain,
% 2.66/2.24 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.66/2.24 inference(symmetry,[status(thm)],[7047])).
% 2.66/2.24 tff(7049,plain,
% 2.66/2.24 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.66/2.24 inference(modus_ponens,[status(thm)],[5525, 7048])).
% 2.66/2.24 tff(7050,plain,
% 2.66/2.24 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[88, 6893])).
% 2.66/2.24 tff(7051,plain,
% 2.66/2.24 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[90, 7050])).
% 2.66/2.24 tff(7052,plain,
% 2.66/2.24 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[269, 277, 7051])).
% 2.66/2.24 tff(7053,plain,
% 2.66/2.24 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[271, 7052])).
% 2.66/2.24 tff(7054,plain,
% 2.66/2.24 (~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[316, 297, 7053])).
% 2.66/2.24 tff(7055,plain,
% 2.66/2.24 ($false),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7054, 7049])).
% 2.66/2.24 tff(7056,plain,((~(tptp_fun_X1_13(X!1, X!1) = X!1)) | (~big_f(tptp_fun_X_2(Y!0), X!1)) | (~(tptp_fun_Y1_11(X!1) = X!1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.24 tff(7057,plain,
% 2.66/2.24 (~(tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7056, 7045, 7026])).
% 2.66/2.24 tff(7058,plain,
% 2.66/2.24 (tptp_fun_X1_13(X!1, X!1) = Y!0),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[285, 7057])).
% 2.66/2.24 tff(7059,plain,
% 2.66/2.24 (tptp_fun_X1_13(X!1, X!1) = W1!8),
% 2.66/2.24 inference(modus_ponens,[status(thm)],[7058, 23])).
% 2.66/2.24 tff(7060,assumption,(tptp_fun_X1_13(X!1, X!1) = W1!8), introduced(assumption)).
% 2.66/2.24 tff(7061,plain,
% 2.66/2.24 ((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~((~((tptp_fun_X1_13(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_13(X!1, X!1)), tptp_fun_X1_13(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_13(X!1, X!1)) = Z1)))) | (~((~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))))))),
% 2.66/2.24 inference(quant_inst,[status(thm)],[])).
% 2.66/2.24 tff(7062,plain,
% 2.66/2.24 (~((~((tptp_fun_X1_13(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_13(X!1, X!1)), tptp_fun_X1_13(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_13(X!1, X!1)) = Z1)))) | (~((~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)))))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7061, 1268])).
% 2.66/2.24 tff(7063,plain,
% 2.66/2.24 (((~((tptp_fun_X1_13(X!1, X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X1_13(X!1, X!1)), tptp_fun_X1_13(X!1, X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X1_13(X!1, X!1)) = Z1)))) | (~((~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))))) | ((~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)))))),
% 2.66/2.24 inference(tautology,[status(thm)],[])).
% 2.66/2.24 tff(7064,plain,
% 2.66/2.24 ((~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7063, 7062])).
% 2.66/2.24 tff(7065,plain,
% 2.66/2.24 ((~((~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)))))) | (~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))),
% 2.66/2.24 inference(tautology,[status(thm)],[])).
% 2.66/2.24 tff(7066,plain,
% 2.66/2.24 (![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7065, 7064, 7060])).
% 2.66/2.24 tff(7067,plain,
% 2.66/2.24 ((~![X1: $i] : (big_f(X1, tptp_fun_X1_13(X!1, X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))) | (big_f(Y!0, tptp_fun_X1_13(X!1, X!1)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))),
% 2.66/2.24 inference(quant_inst,[status(thm)],[])).
% 2.66/2.24 tff(7068,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_X1_13(X!1, X!1)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)))),
% 2.66/2.24 inference(unit_resolution,[status(thm)],[7067, 7066])).
% 2.66/2.24 tff(7069,assumption,(tptp_fun_X1_13(X!1, X!1) = Y!0), introduced(assumption)).
% 2.66/2.24 tff(7070,plain,
% 2.66/2.24 (tptp_fun_X1_13(X!1, X!1) = tptp_fun_Y1_11(Y!0)),
% 2.66/2.24 inference(transitivity,[status(thm)],[7069, 146])).
% 2.66/2.24 tff(7071,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_X1_13(X!1, X!1)) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.24 inference(monotonicity,[status(thm)],[7070])).
% 2.66/2.24 tff(7072,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Y!0, tptp_fun_X1_13(X!1, X!1))),
% 2.66/2.24 inference(symmetry,[status(thm)],[7071])).
% 2.66/2.24 tff(7073,plain,
% 2.66/2.24 (big_f(Y!0, tptp_fun_X1_13(X!1, X!1))),
% 2.66/2.24 inference(modus_ponens,[status(thm)],[135, 7072])).
% 2.66/2.25 tff(7074,plain,
% 2.66/2.25 (![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0)))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[3289, 3287, 3109])).
% 2.66/2.25 tff(7075,plain,
% 2.66/2.25 (big_f(X!1, Y!0) <=> (X!1 = tptp_fun_Z1_9(Y!0))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[3291, 7074])).
% 2.66/2.25 tff(7076,plain,
% 2.66/2.25 (X!1 = tptp_fun_Z1_9(Y!0)),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[6976, 7075])).
% 2.66/2.25 tff(7077,plain,
% 2.66/2.25 (tptp_fun_Z1_9(Y!0) = X!1),
% 2.66/2.25 inference(symmetry,[status(thm)],[7076])).
% 2.66/2.25 tff(7078,plain,
% 2.66/2.25 (tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)) = tptp_fun_Z1_9(Y!0)),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7069])).
% 2.66/2.25 tff(7079,plain,
% 2.66/2.25 (tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)) = X!1),
% 2.66/2.25 inference(transitivity,[status(thm)],[7078, 7077])).
