TSTP Solution File: SYN417+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 23:55:14 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 03:24:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(f_type, type, (
% 0.19/0.38 f: $i > $i)).
% 0.19/0.38 tff(g_type, type, (
% 0.19/0.38 g: $i > $i)).
% 0.19/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.38 tptp_fun_Y_0: $i > $i)).
% 0.19/0.38 tff(tptp_fun_X_1_type, type, (
% 0.19/0.38 tptp_fun_X_1: $i)).
% 0.19/0.38 tff(tptp_fun_X_2_type, type, (
% 0.19/0.38 tptp_fun_X_2: $i)).
% 0.19/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.38 tptp_fun_Y_3: $i > $i)).
% 0.19/0.38 tff(1,assumption,(~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) | (X!2 = g(f(X!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (X!2 = g(f(X!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.38 tff(4,assumption,(X!2 = g(f(X!2))), introduced(assumption)).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (g(f(X!2)) = X!2),
% 0.19/0.38 inference(symmetry,[status(thm)],[4])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (f(g(f(X!2))) = f(X!2)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (f(X!2) = f(g(f(X!2)))),
% 0.19/0.38 inference(symmetry,[status(thm)],[6])).
% 0.19/0.38 tff(8,assumption,(~(f(X!2) = f(g(f(X!2))))), introduced(assumption)).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,((f(X!2) = f(g(f(X!2)))) | (~(X!2 = g(f(X!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (f(X!2) = f(g(f(X!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[10, 3])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (f(g(f(X!2))) = f(X!2)),
% 0.19/0.38 inference(symmetry,[status(thm)],[11])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (g(f(g(f(X!2)))) = g(f(X!2))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (g(f(X!2)) = g(f(g(f(X!2))))),
% 0.19/0.38 inference(symmetry,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (f(X!2) = f(g(f(X!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[10, 4])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (f(g(f(X!2))) = f(X!2)),
% 0.19/0.38 inference(symmetry,[status(thm)],[15])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (g(f(g(f(X!2)))) = g(f(X!2))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (g(f(g(f(X!2)))) = X!2),
% 0.19/0.38 inference(transitivity,[status(thm)],[17, 5])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (f(g(f(g(f(X!2))))) = f(X!2)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (f(X!2) = f(g(f(g(f(X!2)))))),
% 0.19/0.38 inference(symmetry,[status(thm)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (f(g(f(X!2))) = f(g(f(g(f(X!2)))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[16, 20])).
% 0.19/0.38 tff(22,assumption,(~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))), introduced(assumption)).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.38 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,[]))).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (f(g(f(X!2))) = f(g(f(g(f(X!2)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[24, 3])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) | ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.19/0.38 tff(28,assumption,(~((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2))))), introduced(assumption)).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2)))) | (tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (f(g(tptp_fun_Y_0(f(X!2)))) = tptp_fun_Y_0(f(X!2))),
% 0.19/0.38 inference(symmetry,[status(thm)],[30])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (g(f(g(tptp_fun_Y_0(f(X!2))))) = g(tptp_fun_Y_0(f(X!2)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2)))))),
% 0.19/0.38 inference(symmetry,[status(thm)],[32])).
% 0.19/0.38 tff(34,assumption,(![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))), introduced(assumption)).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | ((~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (X!2 = g(tptp_fun_Y_0(f(X!2)))))) <=> ((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | (~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (X!2 = g(tptp_fun_Y_0(f(X!2)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | ((~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (X!2 = g(tptp_fun_Y_0(f(X!2)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | (~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (X!2 = g(tptp_fun_Y_0(f(X!2))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~(g(tptp_fun_Y_0(f(X!2))) = g(f(g(tptp_fun_Y_0(f(X!2))))))) | (X!2 = g(tptp_fun_Y_0(f(X!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (X!2 = g(tptp_fun_Y_0(f(X!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (f(X!2) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (f(X!2) = tptp_fun_Y_0(f(X!2))),
% 0.19/0.39 inference(transitivity,[status(thm)],[40, 31])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2)))) | (~(f(X!2) = tptp_fun_Y_0(f(X!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (~(f(X!2) = tptp_fun_Y_0(f(X!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 28])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[43, 41])).
% 0.19/0.39 tff(45,plain,(((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[45, 27])).
% 0.19/0.39 tff(47,assumption,((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2)))), introduced(assumption)).
