TSTP Solution File: SYN551+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:56:23 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.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 05:40:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(tptp_fun_X_1_type, type, (
% 0.20/0.39 tptp_fun_X_1: $i)).
% 0.20/0.39 tff(f_type, type, (
% 0.20/0.39 f: $i > $i)).
% 0.20/0.39 tff(g_type, type, (
% 0.20/0.39 g: $i > $i)).
% 0.20/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.39 tptp_fun_Y_0: $i > $i)).
% 0.20/0.39 tff(tptp_fun_X_2_type, type, (
% 0.20/0.39 tptp_fun_X_2: $i)).
% 0.20/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.39 tptp_fun_Y_3: $i > $i)).
% 0.20/0.39 tff(1,assumption,(~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))))), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) | (X!2 = g(f(X!2)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (X!2 = g(f(X!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.39 tff(4,assumption,(X!2 = g(f(X!2))), introduced(assumption)).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (g(f(X!2)) = X!2),
% 0.20/0.39 inference(symmetry,[status(thm)],[4])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (f(X!2) = f(g(f(X!2)))),
% 0.20/0.39 inference(symmetry,[status(thm)],[6])).
% 0.20/0.39 tff(8,assumption,(~(f(X!2) = f(g(f(X!2))))), introduced(assumption)).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,((f(X!2) = f(g(f(X!2)))) | (~(X!2 = g(f(X!2))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (f(X!2) = f(g(f(X!2)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[10, 3])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.39 inference(symmetry,[status(thm)],[11])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (g(f(g(f(X!2)))) = g(f(X!2))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (g(f(X!2)) = g(f(g(f(X!2))))),
% 0.20/0.39 inference(symmetry,[status(thm)],[13])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (f(X!2) = f(g(f(X!2)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[10, 4])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.39 inference(symmetry,[status(thm)],[15])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (g(f(g(f(X!2)))) = g(f(X!2))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (g(f(g(f(X!2)))) = X!2),
% 0.20/0.39 inference(transitivity,[status(thm)],[17, 5])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (f(g(f(g(f(X!2))))) = f(X!2)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (f(X!2) = f(g(f(g(f(X!2)))))),
% 0.20/0.39 inference(symmetry,[status(thm)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (f(g(f(X!2))) = f(g(f(g(f(X!2)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[16, 20])).
% 0.20/0.39 tff(22,assumption,(~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))), introduced(assumption)).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.39 tff(24,plain,((f(g(f(X!2))) = f(g(f(g(f(X!2)))))) | (~(X!2 = g(f(X!2))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (f(g(f(X!2))) = f(g(f(g(f(X!2)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[24, 3])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) | ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.20/0.39 tff(28,assumption,(~((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2)))), introduced(assumption)).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2))) | (tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (f(g(tptp_fun_Y_0(f(X!2)))) = tptp_fun_Y_0(f(X!2))),
% 0.20/0.39 inference(symmetry,[status(thm)],[30])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (g(f(g(tptp_fun_Y_0(f(X!2))))) = g(tptp_fun_Y_0(f(X!2)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2)))))),
% 0.20/0.39 inference(symmetry,[status(thm)],[32])).
% 0.20/0.39 tff(34,assumption,(![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))), introduced(assumption)).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | ((~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (g(tptp_fun_Y_0(f(X!2))) = X!2))) <=> ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | (~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (g(tptp_fun_Y_0(f(X!2))) = X!2))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | ((~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (g(tptp_fun_Y_0(f(X!2))) = X!2))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | (~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (g(tptp_fun_Y_0(f(X!2))) = X!2)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (g(tptp_fun_Y_0(f(X!2))) = X!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (g(tptp_fun_Y_0(f(X!2))) = X!2),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (X!2 = g(tptp_fun_Y_0(f(X!2)))),
% 0.20/0.39 inference(symmetry,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (f(X!2) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (f(g(tptp_fun_Y_0(f(X!2)))) = f(X!2)),
% 0.20/0.39 inference(symmetry,[status(thm)],[41])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (tptp_fun_Y_0(f(X!2)) = f(X!2)),
% 0.20/0.39 inference(transitivity,[status(thm)],[30, 42])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2))) | (~(tptp_fun_Y_0(f(X!2)) = f(X!2)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (~(tptp_fun_Y_0(f(X!2)) = f(X!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[44, 28])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 43])).