% 2.66/2.25 tff(7080,plain,
% 2.66/2.25 ((Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))) <=> (Y!0 = X!1)),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7079])).
% 2.66/2.25 tff(7081,plain,
% 2.66/2.25 ((Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))) <=> (X!1 = Y!0)),
% 2.66/2.25 inference(transitivity,[status(thm)],[7080, 46])).
% 2.66/2.25 tff(7082,plain,
% 2.66/2.25 ((X!1 = Y!0) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)))),
% 2.66/2.25 inference(symmetry,[status(thm)],[7081])).
% 2.66/2.25 tff(7083,plain,
% 2.66/2.25 ((~(X!1 = Y!0)) <=> (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7082])).
% 2.66/2.25 tff(7084,plain,
% 2.66/2.25 (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)))),
% 2.66/2.25 inference(modus_ponens,[status(thm)],[741, 7083])).
% 2.66/2.25 tff(7085,plain,
% 2.66/2.25 ((~(big_f(Y!0, tptp_fun_X1_13(X!1, X!1)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1))))) | (~big_f(Y!0, tptp_fun_X1_13(X!1, X!1))) | (Y!0 = tptp_fun_Z1_9(tptp_fun_X1_13(X!1, X!1)))),
% 2.66/2.25 inference(tautology,[status(thm)],[])).
% 2.66/2.25 tff(7086,plain,
% 2.66/2.25 ($false),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[7085, 7084, 7073, 7068])).
% 2.66/2.25 tff(7087,plain,((~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))) | (~(tptp_fun_X1_13(X!1, X!1) = Y!0)) | (~big_f(Y!0, tptp_fun_Y1_11(Y!0))) | (~(tptp_fun_Y1_11(Y!0) = Y!0)) | (~(tptp_fun_X1_13(X!1, X!1) = W1!8)) | (~(Y!0 = W1!8))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.25 tff(7088,plain,
% 2.66/2.25 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[7087, 7058, 7039, 7034, 7059, 21])).
% 2.66/2.25 tff(7089,plain,
% 2.66/2.25 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[462, 7088])).
% 2.66/2.25 tff(7090,plain,
% 2.66/2.25 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[385, 7089])).
% 2.66/2.25 tff(7091,plain,
% 2.66/2.25 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[387, 7090])).
% 2.66/2.25 tff(7092,plain,
% 2.66/2.25 (Y!0 = tptp_fun_Y1_11(Y!0)),
% 2.66/2.25 inference(symmetry,[status(thm)],[7034])).
% 2.66/2.25 tff(7093,plain,
% 2.66/2.25 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.66/2.25 inference(monotonicity,[status(thm)],[6043, 7045])).
% 2.66/2.25 tff(7094,plain,
% 2.66/2.25 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.66/2.25 inference(symmetry,[status(thm)],[7093])).
% 2.66/2.25 tff(7095,plain,
% 2.66/2.25 (big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.66/2.25 inference(modus_ponens,[status(thm)],[7026, 7094])).
% 2.66/2.25 tff(7096,plain,
% 2.66/2.25 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[5881, 7095, 7045])).
% 2.66/2.25 tff(7097,plain,
% 2.66/2.25 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[342, 7089])).
% 2.66/2.25 tff(7098,plain,
% 2.66/2.25 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[344, 7097])).
% 2.66/2.25 tff(7099,plain,
% 2.66/2.25 (~(X!1 = Z!5)),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[346, 7098, 7096])).
% 2.66/2.25 tff(7100,plain,
% 2.66/2.25 (~(Z!5 = X!1)),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[353, 7099])).
% 2.66/2.25 tff(7101,plain,
% 2.66/2.25 (Z!5 = Y!0),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[361, 7100])).
% 2.66/2.25 tff(7102,plain,
% 2.66/2.25 (big_f(Z!5, Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7101, 7092])).
% 2.66/2.25 tff(7103,plain,
% 2.66/2.25 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, Y!0)),
% 2.66/2.25 inference(symmetry,[status(thm)],[7102])).
% 2.66/2.25 tff(7104,plain,
% 2.66/2.25 (big_f(Z!5, Y!0)),
% 2.66/2.25 inference(modus_ponens,[status(thm)],[7039, 7103])).
% 2.66/2.25 tff(7105,plain,
% 2.66/2.25 (Y!0 = tptp_fun_W_6(Z!5)),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[1209, 7104, 7091])).
% 2.66/2.25 tff(7106,plain,
% 2.66/2.25 (tptp_fun_W_6(Z!5) = Y!0),
% 2.66/2.25 inference(symmetry,[status(thm)],[7105])).
% 2.66/2.25 tff(7107,plain,
% 2.66/2.25 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[983, 7090])).
% 2.66/2.25 tff(7108,plain,
% 2.66/2.25 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7101, 6043])).
% 2.66/2.25 tff(7109,plain,
% 2.66/2.25 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Z!5, X!1)),
% 2.66/2.25 inference(symmetry,[status(thm)],[7108])).
% 2.66/2.25 tff(7110,plain,
% 2.66/2.25 (tptp_fun_Y1_11(X!1) = tptp_fun_X_2(Y!0)),
% 2.66/2.25 inference(transitivity,[status(thm)],[7045, 6043])).
% 2.66/2.25 tff(7111,plain,
% 2.66/2.25 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7058, 7110])).
% 2.66/2.25 tff(7112,plain,
% 2.66/2.25 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[90, 7032])).
% 2.66/2.25 tff(7113,plain,
% 2.66/2.25 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[269, 7045, 7112])).
% 2.66/2.25 tff(7114,plain,
% 2.66/2.25 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[271, 7113])).
% 2.66/2.25 tff(7115,plain,
% 2.66/2.25 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[291, 7057, 7114])).
% 2.66/2.25 tff(7116,plain,
% 2.66/2.25 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.66/2.25 inference(modus_ponens,[status(thm)],[7115, 7111])).