% 0.19/0.39 tff(48,assumption,(f(X!2) = f(g(f(X!2)))), introduced(assumption)).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (tptp_fun_Y_0(f(X!2)) = tptp_fun_Y_0(f(g(f(X!2))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (tptp_fun_Y_0(f(g(f(X!2)))) = tptp_fun_Y_0(f(X!2))),
% 0.19/0.39 inference(symmetry,[status(thm)],[49])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (f(g(f(X!2))) = f(X!2)),
% 0.19/0.39 inference(symmetry,[status(thm)],[48])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2))))) <=> (f(X!2) = tptp_fun_Y_0(f(X!2)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~(f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2)))))) <=> (~(f(X!2) = tptp_fun_Y_0(f(X!2))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.39 tff(54,assumption,(~((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2))))))), introduced(assumption)).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(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))) = tptp_fun_Y_0(f(g(f(X!2))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (~(f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (~(f(X!2) = tptp_fun_Y_0(f(X!2)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[56, 53])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (g(tptp_fun_Y_0(f(g(f(X!2))))) = g(tptp_fun_Y_0(f(X!2)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (f(g(tptp_fun_Y_0(f(g(f(X!2)))))) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((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)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[50, 59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(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)))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 54])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 60])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~((~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2))))) | (~(tptp_fun_Y_0(f(X!2)) = f(g(tptp_fun_Y_0(f(X!2)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[64, 63, 57, 47])).
% 0.19/0.39 tff(66,plain,(((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (f(g(f(X!2))) = 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)))))) | (f(X!2) = tptp_fun_Y_0(f(X!2))))) | (~(f(X!2) = f(g(f(X!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[66, 46, 11])).
% 0.19/0.39 tff(68,assumption,(f(g(f(X!2))) = f(g(f(g(f(X!2)))))), introduced(assumption)).
% 0.19/0.39 tff(69,assumption,((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2)))))), introduced(assumption)).
% 0.19/0.39 tff(70,assumption,(![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))), introduced(assumption)).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))) | ((~(f(g(f(X!2))) = f(g(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)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2))))))))) <=> ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))) | (~(f(g(f(X!2))) = f(g(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)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))) | ((~(f(g(f(X!2))) = f(g(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)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))) | (~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))) | (~((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(tptp_fun_Y_0(f(g(f(X!2)))))))) | (f(g(f(X!2))) = tptp_fun_Y_0(f(g(f(X!2)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[73, 70, 69, 68])).
% 0.19/0.39 tff(75,plain,((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))) | (~((~(tptp_fun_Y_0(f(g(f(X!2)))) = f(g(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))) = f(g(f(g(f(X!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[75, 67, 25])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 ((![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))) <=> (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 ((![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))) <=> (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) <=> ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) <=> ((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) <=> (((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[80, 79])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (((((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) & (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X))))))) <=> ((((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) & (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[81, 78])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))) <=> ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
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% 0.19/0.39 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y))))) <=> ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (X = Y))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (X = Y)))) <=> (?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (X = Y))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (X = Y))))) <=> (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (X = Y))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (X = Y))))) <=> ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[86, 84])).
% 0.19/0.39 tff(88,axiom,(~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (X = Y))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (X = Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cute')).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[89, 83])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[91, 83])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[92, 83])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 ((~?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X = Y)))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[94, 83])).
