TSTP Solution File: SYN015-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 23:53:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 01:04:26 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.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(element_type, type, (
% 0.20/0.41 element: ( $i * $i ) > $o)).
% 0.20/0.41 tff(j_type, type, (
% 0.20/0.41 j: $i)).
% 0.20/0.41 tff(m_type, type, (
% 0.20/0.41 m: $i)).
% 0.20/0.41 tff(k_type, type, (
% 0.20/0.41 k: $i)).
% 0.20/0.41 tff(n_type, type, (
% 0.20/0.41 n: $i)).
% 0.20/0.41 tff(g_type, type, (
% 0.20/0.41 g: $i > $i)).
% 0.20/0.41 tff(f_type, type, (
% 0.20/0.41 f: $i > $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 ((n = k) <=> (k = n)),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((k = n) <=> (n = k)),
% 0.20/0.41 inference(symmetry,[status(thm)],[1])).
% 0.20/0.41 tff(3,assumption,(~(n = k)), introduced(assumption)).
% 0.20/0.41 tff(4,assumption,(~(k = n)), introduced(assumption)).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (^[Y: $i] : refl(((Y = k) | element(Y, k) | (~(Y = n))) <=> ((Y = k) | element(Y, k) | (~(Y = n))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (^[Y: $i] : trans(monotonicity(rewrite(((Y = k) | (~(Y = n))) <=> ((Y = k) | (~(Y = n)))), ((((Y = k) | (~(Y = n))) | element(Y, k)) <=> (((Y = k) | (~(Y = n))) | element(Y, k)))), rewrite((((Y = k) | (~(Y = n))) | element(Y, k)) <=> ((Y = k) | element(Y, k) | (~(Y = n)))), ((((Y = k) | (~(Y = n))) | element(Y, k)) <=> ((Y = k) | element(Y, k) | (~(Y = n)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.41 tff(10,axiom,(![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_15')).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.41 tff(13,plain,(
% 0.20/0.41 ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | ((n = k) | element(n, k))) <=> ((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | (n = k) | element(n, k))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (((n = k) | element(n, k) | $false) <=> ((n = k) | element(n, k))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 ((~$true) <=> $false),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 ((n = n) <=> $true),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 ((~(n = n)) <=> (~$true)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~(n = n)) <=> $false),
% 0.20/0.41 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (((n = k) | element(n, k) | (~(n = n))) <=> ((n = k) | element(n, k) | $false)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (((n = k) | element(n, k) | (~(n = n))) <=> ((n = k) | element(n, k))),
% 0.20/0.41 inference(transitivity,[status(thm)],[21, 16])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | ((n = k) | element(n, k) | (~(n = n)))) <=> ((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | ((n = k) | element(n, k)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | ((n = k) | element(n, k) | (~(n = n)))) <=> ((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | (n = k) | element(n, k))),
% 0.20/0.41 inference(transitivity,[status(thm)],[23, 15])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | ((n = k) | element(n, k) | (~(n = n)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | (n = k) | element(n, k)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((n = k) | element(n, k)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 14])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (element(n, k)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 3])).
% 0.20/0.41 tff(29,assumption,(k = m), introduced(assumption)).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (element(f(n), k) <=> element(f(n), m)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (element(f(n), m) <=> element(f(n), k)),
% 0.20/0.41 inference(symmetry,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((n = f(n)) <=> (f(n) = n)),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((f(n) = n) <=> (n = f(n))),
% 0.20/0.41 inference(symmetry,[status(thm)],[32])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~(f(n) = n)) <=> (~(n = f(n)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 ((n = m) <=> (m = n)),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((m = n) <=> (n = m)),
% 0.20/0.41 inference(symmetry,[status(thm)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~(m = n)) <=> (~(n = m))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~(m = n)) <=> (~(m = n))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(39,axiom,(~(m = n)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_1')).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (~(m = n)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (~(n = m)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (element(n, k) <=> element(n, m)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.41 tff(43,assumption,(element(n, k)), introduced(assumption)).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (element(n, m)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[Y: $i] : trans(monotonicity(rewrite(((Y = m) | (~element(Y, m))) <=> ((~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> (((~element(Y, m)) | (Y = m)) | (~(f(Y) = Y))))), rewrite((((~element(Y, m)) | (Y = m)) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_5')).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.41 tff(53,plain,(
% 0.20/0.41 ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((n = m) | (~element(n, m)) | (~(f(n) = n)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (n = m) | (~element(n, m)) | (~(f(n) = n)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (((~element(n, m)) | (n = m) | (~(f(n) = n))) <=> ((n = m) | (~element(n, m)) | (~(f(n) = n)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(n, m)) | (n = m) | (~(f(n) = n)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((n = m) | (~element(n, m)) | (~(f(n) = n))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(n, m)) | (n = m) | (~(f(n) = n)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (n = m) | (~element(n, m)) | (~(f(n) = n)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(n, m)) | (n = m) | (~(f(n) = n)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (n = m) | (~element(n, m)) | (~(f(n) = n))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (~(f(n) = n)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 54, 44, 41])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (~(n = f(n))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 34])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (^[Y: $i] : refl(((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (^[Y: $i] : trans(monotonicity(rewrite(((Y = m) | (~element(Y, m))) <=> ((~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> (((~element(Y, m)) | (Y = m)) | (~(f(Y) = m))))), rewrite((((~element(Y, m)) | (Y = m)) | (~(f(Y) = m))) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.41 tff(68,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_4')).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.41 tff(71,plain,(
% 0.20/0.41 ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.41 inference(skolemize,[status(sab)],[70])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((n = m) | (~element(n, m)) | (~(f(n) = m)))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | (~(f(n) = m)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (((~(f(n) = m)) | (~element(n, m)) | (n = m)) <=> ((n = m) | (~element(n, m)) | (~(f(n) = m)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((n = m) | (~element(n, m)) | (~(f(n) = m))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | (~(f(n) = m)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | (~(f(n) = m))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (~(f(n) = m)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[78, 72, 44, 41])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (^[Y: $i] : refl((element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (^[Y: $i] : trans(monotonicity(rewrite(((Y = m) | (~element(Y, m))) <=> ((~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | element(Y, f(Y))) <=> (((~element(Y, m)) | (Y = m)) | element(Y, f(Y))))), rewrite((((~element(Y, m)) | (Y = m)) | element(Y, f(Y))) <=> (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | element(Y, f(Y))) <=> (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y))) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.42 tff(85,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_6')).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.42 tff(88,plain,(