% 2.66/2.25 tff(7117,plain,
% 2.66/2.25 (big_f(Z!5, X!1)),
% 2.66/2.25 inference(modus_ponens,[status(thm)],[7116, 7109])).
% 2.66/2.25 tff(7118,plain,
% 2.66/2.25 (X!1 = tptp_fun_W_6(Z!5)),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[989, 7117, 7107])).
% 2.66/2.25 tff(7119,plain,
% 2.66/2.25 (X!1 = Y!0),
% 2.66/2.25 inference(transitivity,[status(thm)],[7118, 7106])).
% 2.66/2.25 tff(7120,plain,
% 2.66/2.25 ($false),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[741, 7119])).
% 2.66/2.25 tff(7121,plain,(W1!8 = X!1), inference(lemma,lemma(discharge,[]))).
% 2.66/2.25 tff(7122,plain,
% 2.66/2.25 ((tptp_fun_X1_10(W1!8, Y!0) = W1!8) <=> (tptp_fun_X1_10(W1!8, Y!0) = X!1)),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7121])).
% 2.66/2.25 tff(7123,plain,
% 2.66/2.25 ((~(tptp_fun_X1_10(W1!8, Y!0) = W1!8)) <=> (~(tptp_fun_X1_10(W1!8, Y!0) = X!1))),
% 2.66/2.25 inference(monotonicity,[status(thm)],[7122])).
% 2.66/2.25 tff(7124,plain,
% 2.66/2.25 (~big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[1157, 6923, 6912])).
% 2.66/2.25 tff(7125,plain,
% 2.66/2.25 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[3631, 7124, 40, 6888, 6913])).
% 2.66/2.25 tff(7126,plain,
% 2.66/2.25 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[1110, 7125])).
% 2.66/2.25 tff(7127,plain,
% 2.66/2.25 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[6578, 7126, 6901])).
% 2.66/2.25 tff(7128,plain,
% 2.66/2.25 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.66/2.25 inference(unit_resolution,[status(thm)],[462, 7127])).
% 2.74/2.25 tff(7129,plain,
% 2.74/2.25 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[3003, 7128])).
% 2.74/2.25 tff(7130,plain,
% 2.74/2.25 ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[3005, 7129])).
% 2.74/2.25 tff(7131,plain,
% 2.74/2.25 ((W1!8 = Y!0) <=> (X!1 = Y!0)),
% 2.74/2.25 inference(monotonicity,[status(thm)],[7121])).
% 2.74/2.25 tff(7132,plain,
% 2.74/2.25 ((X!1 = Y!0) <=> (W1!8 = Y!0)),
% 2.74/2.25 inference(symmetry,[status(thm)],[7131])).
% 2.74/2.25 tff(7133,plain,
% 2.74/2.25 ((X!1 = Y!0) <=> (Y!0 = W1!8)),
% 2.74/2.25 inference(transitivity,[status(thm)],[7132, 2])).
% 2.74/2.25 tff(7134,plain,
% 2.74/2.25 ((~(X!1 = Y!0)) <=> (~(Y!0 = W1!8))),
% 2.74/2.25 inference(monotonicity,[status(thm)],[7133])).
% 2.74/2.25 tff(7135,plain,
% 2.74/2.25 (~(Y!0 = W1!8)),
% 2.74/2.25 inference(modus_ponens,[status(thm)],[741, 7134])).
% 2.74/2.25 tff(7136,plain,
% 2.74/2.25 ((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[3114, 7135])).
% 2.74/2.25 tff(7137,plain,
% 2.74/2.25 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[7136, 7130])).
% 2.74/2.25 tff(7138,plain,
% 2.74/2.25 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))) | ((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8))),
% 2.74/2.25 inference(quant_inst,[status(thm)],[])).
% 2.74/2.25 tff(7139,plain,
% 2.74/2.25 ((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8)),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[7138, 7137])).
% 2.74/2.25 tff(7140,assumption,((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8)), introduced(assumption)).
% 2.74/2.25 tff(7141,assumption,(~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)), introduced(assumption)).
% 2.74/2.25 tff(7142,plain,
% 2.74/2.25 ((~((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8))) | big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0) | (tptp_fun_X1_10(W1!8, Y!0) = W1!8)),
% 2.74/2.25 inference(tautology,[status(thm)],[])).
% 2.74/2.25 tff(7143,plain,
% 2.74/2.25 (tptp_fun_X1_10(W1!8, Y!0) = W1!8),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[7142, 7141, 7140])).
% 2.74/2.25 tff(7144,plain,
% 2.74/2.25 (W1!8 = tptp_fun_X1_10(W1!8, Y!0)),
% 2.74/2.25 inference(symmetry,[status(thm)],[7143])).
% 2.74/2.25 tff(7145,plain,
% 2.74/2.25 (X!1 = tptp_fun_X1_10(W1!8, Y!0)),
% 2.74/2.25 inference(transitivity,[status(thm)],[1469, 7144])).
% 2.74/2.25 tff(7146,plain,
% 2.74/2.25 (big_f(X!1, Y!0) <=> big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)),
% 2.74/2.25 inference(monotonicity,[status(thm)],[7145])).
% 2.74/2.25 tff(7147,plain,
% 2.74/2.25 (big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0) <=> big_f(X!1, Y!0)),
% 2.74/2.25 inference(symmetry,[status(thm)],[7146])).
% 2.74/2.25 tff(7148,plain,
% 2.74/2.25 ((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (~big_f(X!1, Y!0))),
% 2.74/2.25 inference(monotonicity,[status(thm)],[7147])).
% 2.74/2.25 tff(7149,plain,
% 2.74/2.25 (~big_f(X!1, Y!0)),
% 2.74/2.25 inference(modus_ponens,[status(thm)],[7141, 7148])).