% 0.20/0.39 tff(47,plain,(((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 27])).
% 0.20/0.39 tff(49,assumption,((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2))), introduced(assumption)).
% 0.20/0.39 tff(50,assumption,(f(X!2) = f(g(f(X!2)))), introduced(assumption)).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.39 inference(symmetry,[status(thm)],[50])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (tptp_fun_Y_0(f(X!2)) = tptp_fun_Y_0(f(g(f(X!2))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (tptp_fun_Y_0(f(g(f(X!2)))) = tptp_fun_Y_0(f(X!2))),
% 0.20/0.39 inference(symmetry,[status(thm)],[52])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2)))) <=> (tptp_fun_Y_0(f(X!2)) = f(X!2))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[53, 51])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2))))) <=> (~(tptp_fun_Y_0(f(X!2)) = f(X!2)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.39 tff(56,assumption,(~((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2)))))), introduced(assumption)).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2))))) | (~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (~(tptp_fun_Y_0(f(X!2)) = f(X!2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (g(tptp_fun_Y_0(f(g(f(X!2))))) = g(tptp_fun_Y_0(f(X!2)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (f(g(tptp_fun_Y_0(f(g(f(X!2)))))) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2))))))) <=> (tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[53, 61])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2))))) | (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[63, 56])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 62])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ((~((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2)))) | (~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 65, 59, 49])).
% 0.20/0.40 tff(68,plain,(((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2))))) | (~((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (tptp_fun_Y_0(f(X!2)) = f(X!2)))) | (~(f(X!2) = f(g(f(X!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 48, 11])).
% 0.20/0.40 tff(70,assumption,(f(g(f(X!2))) = f(g(f(g(f(X!2)))))), introduced(assumption)).
% 0.20/0.40 tff(71,assumption,((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(f(X!2))))), introduced(assumption)).
% 0.20/0.40 tff(72,assumption,(![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (tptp_fun_Y_0(X) = X))))), introduced(assumption)).
% 0.20/0.40 tff(73,plain,
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% 0.20/0.40 inference(rewrite,[status(thm)],[])).
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% 0.20/0.40 inference(rewrite,[status(thm)],[])).
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% 0.20/0.40 inference(monotonicity,[status(thm)],[87])).
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% 0.20/0.40 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (Y = X))))) <=> ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.40 tff(90,axiom,(~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (Y = X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_cute_thing')).
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% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 85])).
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% 0.20/0.40 inference(modus_ponens,[status(thm)],[92, 85])).
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% 0.20/0.40 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[93, 85])).
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% 0.20/0.40 inference(modus_ponens,[status(thm)],[94, 85])).
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% 0.20/0.40 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[95, 85])).
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% 0.20/0.40 inference(modus_ponens,[status(thm)],[96, 85])).
% 0.20/0.40 tff(98,plain,(
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% 0.20/0.40 inference(modus_ponens,[status(thm)],[98, 84])).
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% 0.20/0.40 inference(modus_ponens,[status(thm)],[100, 79])).
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% 0.20/0.40 inference(unit_resolution,[status(thm)],[101, 78])).
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% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
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% 0.20/0.40 (~((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (tptp_fun_Y_3(g(f(X!2))) = g(f(X!2))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[105, 102, 14])).
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% 0.20/0.40 (tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[107, 106])).
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% 0.20/0.40 inference(symmetry,[status(thm)],[108])).
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% 0.20/0.40 ((g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2) <=> (tptp_fun_Y_3(g(f(X!2))) = g(f(X!2)))),
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% 0.20/0.40 ((tptp_fun_Y_3(g(f(X!2))) = g(f(X!2))) <=> (g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2)),
% 0.20/0.40 inference(symmetry,[status(thm)],[110])).