% 0.19/0.39 tff(96,plain,(
% 0.19/0.39 (((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) & (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[95])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 ((((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) & (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[96, 82])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))),
% 0.19/0.39 inference(and_elim,[status(thm)],[97])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X))))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[98, 77])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 76])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))) | ((~(g(f(X!2)) = g(f(g(f(X!2)))))) | (~((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2)))))))) <=> ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))) | (~(g(f(X!2)) = g(f(g(f(X!2)))))) | (~((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))) | ((~(g(f(X!2)) = g(f(g(f(X!2)))))) | (~((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))) | (~(g(f(X!2)) = g(f(g(f(X!2)))))) | (~((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (~((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[103, 100, 14])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2))))) | (tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (g(f(tptp_fun_Y_3(g(f(X!2))))) = tptp_fun_Y_3(g(f(X!2)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[106])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((X!2 = g(f(tptp_fun_Y_3(g(f(X!2)))))) <=> (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[3, 107])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((g(f(X!2)) = tptp_fun_Y_3(g(f(X!2)))) <=> (X!2 = g(f(tptp_fun_Y_3(g(f(X!2))))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[108])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 ((~(g(f(X!2)) = tptp_fun_Y_3(g(f(X!2))))) <=> (~(X!2 = g(f(tptp_fun_Y_3(g(f(X!2)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (((~(tptp_fun_Y_3(g(f(X!2))) = g(f(tptp_fun_Y_3(g(f(X!2))))))) | (g(f(X!2)) = tptp_fun_Y_3(g(f(X!2))))) | (~(g(f(X!2)) = tptp_fun_Y_3(g(f(X!2)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (~(g(f(X!2)) = tptp_fun_Y_3(g(f(X!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 104])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (~(X!2 = g(f(tptp_fun_Y_3(g(f(X!2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[112, 110])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (f(g(f(tptp_fun_Y_3(g(f(X!2)))))) = f(tptp_fun_Y_3(g(f(X!2))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))) = g(f(tptp_fun_Y_3(g(f(X!2)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2)))))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[115])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | ((~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (X!2 = g(f(tptp_fun_Y_3(g(f(X!2)))))))) <=> ((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | (~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (X!2 = g(f(tptp_fun_Y_3(g(f(X!2)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | ((~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (X!2 = g(f(tptp_fun_Y_3(g(f(X!2)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))) | (~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (X!2 = g(f(tptp_fun_Y_3(g(f(X!2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 ((~(g(f(tptp_fun_Y_3(g(f(X!2))))) = g(f(g(f(tptp_fun_Y_3(g(f(X!2))))))))) | (X!2 = g(f(tptp_fun_Y_3(g(f(X!2))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[119, 27])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[120, 116, 113])).
% 0.19/0.40 tff(122,plain,((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))))) <=> ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 ((((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))) <=> ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (((X!1 = f(g(X!1))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[97])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 ((~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))))) | (~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (X!2 = Y)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[126, 123])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (~((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[127, 122])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y)))) | (X!1 = f(g(X!1)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (X!1 = f(g(X!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 (f(g(X!1)) = X!1),
% 0.19/0.40 inference(symmetry,[status(thm)],[130])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 (g(f(g(X!1))) = g(X!1)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 (g(X!1) = g(f(g(X!1)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[132])).
% 0.19/0.40 tff(134,assumption,(~(g(X!1) = g(f(g(X!1))))), introduced(assumption)).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.40 tff(136,plain,(g(X!1) = g(f(g(X!1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 (g(f(g(X!1))) = g(X!1)),
% 0.19/0.40 inference(symmetry,[status(thm)],[136])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 (f(g(f(g(X!1)))) = f(g(X!1))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 (f(g(X!1)) = f(g(f(g(X!1))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[138])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (f(g(f(g(X!1)))) = X!1),
% 0.19/0.40 inference(transitivity,[status(thm)],[138, 131])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 (g(f(g(f(g(X!1))))) = g(X!1)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (g(X!1) = g(f(g(f(g(X!1)))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[141])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 (g(f(g(X!1))) = g(f(g(f(g(X!1)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[137, 142])).
% 0.19/0.40 tff(144,assumption,(~(g(f(g(X!1))) = g(f(g(f(g(X!1))))))), introduced(assumption)).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.19/0.40 tff(146,plain,(g(f(g(X!1))) = g(f(g(f(g(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(147,assumption,(~((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (g(X!1) = tptp_fun_Y_3(g(X!1))))), introduced(assumption)).
% 0.19/0.40 tff(148,plain,
% 0.19/0.40 (((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (g(X!1) = tptp_fun_Y_3(g(X!1)))) | (tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(149,plain,
% 0.19/0.40 (tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.40 tff(150,plain,
% 0.19/0.40 (g(f(tptp_fun_Y_3(g(X!1)))) = tptp_fun_Y_3(g(X!1))),
% 0.19/0.40 inference(symmetry,[status(thm)],[149])).
% 0.19/0.40 tff(151,plain,
% 0.19/0.40 (f(g(f(tptp_fun_Y_3(g(X!1))))) = f(tptp_fun_Y_3(g(X!1)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[150])).
% 0.19/0.40 tff(152,plain,
% 0.19/0.40 (f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1)))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[151])).
% 0.19/0.40 tff(153,plain,
% 0.19/0.40 (((~(X!1 = f(g(X!1)))) | (~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y)))) | ![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(154,plain,
% 0.19/0.40 (![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[153, 128])).