% 2.74/2.25 tff(7150,plain,
% 2.74/2.25 ($false),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[4769, 7149])).
% 2.74/2.25 tff(7151,plain,(big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0) | (~(W1!8 = X!1)) | (~((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.25 tff(7152,plain,
% 2.74/2.25 (big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0) | (~((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8)))),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[7151, 7121])).
% 2.74/2.25 tff(7153,plain,
% 2.74/2.25 (big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[7152, 7139])).
% 2.74/2.25 tff(7154,plain,
% 2.74/2.25 ((~((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8))) | (~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) | (~(tptp_fun_X1_10(W1!8, Y!0) = W1!8))),
% 2.74/2.25 inference(tautology,[status(thm)],[])).
% 2.74/2.25 tff(7155,plain,
% 2.74/2.25 (~(tptp_fun_X1_10(W1!8, Y!0) = W1!8)),
% 2.74/2.25 inference(unit_resolution,[status(thm)],[7154, 7153, 7139])).
% 2.74/2.26 tff(7156,plain,
% 2.74/2.26 (~(tptp_fun_X1_10(W1!8, Y!0) = X!1)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[7155, 7123])).
% 2.74/2.26 tff(7157,plain,
% 2.74/2.26 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, Y!0) = X!1) | (tptp_fun_X1_10(W1!8, Y!0) = Y!0))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(W1!8, Y!0) = X!1) | (tptp_fun_X1_10(W1!8, Y!0) = Y!0))),
% 2.74/2.26 inference(rewrite,[status(thm)],[])).
% 2.74/2.26 tff(7158,plain,
% 2.74/2.26 (((tptp_fun_X1_10(W1!8, Y!0) = Y!0) | (tptp_fun_X1_10(W1!8, Y!0) = X!1)) <=> ((tptp_fun_X1_10(W1!8, Y!0) = X!1) | (tptp_fun_X1_10(W1!8, Y!0) = Y!0))),
% 2.74/2.26 inference(rewrite,[status(thm)],[])).
% 2.74/2.26 tff(7159,plain,
% 2.74/2.26 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, Y!0) = Y!0) | (tptp_fun_X1_10(W1!8, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, Y!0) = X!1) | (tptp_fun_X1_10(W1!8, Y!0) = Y!0)))),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7158])).
% 2.74/2.26 tff(7160,plain,
% 2.74/2.26 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, Y!0) = Y!0) | (tptp_fun_X1_10(W1!8, Y!0) = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(W1!8, Y!0) = X!1) | (tptp_fun_X1_10(W1!8, Y!0) = Y!0))),
% 2.74/2.26 inference(transitivity,[status(thm)],[7159, 7157])).
% 2.74/2.26 tff(7161,plain,
% 2.74/2.26 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((tptp_fun_X1_10(W1!8, Y!0) = Y!0) | (tptp_fun_X1_10(W1!8, Y!0) = X!1))),
% 2.74/2.26 inference(quant_inst,[status(thm)],[])).
% 2.74/2.26 tff(7162,plain,
% 2.74/2.26 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (tptp_fun_X1_10(W1!8, Y!0) = X!1) | (tptp_fun_X1_10(W1!8, Y!0) = Y!0)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[7161, 7160])).
% 2.74/2.26 tff(7163,plain,
% 2.74/2.26 ((tptp_fun_X1_10(W1!8, Y!0) = X!1) | (tptp_fun_X1_10(W1!8, Y!0) = Y!0)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7162, 12])).
% 2.74/2.26 tff(7164,plain,
% 2.74/2.26 (tptp_fun_X1_10(W1!8, Y!0) = Y!0),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7163, 7156])).
% 2.74/2.26 tff(7165,plain,
% 2.74/2.26 (Y!0 = tptp_fun_X1_10(W1!8, Y!0)),
% 2.74/2.26 inference(symmetry,[status(thm)],[7164])).
% 2.74/2.26 tff(7166,plain,
% 2.74/2.26 (tptp_fun_X_2(X!1) = tptp_fun_X1_10(W1!8, Y!0)),
% 2.74/2.26 inference(transitivity,[status(thm)],[6913, 7165])).
% 2.74/2.26 tff(7167,plain,
% 2.74/2.26 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7166])).
% 2.74/2.26 tff(7168,plain,
% 2.74/2.26 (big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.74/2.26 inference(symmetry,[status(thm)],[7167])).
% 2.74/2.26 tff(7169,plain,
% 2.74/2.26 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[7153, 7168])).
% 2.74/2.26 tff(7170,plain,
% 2.74/2.26 ($false),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7124, 7169])).
% 2.74/2.26 tff(7171,plain,(tptp_fun_Y1_11(Y!0) = Y!0), inference(lemma,lemma(discharge,[]))).
% 2.74/2.26 tff(7172,plain,
% 2.74/2.26 (Y!0 = tptp_fun_Y1_11(Y!0)),
% 2.74/2.26 inference(symmetry,[status(thm)],[7171])).
% 2.74/2.26 tff(7173,plain,
% 2.74/2.26 (~((~big_f(tptp_fun_X1_13(X!1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(X!1, Y!0) = X!1))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[5602, 41, 7171])).
% 2.74/2.26 tff(7174,plain,
% 2.74/2.26 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[958, 7173])).
% 2.74/2.26 tff(7175,plain,
% 2.74/2.26 (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[113, 7174, 7171])).
% 2.74/2.26 tff(7176,plain,
% 2.74/2.26 ((~((tptp_fun_Y1_11(Y!0) = Y!0) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(Y!0)) <=> (X1 = tptp_fun_Z1_12(Y!0))))) | (~((~(tptp_fun_Y1_11(Y!0) = Y!0)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, Y!0), tptp_fun_Y1_11(Y!0))) <=> (tptp_fun_X1_13(Z1, Y!0) = Z1))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[86, 7175])).