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% 0.20/0.40 ((~(tptp_fun_Y_3(g(f(X!2))) = g(f(X!2)))) <=> (~(g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (tptp_fun_Y_3(g(f(X!2))) = g(f(X!2)))) | (~(tptp_fun_Y_3(g(f(X!2))) = g(f(X!2))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (~(tptp_fun_Y_3(g(f(X!2))) = g(f(X!2)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[113, 106])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (~(g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[114, 112])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (f(g(f(tptp_fun_Y_3(g(f(X!2)))))) = f(tptp_fun_Y_3(g(f(X!2))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 (g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))) = g(f(tptp_fun_Y_3(g(f(X!2)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 (g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2)))))))),
% 0.20/0.40 inference(symmetry,[status(thm)],[117])).
% 0.20/0.40 tff(119,plain,
% 0.20/0.40 (((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | ((~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2))) <=> ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | (~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | ((~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | (~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.40 tff(122,plain,
% 0.20/0.40 ((~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (g(f(tptp_fun_Y_3(g(f(X!2))))) = X!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[121, 27])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 118, 115])).
% 0.20/0.41 tff(124,plain,((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))))) <=> ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 ((((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) <=> ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[99])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[128, 125])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[129, 124])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1)))) | (X!1 = f(g(X!1)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (X!1 = f(g(X!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (f(g(X!1)) = X!1),
% 0.20/0.41 inference(symmetry,[status(thm)],[132])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 (g(f(g(X!1))) = g(X!1)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (g(X!1) = g(f(g(X!1)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[134])).
% 0.20/0.41 tff(136,assumption,(~(g(X!1) = g(f(g(X!1))))), introduced(assumption)).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.41 tff(138,plain,(g(X!1) = g(f(g(X!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 (g(f(g(X!1))) = g(X!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[138])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 (f(g(f(g(X!1)))) = f(g(X!1))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 (f(g(X!1)) = f(g(f(g(X!1))))),
% 0.20/0.41 inference(symmetry,[status(thm)],[140])).
% 0.20/0.41 tff(142,plain,
% 0.20/0.41 (f(g(f(g(X!1)))) = X!1),
% 0.20/0.41 inference(transitivity,[status(thm)],[140, 133])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 (g(f(g(f(g(X!1))))) = g(X!1)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 (g(X!1) = g(f(g(f(g(X!1)))))),
% 0.20/0.41 inference(symmetry,[status(thm)],[143])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 (g(f(g(X!1))) = g(f(g(f(g(X!1)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[139, 144])).
% 0.20/0.41 tff(146,assumption,(~(g(f(g(X!1))) = g(f(g(f(g(X!1))))))), introduced(assumption)).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.41 tff(148,plain,(g(f(g(X!1))) = g(f(g(f(g(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(149,assumption,(~((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (tptp_fun_Y_3(g(X!1)) = g(X!1)))), introduced(assumption)).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 (((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (tptp_fun_Y_3(g(X!1)) = g(X!1))) | (tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(151,plain,
% 0.20/0.41 (tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.41 tff(152,plain,
% 0.20/0.41 (g(f(tptp_fun_Y_3(g(X!1)))) = tptp_fun_Y_3(g(X!1))),
% 0.20/0.41 inference(symmetry,[status(thm)],[151])).
% 0.20/0.41 tff(153,plain,
% 0.20/0.41 (f(g(f(tptp_fun_Y_3(g(X!1))))) = f(tptp_fun_Y_3(g(X!1)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[152])).
% 0.20/0.41 tff(154,plain,
% 0.20/0.41 (f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1)))))),
% 0.20/0.41 inference(symmetry,[status(thm)],[153])).
% 0.20/0.41 tff(155,plain,
% 0.20/0.41 (((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1)))) | ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(156,plain,
% 0.20/0.41 (![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[155, 130])).