% 0.20/0.42 ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.42 inference(skolemize,[status(sab)],[87])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((n = m) | (~element(n, m)) | element(n, f(n)))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | element(n, f(n)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ((element(n, f(n)) | (~element(n, m)) | (n = m)) <=> ((n = m) | (~element(n, m)) | element(n, f(n)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((n = m) | (~element(n, m)) | element(n, f(n))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | element(n, f(n)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | element(n, f(n))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (element(n, f(n))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[95, 89, 44, 41])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ((~element(Y, m)) | (Y = m) | element(f(Y), Y)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (^[Y: $i] : trans(monotonicity(rewrite(((Y = m) | (~element(Y, m))) <=> ((~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | element(f(Y), Y)) <=> (((~element(Y, m)) | (Y = m)) | element(f(Y), Y)))), rewrite((((~element(Y, m)) | (Y = m)) | element(f(Y), Y)) <=> ((~element(Y, m)) | (Y = m) | element(f(Y), Y))), ((((Y = m) | (~element(Y, m))) | element(f(Y), Y)) <=> ((~element(Y, m)) | (Y = m) | element(f(Y), Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.42 tff(102,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_7')).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.42 tff(105,plain,(
% 0.20/0.42 ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.42 inference(skolemize,[status(sab)],[104])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(n, m)) | (n = m) | element(f(n), n))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(n, m)) | (n = m) | element(f(n), n))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(n, m)) | (n = m) | element(f(n), n))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(n, m)) | (n = m) | element(f(n), n)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (element(f(n), n)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[109, 106, 44, 41])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (^[Y: $i, V1: $i] : refl(((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) <=> ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) <=> ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) <=> ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (^[Y: $i, V1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((Y = m) | element(Y, m)) | (V1 = m)) <=> ((V1 = m) | element(Y, m) | (Y = m))), (((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) <=> (((V1 = m) | element(Y, m) | (Y = m)) | (V1 = Y)))), rewrite((((V1 = m) | element(Y, m) | (Y = m)) | (V1 = Y)) <=> ((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m))), (((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) <=> ((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m)))), ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) <=> (((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(Y, V1))))), rewrite((((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(Y, V1))) <=> ((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))), ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) <=> ((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)))), (((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y))) <=> (((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(V1, Y))))), rewrite((((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(V1, Y))) <=> ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))), (((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y))) <=> ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (![Y: $i, V1: $i] : ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y))) <=> ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.43 tff(116,axiom,(![Y: $i, V1: $i] : ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_8')).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.43 tff(119,plain,(
% 0.20/0.43 ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.43 inference(skolemize,[status(sab)],[118])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (f(n) = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = m) | (f(n) = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (((n = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m) | (f(n) = m)) <=> ((n = m) | (f(n) = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m) | (f(n) = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (f(n) = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m) | (f(n) = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = m) | (f(n) = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m))),
% 0.20/0.43 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m) | (f(n) = m))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = m) | (f(n) = m) | (~element(n, f(n))) | (~element(f(n), n)) | (n = f(n)) | element(f(n), m)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ((n = f(n)) | element(f(n), m)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[126, 120, 41, 110, 96, 79])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (element(f(n), m)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[127, 62])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (element(f(n), k)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[128, 31])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 ((f(n) = k) <=> (f(n) = m)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 ((f(n) = m) <=> (f(n) = k)),
% 0.20/0.43 inference(symmetry,[status(thm)],[130])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 ((~(f(n) = m)) <=> (~(f(n) = k))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (~(f(n) = k)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 132])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (^[Y: $i] : refl(((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (^[Y: $i] : trans(monotonicity(rewrite((((Y = k) | (Y = m)) | (Y = n)) <=> ((Y = k) | (Y = m) | (Y = n))), (((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> (((Y = k) | (Y = m) | (Y = n)) | (~element(Y, k))))), rewrite((((Y = k) | (Y = m) | (Y = n)) | (~element(Y, k))) <=> ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))), (((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.43 tff(139,axiom,(![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_16')).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.43 tff(142,plain,(
% 0.20/0.43 ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[141])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((~element(f(n), k)) | (f(n) = k) | (f(n) = m) | (f(n) = n))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (~element(f(n), k)) | (f(n) = k) | (f(n) = m) | (f(n) = n))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k))) <=> ((~element(f(n), k)) | (f(n) = k) | (f(n) = m) | (f(n) = n))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((~element(f(n), k)) | (f(n) = k) | (f(n) = m) | (f(n) = n)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (~element(f(n), k)) | (f(n) = k) | (f(n) = m) | (f(n) = n))),
% 0.20/0.43 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (~element(f(n), k)) | (f(n) = k) | (f(n) = m) | (f(n) = n)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 ((~element(f(n), k)) | (f(n) = k)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[149, 143, 79, 61])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[150, 133, 129])).