% 0.19/0.40 tff(155,plain,
% 0.19/0.40 (((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (X!1 = f(tptp_fun_Y_3(g(X!1)))))) <=> ((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | (~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (X!1 = f(tptp_fun_Y_3(g(X!1)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(156,plain,
% 0.19/0.40 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (X!1 = f(tptp_fun_Y_3(g(X!1)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(157,plain,
% 0.19/0.40 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | (~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (X!1 = f(tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.40 tff(158,plain,
% 0.19/0.40 ((~(f(tptp_fun_Y_3(g(X!1))) = f(g(f(tptp_fun_Y_3(g(X!1))))))) | (X!1 = f(tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.19/0.40 tff(159,plain,
% 0.19/0.40 (X!1 = f(tptp_fun_Y_3(g(X!1)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[158, 152])).
% 0.19/0.40 tff(160,plain,
% 0.19/0.40 (g(X!1) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.40 tff(161,plain,
% 0.19/0.40 (g(X!1) = tptp_fun_Y_3(g(X!1))),
% 0.19/0.40 inference(transitivity,[status(thm)],[160, 150])).
% 0.19/0.40 tff(162,plain,
% 0.19/0.40 (((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (g(X!1) = tptp_fun_Y_3(g(X!1)))) | (~(g(X!1) = tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(163,plain,
% 0.19/0.40 (~(g(X!1) = tptp_fun_Y_3(g(X!1)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[162, 147])).
% 0.19/0.40 tff(164,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[163, 161])).
% 0.19/0.40 tff(165,plain,((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (g(X!1) = tptp_fun_Y_3(g(X!1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(166,plain,
% 0.19/0.40 (tptp_fun_Y_3(g(X!1)) = tptp_fun_Y_3(g(f(g(X!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[136])).
% 0.19/0.40 tff(167,plain,
% 0.19/0.40 (tptp_fun_Y_3(g(f(g(X!1)))) = tptp_fun_Y_3(g(X!1))),
% 0.19/0.40 inference(symmetry,[status(thm)],[166])).
% 0.19/0.40 tff(168,plain,
% 0.19/0.40 ((g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1))))) <=> (g(X!1) = tptp_fun_Y_3(g(X!1)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[137, 167])).
% 0.19/0.40 tff(169,plain,
% 0.19/0.40 ((~(g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1)))))) <=> (~(g(X!1) = tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.40 tff(170,assumption,(~((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1))))))), introduced(assumption)).
% 0.19/0.40 tff(171,plain,
% 0.19/0.40 (((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(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))) = tptp_fun_Y_3(g(f(g(X!1))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(172,plain,
% 0.19/0.40 (~(g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.19/0.40 tff(173,plain,
% 0.19/0.40 (~(g(X!1) = tptp_fun_Y_3(g(X!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[172, 169])).
% 0.19/0.40 tff(174,plain,
% 0.19/0.40 (f(tptp_fun_Y_3(g(f(g(X!1))))) = f(tptp_fun_Y_3(g(X!1)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.40 tff(175,plain,
% 0.19/0.40 (g(f(tptp_fun_Y_3(g(f(g(X!1)))))) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.40 tff(176,plain,
% 0.19/0.40 ((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)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[167, 175])).
% 0.19/0.40 tff(177,plain,
% 0.19/0.40 (((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (g(f(g(X!1))) = tptp_fun_Y_3(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)))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(178,plain,
% 0.19/0.40 (tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[177, 170])).
% 0.19/0.40 tff(179,plain,
% 0.19/0.40 (tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[178, 176])).
% 0.19/0.40 tff(180,plain,
% 0.19/0.40 ((~((~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (g(X!1) = tptp_fun_Y_3(g(X!1))))) | (~(tptp_fun_Y_3(g(X!1)) = g(f(tptp_fun_Y_3(g(X!1)))))) | (g(X!1) = tptp_fun_Y_3(g(X!1)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(181,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[180, 179, 173, 165])).
% 0.19/0.40 tff(182,plain,((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(183,assumption,(![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))), introduced(assumption)).