% 0.20/0.41 tff(157,plain,
% 0.20/0.41 (((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | ((~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (f(tptp_fun_Y_3(g(X!1))) = X!1))) <=> ((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | (~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (f(tptp_fun_Y_3(g(X!1))) = X!1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(158,plain,
% 0.20/0.41 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | ((~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (f(tptp_fun_Y_3(g(X!1))) = X!1))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(159,plain,
% 0.20/0.41 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | (~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (f(tptp_fun_Y_3(g(X!1))) = X!1)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.41 tff(160,plain,
% 0.20/0.41 ((~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (f(tptp_fun_Y_3(g(X!1))) = X!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[159, 156])).
% 0.20/0.41 tff(161,plain,
% 0.20/0.41 (f(tptp_fun_Y_3(g(X!1))) = X!1),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[160, 154])).
% 0.20/0.41 tff(162,plain,
% 0.20/0.41 (X!1 = f(tptp_fun_Y_3(g(X!1)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[161])).
% 0.20/0.41 tff(163,plain,
% 0.20/0.41 (g(X!1) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[162])).
% 0.20/0.41 tff(164,plain,
% 0.20/0.41 (g(f(tptp_fun_Y_3(g(X!1)))) = g(X!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[163])).
% 0.20/0.41 tff(165,plain,
% 0.20/0.41 (tptp_fun_Y_3(g(X!1)) = g(X!1)),
% 0.20/0.41 inference(transitivity,[status(thm)],[151, 164])).
% 0.20/0.41 tff(166,plain,
% 0.20/0.41 (((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (tptp_fun_Y_3(g(X!1)) = g(X!1))) | (~(tptp_fun_Y_3(g(X!1)) = g(X!1)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(167,plain,
% 0.20/0.41 (~(tptp_fun_Y_3(g(X!1)) = g(X!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[166, 149])).
% 0.20/0.41 tff(168,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[167, 165])).
% 0.20/0.41 tff(169,plain,((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (tptp_fun_Y_3(g(X!1)) = g(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(170,plain,
% 0.20/0.41 (tptp_fun_Y_3(g(X!1)) = tptp_fun_Y_3(g(f(g(X!1))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[138])).
% 0.20/0.41 tff(171,plain,
% 0.20/0.41 (tptp_fun_Y_3(g(f(g(X!1)))) = tptp_fun_Y_3(g(X!1))),
% 0.20/0.41 inference(symmetry,[status(thm)],[170])).
% 0.20/0.41 tff(172,plain,
% 0.20/0.41 ((tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1)))) <=> (tptp_fun_Y_3(g(X!1)) = g(X!1))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[171, 139])).
% 0.20/0.41 tff(173,plain,
% 0.20/0.41 ((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1))))) <=> (~(tptp_fun_Y_3(g(X!1)) = g(X!1)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.41 tff(174,assumption,(~((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1)))))), introduced(assumption)).
% 0.20/0.41 tff(175,plain,
% 0.20/0.41 (((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1))))) | (~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(176,plain,
% 0.20/0.41 (~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.20/0.41 tff(177,plain,
% 0.20/0.41 (~(tptp_fun_Y_3(g(X!1)) = g(X!1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.20/0.41 tff(178,plain,
% 0.20/0.41 (f(tptp_fun_Y_3(g(f(g(X!1))))) = f(tptp_fun_Y_3(g(X!1)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.41 tff(179,plain,
% 0.20/0.41 (g(f(tptp_fun_Y_3(g(f(g(X!1)))))) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[178])).
% 0.20/0.41 tff(180,plain,
% 0.20/0.41 ((tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1))))))) <=> (tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[171, 179])).
% 0.20/0.41 tff(181,plain,
% 0.20/0.41 (((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(182,plain,
% 0.20/0.41 (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[181, 174])).
% 0.20/0.41 tff(183,plain,
% 0.20/0.41 (tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[182, 180])).
% 0.20/0.41 tff(184,plain,
% 0.20/0.41 ((~((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (tptp_fun_Y_3(g(X!1)) = g(X!1)))) | (~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (tptp_fun_Y_3(g(X!1)) = g(X!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(185,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[184, 183, 177, 169])).
% 0.20/0.41 tff(186,plain,((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(187,assumption,(![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))), introduced(assumption)).