% 2.74/2.26 tff(7177,plain,
% 2.74/2.26 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[84, 7176])).
% 2.74/2.26 tff(7178,plain,
% 2.74/2.26 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[82, 7177])).
% 2.74/2.26 tff(7179,plain,
% 2.74/2.26 (~((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W)))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[56, 7178])).
% 2.74/2.26 tff(7180,plain,
% 2.74/2.26 ((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[2663, 7179])).
% 2.74/2.26 tff(7181,plain,
% 2.74/2.26 (![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6866, 7180])).
% 2.74/2.26 tff(7182,plain,
% 2.74/2.26 (~big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6673, 7181])).
% 2.74/2.26 tff(7183,plain,
% 2.74/2.26 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[220, 7178])).
% 2.74/2.26 tff(7184,plain,
% 2.74/2.26 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[222, 7183])).
% 2.74/2.26 tff(7185,plain,
% 2.74/2.26 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[1713, 7183])).
% 2.74/2.26 tff(7186,plain,
% 2.74/2.26 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6736, 7182, 7185])).
% 2.74/2.26 tff(7187,plain,
% 2.74/2.26 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6738, 7186, 41, 7171, 7184])).
% 2.74/2.26 tff(7188,plain,
% 2.74/2.26 (~((~big_f(Y!0, tptp_fun_Y_7(X!1, Y!0))) <=> (tptp_fun_Y_7(X!1, Y!0) = X!1))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6740, 7187, 41, 7171])).
% 2.74/2.26 tff(7189,plain,
% 2.74/2.26 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[1110, 7188])).
% 2.74/2.26 tff(7190,plain,
% 2.74/2.26 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6578, 7189, 7182])).
% 2.74/2.26 tff(7191,plain,
% 2.74/2.26 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[462, 7190])).
% 2.74/2.26 tff(7192,plain,
% 2.74/2.26 (~((~((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1)))) | (~((~(Y!0 = W1!8)) | ![X1: $i] : (big_f(X1, Y!0) <=> (X1 = tptp_fun_Z1_9(Y!0))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[3003, 7191])).
% 2.74/2.26 tff(7193,plain,
% 2.74/2.26 ((Y!0 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[3005, 7192])).
% 2.74/2.26 tff(7194,plain,
% 2.74/2.26 (![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y!0), Y!0)) <=> (tptp_fun_X1_10(Z1, Y!0) = Z1))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7136, 7193])).
% 2.74/2.26 tff(7195,plain,
% 2.74/2.26 ((~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)) <=> (tptp_fun_X1_10(W1!8, Y!0) = W1!8)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7138, 7194])).
% 2.74/2.26 tff(7196,plain,
% 2.74/2.26 (big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7152, 7195])).
% 2.74/2.26 tff(7197,plain,
% 2.74/2.26 (~(tptp_fun_X1_10(W1!8, Y!0) = W1!8)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7154, 7196, 7195])).
% 2.74/2.26 tff(7198,plain,
% 2.74/2.26 (~(tptp_fun_X1_10(W1!8, Y!0) = X!1)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[7197, 7123])).
% 2.74/2.26 tff(7199,plain,
% 2.74/2.26 (tptp_fun_X1_10(W1!8, Y!0) = Y!0),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7163, 7198])).
% 2.74/2.26 tff(7200,plain,
% 2.74/2.26 (big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7199, 7172])).
% 2.74/2.26 tff(7201,plain,
% 2.74/2.26 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)),
% 2.74/2.26 inference(symmetry,[status(thm)],[7200])).
% 2.74/2.26 tff(7202,plain,
% 2.74/2.26 ((~big_f(Y!0, tptp_fun_Y1_11(Y!0))) <=> (~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0))),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7201])).
% 2.74/2.26 tff(7203,plain,
% 2.74/2.26 (~big_f(tptp_fun_X1_10(W1!8, Y!0), Y!0)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[41, 7202])).
% 2.74/2.26 tff(7204,plain,
% 2.74/2.26 ($false),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7196, 7203])).
% 2.74/2.26 tff(7205,plain,(big_f(Y!0, tptp_fun_Y1_11(Y!0))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.26 tff(7206,plain,
% 2.74/2.26 (~((~big_f(tptp_fun_X1_13(Y!0, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Y!0, X!1) = Y!0))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6939, 3230, 6927, 5823])).
% 2.74/2.26 tff(7207,plain,
% 2.74/2.26 (~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[879, 7206])).
% 2.74/2.26 tff(7208,plain,
% 2.74/2.26 (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[269, 7207, 6927])).
% 2.74/2.26 tff(7209,plain,
% 2.74/2.26 ((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[90, 7208])).
% 2.74/2.26 tff(7210,plain,
% 2.74/2.26 (~![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[88, 7209])).
% 2.74/2.26 tff(7211,plain,
% 2.74/2.26 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[82, 7210])).
% 2.74/2.26 tff(7212,plain,
% 2.74/2.26 (~((~((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1))))) | (~((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W)))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[220, 7211])).
% 2.74/2.26 tff(7213,plain,
% 2.74/2.26 ((tptp_fun_X_2(X!1) = X!1) | ![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[222, 7212])).
% 2.74/2.26 tff(7214,plain,
% 2.74/2.26 ((~(tptp_fun_X_2(X!1) = X!1)) | ![W: $i] : ((~big_f(tptp_fun_X_2(X!1), tptp_fun_Y_4(W, X!1))) <=> (tptp_fun_Y_4(W, X!1) = W))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[1713, 7212])).
% 2.74/2.26 tff(7215,plain,
% 2.74/2.26 (~(tptp_fun_X_2(X!1) = X!1)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6736, 7214, 5823])).