% 0.19/0.40 tff(184,plain,
% 0.19/0.40 (((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(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)))))))) | (g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1))))))))) <=> ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(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)))))))) | (g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(185,plain,
% 0.19/0.40 ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(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)))))))) | (g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(186,plain,
% 0.19/0.40 ((~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))) | (~(g(f(g(X!1))) = g(f(g(f(g(X!1))))))) | (~((~(tptp_fun_Y_3(g(f(g(X!1)))) = g(f(tptp_fun_Y_3(g(f(g(X!1)))))))) | (g(f(g(X!1))) = tptp_fun_Y_3(g(f(g(X!1)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.40 tff(187,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[186, 183, 182, 146])).
% 0.19/0.40 tff(188,plain,(~![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (X = tptp_fun_Y_3(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(189,plain,
% 0.19/0.40 (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(X)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 188])).
% 0.19/0.40 tff(190,plain,
% 0.19/0.40 (((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(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))))))) | (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1)))))))) <=> ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(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))))))) | (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(191,plain,
% 0.19/0.40 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(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))))))) | (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(192,plain,
% 0.19/0.40 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_0(X) = f(g(tptp_fun_Y_0(X))))) | (X = tptp_fun_Y_0(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))))))) | (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.40 tff(193,plain,
% 0.19/0.40 (~((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[192, 189, 139])).
% 0.19/0.40 tff(194,plain,
% 0.19/0.40 (((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1))))) | (tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(195,plain,
% 0.19/0.40 (tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.19/0.40 tff(196,plain,
% 0.19/0.40 (f(g(tptp_fun_Y_0(f(g(X!1))))) = tptp_fun_Y_0(f(g(X!1)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[195])).
% 0.19/0.40 tff(197,plain,
% 0.19/0.40 ((X!1 = f(g(tptp_fun_Y_0(f(g(X!1)))))) <=> (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[130, 196])).
% 0.19/0.40 tff(198,plain,
% 0.19/0.40 ((f(g(X!1)) = tptp_fun_Y_0(f(g(X!1)))) <=> (X!1 = f(g(tptp_fun_Y_0(f(g(X!1))))))),
% 0.19/0.40 inference(symmetry,[status(thm)],[197])).
% 0.19/0.40 tff(199,plain,
% 0.19/0.40 ((~(f(g(X!1)) = tptp_fun_Y_0(f(g(X!1))))) <=> (~(X!1 = f(g(tptp_fun_Y_0(f(g(X!1)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.40 tff(200,plain,
% 0.19/0.40 (((~(tptp_fun_Y_0(f(g(X!1))) = f(g(tptp_fun_Y_0(f(g(X!1))))))) | (f(g(X!1)) = tptp_fun_Y_0(f(g(X!1))))) | (~(f(g(X!1)) = tptp_fun_Y_0(f(g(X!1)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(201,plain,
% 0.19/0.41 (~(f(g(X!1)) = tptp_fun_Y_0(f(g(X!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[200, 193])).
% 0.19/0.41 tff(202,plain,
% 0.19/0.41 (~(X!1 = f(g(tptp_fun_Y_0(f(g(X!1))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[201, 199])).
% 0.19/0.41 tff(203,plain,
% 0.19/0.41 (g(f(g(tptp_fun_Y_0(f(g(X!1)))))) = g(tptp_fun_Y_0(f(g(X!1))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[196])).
% 0.19/0.41 tff(204,plain,
% 0.19/0.41 (f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))) = f(g(tptp_fun_Y_0(f(g(X!1)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[203])).
% 0.19/0.41 tff(205,plain,
% 0.19/0.41 (f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1)))))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[204])).
% 0.19/0.41 tff(206,plain,
% 0.19/0.41 (((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (X!1 = f(g(tptp_fun_Y_0(f(g(X!1)))))))) <=> ((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | (~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (X!1 = f(g(tptp_fun_Y_0(f(g(X!1)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(207,plain,
% 0.19/0.41 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | ((~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (X!1 = f(g(tptp_fun_Y_0(f(g(X!1)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(208,plain,
% 0.19/0.41 ((~![Y: $i] : ((~(Y = f(g(Y)))) | (X!1 = Y))) | (~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (X!1 = f(g(tptp_fun_Y_0(f(g(X!1))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.41 tff(209,plain,
% 0.19/0.41 ((~(f(g(tptp_fun_Y_0(f(g(X!1))))) = f(g(f(g(tptp_fun_Y_0(f(g(X!1))))))))) | (X!1 = f(g(tptp_fun_Y_0(f(g(X!1))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[208, 154])).
% 0.19/0.41 tff(210,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[209, 205, 202])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------