% 0.20/0.41 tff(188,plain,
% 0.20/0.41 (((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))) | ((~(g(f(g(X!1))) = g(f(g(f(g(X!1))))))) | (~((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1)))))))) <=> ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))) | (~(g(f(g(X!1))) = g(f(g(f(g(X!1))))))) | (~((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(189,plain,
% 0.20/0.41 ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))) | ((~(g(f(g(X!1))) = g(f(g(f(g(X!1))))))) | (~((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(190,plain,
% 0.20/0.41 ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))) | (~(g(f(g(X!1))) = g(f(g(f(g(X!1))))))) | (~((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(g(X!1))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.41 tff(191,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[190, 187, 186, 148])).
% 0.20/0.41 tff(192,plain,(~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(193,plain,
% 0.20/0.41 (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (tptp_fun_Y_0(X) = X))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 192])).
% 0.20/0.41 tff(194,plain,
% 0.20/0.41 (((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (tptp_fun_Y_0(X) = X))))) | ((~(f(g(X!1)) = f(g(f(g(X!1)))))) | (~((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1))))))) <=> ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (tptp_fun_Y_0(X) = X))))) | (~(f(g(X!1)) = f(g(f(g(X!1)))))) | (~((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(195,plain,
% 0.20/0.41 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (tptp_fun_Y_0(X) = X))))) | ((~(f(g(X!1)) = f(g(f(g(X!1)))))) | (~((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(196,plain,
% 0.20/0.41 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (tptp_fun_Y_0(X) = X))))) | (~(f(g(X!1)) = f(g(f(g(X!1)))))) | (~((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.41 tff(197,plain,
% 0.20/0.41 (~((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[196, 193, 141])).
% 0.20/0.41 tff(198,plain,
% 0.20/0.41 (((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1)))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(199,plain,
% 0.20/0.41 (tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.41 tff(200,plain,
% 0.20/0.41 (f(g(tptp_fun_Y_0(f(g(X!1))))) = tptp_fun_Y_0(f(g(X!1)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[199])).
% 0.20/0.41 tff(201,plain,
% 0.20/0.41 ((f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1) <=> (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[200, 132])).
% 0.20/0.42 tff(202,plain,
% 0.20/0.42 ((tptp_fun_Y_0(f(g(X!1))) = f(g(X!1))) <=> (f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1)),
% 0.20/0.42 inference(symmetry,[status(thm)],[201])).
% 0.20/0.42 tff(203,plain,
% 0.20/0.42 ((~(tptp_fun_Y_0(f(g(X!1))) = f(g(X!1)))) <=> (~(f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.42 tff(204,plain,
% 0.20/0.42 (((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(X!1)))) | (~(tptp_fun_Y_0(f(g(X!1))) = f(g(X!1))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(205,plain,
% 0.20/0.42 (~(tptp_fun_Y_0(f(g(X!1))) = f(g(X!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[204, 197])).
% 0.20/0.42 tff(206,plain,
% 0.20/0.42 (~(f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[205, 203])).
% 0.20/0.42 tff(207,plain,
% 0.20/0.42 (g(f(g(tptp_fun_Y_0(f(g(X!1)))))) = g(tptp_fun_Y_0(f(g(X!1))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[200])).
% 0.20/0.42 tff(208,plain,
% 0.20/0.42 (f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))) = f(g(tptp_fun_Y_0(f(g(X!1)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[207])).
% 0.20/0.42 tff(209,plain,
% 0.20/0.42 (f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1)))))))),
% 0.20/0.42 inference(symmetry,[status(thm)],[208])).
% 0.20/0.42 tff(210,plain,
% 0.20/0.42 (((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | ((~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1))) <=> ((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | (~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(211,plain,
% 0.20/0.42 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | ((~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(212,plain,
% 0.20/0.42 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!1))) | (~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.42 tff(213,plain,
% 0.20/0.42 ((~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (f(g(tptp_fun_Y_0(f(g(X!1))))) = X!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[212, 156])).
% 0.20/0.42 tff(214,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[213, 209, 206])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------