% 2.74/2.26 tff(7216,plain,
% 2.74/2.26 (![Y: $i] : (big_f(tptp_fun_X_2(X!1), Y) <=> (Y = tptp_fun_W_3(X!1)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[224, 7215, 7213])).
% 2.74/2.26 tff(7217,plain,
% 2.74/2.26 (tptp_fun_X_2(X!1) = Y!0),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[105, 7215])).
% 2.74/2.26 tff(7218,plain,
% 2.74/2.26 (big_f(tptp_fun_X_2(X!1), Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7217, 7172])).
% 2.74/2.26 tff(7219,plain,
% 2.74/2.26 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.74/2.26 inference(symmetry,[status(thm)],[7218])).
% 2.74/2.26 tff(7220,plain,
% 2.74/2.26 (big_f(tptp_fun_X_2(X!1), Y!0)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[7205, 7219])).
% 2.74/2.26 tff(7221,plain,
% 2.74/2.26 (big_f(tptp_fun_X_2(X!1), X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7217, 6043])).
% 2.74/2.26 tff(7222,plain,
% 2.74/2.26 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(tptp_fun_X_2(X!1), X!1)),
% 2.74/2.26 inference(symmetry,[status(thm)],[7221])).
% 2.74/2.26 tff(7223,plain,
% 2.74/2.26 (big_f(tptp_fun_X_2(X!1), X!1)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[3230, 7222])).
% 2.74/2.26 tff(7224,plain,
% 2.74/2.26 ($false),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[1157, 7223, 7220, 7216])).
% 2.74/2.26 tff(7225,plain,((~big_f(Y!0, tptp_fun_X_2(Y!0))) | big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.26 tff(7226,plain,
% 2.74/2.26 (~big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7225, 5823])).
% 2.74/2.26 tff(7227,plain,
% 2.74/2.26 (~((~big_f(Y!0, tptp_fun_Y_7(Y!0, Y!0))) <=> (tptp_fun_Y_7(Y!0, Y!0) = Y!0))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6961, 7226, 7171, 7205])).
% 2.74/2.26 tff(7228,plain,
% 2.74/2.26 (~![W: $i] : ((~big_f(Y!0, tptp_fun_Y_7(W, Y!0))) <=> (tptp_fun_Y_7(W, Y!0) = W))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[720, 7227])).
% 2.74/2.26 tff(7229,plain,
% 2.74/2.26 (~![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6578, 7228, 5823])).
% 2.74/2.26 tff(7230,plain,
% 2.74/2.26 (![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[462, 7229])).
% 2.74/2.26 tff(7231,plain,
% 2.74/2.26 (~((~((tptp_fun_X_2(Y!0) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)), tptp_fun_X_2(Y!0))) <=> (tptp_fun_X1_10(Z1, tptp_fun_X_2(Y!0)) = Z1)))) | (~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[3017, 7230])).
% 2.74/2.26 tff(7232,plain,
% 2.74/2.26 ((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[3266, 7231])).
% 2.74/2.26 tff(7233,plain,
% 2.74/2.26 (tptp_fun_X_2(Y!0) = W1!8),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6849, 7121])).
% 2.74/2.26 tff(7234,plain,
% 2.74/2.26 ((~((~(tptp_fun_X_2(Y!0) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))))) | ![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[3268, 7233])).
% 2.74/2.26 tff(7235,plain,
% 2.74/2.26 (![X1: $i] : (big_f(X1, tptp_fun_X_2(Y!0)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7234, 7232])).
% 2.74/2.26 tff(7236,plain,
% 2.74/2.26 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[3235, 7235])).
% 2.74/2.26 tff(7237,plain,
% 2.74/2.26 (~(Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6495, 7236, 7226])).
% 2.74/2.26 tff(7238,plain,
% 2.74/2.26 ((~(tptp_fun_Z1_9(W1!8) = Y!0)) | (Y!0 = tptp_fun_Z1_9(tptp_fun_X_2(Y!0)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6859, 7121])).
% 2.74/2.26 tff(7239,plain,
% 2.74/2.26 (~(tptp_fun_Z1_9(W1!8) = Y!0)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7238, 7237])).
% 2.74/2.26 tff(7240,plain,
% 2.74/2.26 (tptp_fun_Z1_9(W1!8) = X!1),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[522, 7239])).
% 2.74/2.26 tff(7241,plain,
% 2.74/2.26 (tptp_fun_Z1_9(W1!8) = tptp_fun_X_2(Y!0)),
% 2.74/2.26 inference(transitivity,[status(thm)],[7240, 6043])).
% 2.74/2.26 tff(7242,plain,
% 2.74/2.26 (big_f(tptp_fun_Z1_9(W1!8), W1!8) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7241, 7121])).
% 2.74/2.26 tff(7243,plain,
% 2.74/2.26 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.74/2.26 inference(symmetry,[status(thm)],[7242])).
% 2.74/2.26 tff(7244,plain,
% 2.74/2.26 ((~big_f(tptp_fun_X_2(Y!0), X!1)) <=> (~big_f(tptp_fun_Z1_9(W1!8), W1!8))),
% 2.74/2.26 inference(monotonicity,[status(thm)],[7243])).
% 2.74/2.26 tff(7245,plain,
% 2.74/2.26 (~big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.74/2.26 inference(modus_ponens,[status(thm)],[5823, 7244])).
% 2.74/2.26 tff(7246,plain,
% 2.74/2.26 (![X1: $i] : (big_f(X1, W1!8) <=> (X1 = tptp_fun_Z1_9(W1!8)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[481, 7230])).
% 2.74/2.26 tff(7247,plain,
% 2.74/2.26 (big_f(tptp_fun_Z1_9(W1!8), W1!8)),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[1506, 7246])).
% 2.74/2.26 tff(7248,plain,
% 2.74/2.26 ($false),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[7247, 7245])).
% 2.74/2.26 tff(7249,plain,(big_f(tptp_fun_X_2(Y!0), X!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.26 tff(7250,plain,
% 2.74/2.26 (~![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0)))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6673, 7249])).
% 2.74/2.26 tff(7251,plain,
% 2.74/2.26 (~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[6866, 7250])).
% 2.74/2.26 tff(7252,plain,
% 2.74/2.26 ((~((tptp_fun_X_2(Y!0) = Y!0) | ![Y: $i] : (big_f(tptp_fun_X_2(Y!0), Y) <=> (Y = tptp_fun_W_3(Y!0))))) | (~((~(tptp_fun_X_2(Y!0) = Y!0)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Y!0), tptp_fun_Y_4(W, Y!0))) <=> (tptp_fun_Y_4(W, Y!0) = W))))),
% 2.74/2.26 inference(unit_resolution,[status(thm)],[2663, 7251])).
% 2.74/2.26 tff(7253,plain,
% 2.74/2.26 (~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~((~(tptp_fun_X_2(Z) = Z)) | ![W: $i] : ((~big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z))) <=> (tptp_fun_Y_4(W, Z) = W))))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[56, 7252])).
% 2.74/2.27 tff(7254,plain,
% 2.74/2.27 (![W1: $i] : (~((~((tptp_fun_Y1_11(W1) = W1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(W1)) <=> (X1 = tptp_fun_Z1_12(W1))))) | (~((~(tptp_fun_Y1_11(W1) = W1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, W1), tptp_fun_Y1_11(W1))) <=> (tptp_fun_X1_13(Z1, W1) = Z1))))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[82, 7253])).
% 2.74/2.27 tff(7255,plain,
% 2.74/2.27 (~((~((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1))))) | (~((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1)))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[88, 7254])).
% 2.74/2.27 tff(7256,plain,
% 2.74/2.27 ((tptp_fun_Y1_11(X!1) = X!1) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_12(X!1)))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[191, 7255])).
% 2.74/2.27 tff(7257,plain,
% 2.74/2.27 (tptp_fun_Y1_11(X!1) = X!1),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[7044, 7256, 7171, 7205])).
% 2.74/2.27 tff(7258,plain,
% 2.74/2.27 ((~(tptp_fun_Y1_11(X!1) = X!1)) | ![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[90, 7255])).
% 2.74/2.27 tff(7259,plain,
% 2.74/2.27 (![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[269, 7258, 7257])).
% 2.74/2.27 tff(7260,plain,
% 2.74/2.27 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~(W1!8 = X!1)) | (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[4156, 6042])).
% 2.74/2.27 tff(7261,plain,
% 2.74/2.27 ((~![Z1: $i] : ((~big_f(tptp_fun_X1_13(Z1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(Z1, X!1) = Z1))) | (~(tptp_fun_Y1_11(X!1) = X!1)) | (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[7260, 7121])).
% 2.74/2.27 tff(7262,plain,
% 2.74/2.27 (~![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[7261, 7259, 7257])).
% 2.74/2.27 tff(7263,plain,
% 2.74/2.27 ((tptp_fun_Y1_11(X!1) = W1!8) <=> (tptp_fun_Y1_11(X!1) = X!1)),
% 2.74/2.27 inference(monotonicity,[status(thm)],[7121])).
% 2.74/2.27 tff(7264,plain,
% 2.74/2.27 ((tptp_fun_Y1_11(X!1) = X!1) <=> (tptp_fun_Y1_11(X!1) = W1!8)),
% 2.74/2.27 inference(symmetry,[status(thm)],[7263])).
% 2.74/2.27 tff(7265,plain,
% 2.74/2.27 (tptp_fun_Y1_11(X!1) = W1!8),
% 2.74/2.27 inference(modus_ponens,[status(thm)],[7257, 7264])).
% 2.74/2.27 tff(7266,plain,
% 2.74/2.27 (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1)))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[1465, 7265, 7262])).
% 2.74/2.27 tff(7267,plain,
% 2.74/2.27 ((~((tptp_fun_Y1_11(X!1) = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_10(Z1, tptp_fun_Y1_11(X!1)) = Z1)))) | (~((~(tptp_fun_Y1_11(X!1) = W1!8)) | ![X1: $i] : (big_f(X1, tptp_fun_Y1_11(X!1)) <=> (X1 = tptp_fun_Z1_9(tptp_fun_Y1_11(X!1))))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[1459, 7266])).
% 2.74/2.27 tff(7268,plain,
% 2.74/2.27 (~![Y1: $i] : (~((~((Y1 = W1!8) | ![Z1: $i] : ((~big_f(tptp_fun_X1_10(Z1, Y1), Y1)) <=> (tptp_fun_X1_10(Z1, Y1) = Z1)))) | (~((~(Y1 = W1!8)) | ![X1: $i] : (big_f(X1, Y1) <=> (X1 = tptp_fun_Z1_9(Y1)))))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[790, 7267])).
% 2.74/2.27 tff(7269,plain,
% 2.74/2.27 (![X: $i] : (~((~((X = Z!5) | ![W: $i] : ((~big_f(X, tptp_fun_Y_7(W, X))) <=> (tptp_fun_Y_7(W, X) = W)))) | (~((~(X = Z!5)) | ![Y: $i] : (big_f(X, Y) <=> (Y = tptp_fun_W_6(X)))))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[462, 7268])).
% 2.74/2.27 tff(7270,plain,
% 2.74/2.27 (![Y: $i] : (big_f(Z!5, Y) <=> (Y = tptp_fun_W_6(Z!5)))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[385, 7269])).
% 2.74/2.27 tff(7271,plain,
% 2.74/2.27 (big_f(Z!5, Y!0) <=> (Y!0 = tptp_fun_W_6(Z!5))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[387, 7270])).
% 2.74/2.27 tff(7272,plain,
% 2.74/2.27 (big_f(X!1, tptp_fun_Y1_11(X!1)) <=> big_f(tptp_fun_X_2(Y!0), X!1)),
% 2.74/2.27 inference(monotonicity,[status(thm)],[6043, 7257])).
% 2.74/2.27 tff(7273,plain,
% 2.74/2.27 (big_f(tptp_fun_X_2(Y!0), X!1) <=> big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.74/2.27 inference(symmetry,[status(thm)],[7272])).
% 2.74/2.27 tff(7274,plain,
% 2.74/2.27 (big_f(X!1, tptp_fun_Y1_11(X!1))),
% 2.74/2.27 inference(modus_ponens,[status(thm)],[7249, 7273])).
% 2.74/2.27 tff(7275,plain,
% 2.74/2.27 (~![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[5881, 7274, 7257])).
% 2.74/2.27 tff(7276,plain,
% 2.74/2.27 (~((~((X!1 = Z!5) | ![W: $i] : ((~big_f(X!1, tptp_fun_Y_7(W, X!1))) <=> (tptp_fun_Y_7(W, X!1) = W)))) | (~((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1))))))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[342, 7269])).
% 2.74/2.27 tff(7277,plain,
% 2.74/2.27 ((~(X!1 = Z!5)) | ![Y: $i] : (big_f(X!1, Y) <=> (Y = tptp_fun_W_6(X!1)))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[344, 7276])).
% 2.74/2.27 tff(7278,plain,
% 2.74/2.27 (~(X!1 = Z!5)),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[346, 7277, 7275])).
% 2.74/2.27 tff(7279,plain,
% 2.74/2.27 (~(Z!5 = X!1)),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[353, 7278])).
% 2.74/2.27 tff(7280,plain,
% 2.74/2.27 (Z!5 = Y!0),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[361, 7279])).
% 2.74/2.27 tff(7281,plain,
% 2.74/2.27 (big_f(Z!5, Y!0) <=> big_f(Y!0, tptp_fun_Y1_11(Y!0))),
% 2.74/2.27 inference(monotonicity,[status(thm)],[7280, 7172])).
% 2.74/2.27 tff(7282,plain,
% 2.74/2.27 (big_f(Y!0, tptp_fun_Y1_11(Y!0)) <=> big_f(Z!5, Y!0)),
% 2.74/2.27 inference(symmetry,[status(thm)],[7281])).
% 2.74/2.27 tff(7283,plain,
% 2.74/2.27 (big_f(Z!5, Y!0)),
% 2.74/2.27 inference(modus_ponens,[status(thm)],[7205, 7282])).
% 2.74/2.27 tff(7284,plain,
% 2.74/2.27 (Y!0 = tptp_fun_W_6(Z!5)),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[1209, 7283, 7271])).
% 2.74/2.27 tff(7285,plain,
% 2.74/2.27 (tptp_fun_W_6(Z!5) = Y!0),
% 2.74/2.27 inference(symmetry,[status(thm)],[7284])).
% 2.74/2.27 tff(7286,plain,
% 2.74/2.27 (big_f(Z!5, X!1) <=> (X!1 = tptp_fun_W_6(Z!5))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[983, 7270])).
% 2.74/2.27 tff(7287,plain,
% 2.74/2.27 (big_f(Z!5, X!1) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.74/2.27 inference(monotonicity,[status(thm)],[7280, 6043])).
% 2.74/2.27 tff(7288,plain,
% 2.74/2.27 (big_f(Y!0, tptp_fun_X_2(Y!0)) <=> big_f(Z!5, X!1)),
% 2.74/2.27 inference(symmetry,[status(thm)],[7287])).
% 2.74/2.27 tff(7289,plain,
% 2.74/2.27 (tptp_fun_Y1_11(X!1) = tptp_fun_X_2(Y!0)),
% 2.74/2.27 inference(transitivity,[status(thm)],[7257, 6043])).
% 2.74/2.27 tff(7290,plain,
% 2.74/2.27 (~(tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[7056, 7257, 7249])).
% 2.74/2.27 tff(7291,plain,
% 2.74/2.27 (tptp_fun_X1_13(X!1, X!1) = Y!0),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[285, 7290])).
% 2.74/2.27 tff(7292,plain,
% 2.74/2.27 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1)) <=> big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.74/2.27 inference(monotonicity,[status(thm)],[7291, 7289])).
% 2.74/2.27 tff(7293,plain,
% 2.74/2.27 ((~big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))) <=> (tptp_fun_X1_13(X!1, X!1) = X!1)),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[271, 7259])).
% 2.74/2.27 tff(7294,plain,
% 2.74/2.27 (big_f(tptp_fun_X1_13(X!1, X!1), tptp_fun_Y1_11(X!1))),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[291, 7290, 7293])).
% 2.74/2.27 tff(7295,plain,
% 2.74/2.27 (big_f(Y!0, tptp_fun_X_2(Y!0))),
% 2.74/2.27 inference(modus_ponens,[status(thm)],[7294, 7292])).
% 2.74/2.27 tff(7296,plain,
% 2.74/2.27 (big_f(Z!5, X!1)),
% 2.74/2.27 inference(modus_ponens,[status(thm)],[7295, 7288])).
% 2.74/2.27 tff(7297,plain,
% 2.74/2.27 (X!1 = tptp_fun_W_6(Z!5)),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[989, 7296, 7286])).
% 2.74/2.27 tff(7298,plain,
% 2.74/2.27 (X!1 = Y!0),
% 2.74/2.27 inference(transitivity,[status(thm)],[7297, 7285])).
% 2.74/2.27 tff(7299,plain,
% 2.74/2.27 ($false),
% 2.74/2.27 inference(unit_resolution,[status(thm)],[741, 7298])).
% 2.74/2.27 % SZS output end Proof
%------------------------------------------------------------------------------