% 0.20/0.44 tff(152,plain,((~(k = m)) | (~element(n, k))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (~(k = m)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[152, 28])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((m = k) <=> (k = m)),
% 0.20/0.44 inference(commutativity,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((k = m) <=> (m = k)),
% 0.20/0.44 inference(symmetry,[status(thm)],[154])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 ((~(k = m)) <=> (~(m = k))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.44 tff(157,assumption,(~(k = m)), introduced(assumption)).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (~(m = k)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.44 tff(159,assumption,(element(k, n)), introduced(assumption)).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = k) | (k = m) | (~element(k, n)) | (~element(n, k)) | (n = m) | element(k, m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = k) | (k = m) | (~element(k, n)) | (~element(n, k)) | (n = m) | element(k, m))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m)) <=> ((n = k) | (k = m) | (~element(k, n)) | (~element(n, k)) | (n = m) | element(k, m))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = k) | (k = m) | (~element(k, n)) | (~element(n, k)) | (n = m) | element(k, m)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = k) | (k = m) | (~element(k, n)) | (~element(n, k)) | (n = m) | element(k, m))),
% 0.20/0.44 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = k) | (k = m) | (~element(k, n)) | (~element(n, k)) | (n = m) | element(k, m)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 ((k = m) | (~element(k, n)) | (n = m) | element(k, m)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[165, 120, 3, 28])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (element(k, m)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[166, 157, 41, 159])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 (^[V: $i, Y: $i] : refl(((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Y = n) | (~element(Y, n))) <=> ((Y = n) | (~element(Y, n)))), ((((Y = n) | (~element(Y, n))) | (V = n)) <=> (((Y = n) | (~element(Y, n))) | (V = n)))), rewrite((((Y = n) | (~element(Y, n))) | (V = n)) <=> ((Y = n) | (V = n) | (~element(Y, n)))), ((((Y = n) | (~element(Y, n))) | (V = n)) <=> ((Y = n) | (V = n) | (~element(Y, n))))), (((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) <=> (((Y = n) | (V = n) | (~element(Y, n))) | (V = Y)))), rewrite((((Y = n) | (V = n) | (~element(Y, n))) | (V = Y)) <=> ((Y = n) | (V = Y) | (V = n) | (~element(Y, n)))), (((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) <=> ((Y = n) | (V = Y) | (V = n) | (~element(Y, n))))), ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) <=> (((Y = n) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(Y, V))))), rewrite((((Y = n) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(Y, V))) <=> ((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))), ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) <=> ((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))))), (((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> (((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(V, Y))))), rewrite((((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(V, Y))) <=> ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))), (((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 (![V: $i, Y: $i] : ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.44 tff(173,axiom,(![V: $i, Y: $i] : ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_13')).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.20/0.44 tff(176,plain,(
% 0.20/0.44 ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[175])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 (((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((m = n) | (k = n) | (~element(k, n)) | (~element(m, k)) | (~element(k, m)) | (m = k))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (k = n) | (~element(k, n)) | (~element(m, k)) | (~element(k, m)) | (m = k))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 (((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n))) <=> ((m = n) | (k = n) | (~element(k, n)) | (~element(m, k)) | (~element(k, m)) | (m = k))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 (((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((m = n) | (k = n) | (~element(k, n)) | (~element(m, k)) | (~element(k, m)) | (m = k)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 (((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (k = n) | (~element(k, n)) | (~element(m, k)) | (~element(k, m)) | (m = k))),
% 0.20/0.44 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.44 tff(182,plain,
% 0.20/0.44 ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(183,plain,
% 0.20/0.44 ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (k = n) | (~element(k, n)) | (~element(m, k)) | (~element(k, m)) | (m = k)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.44 tff(184,plain,
% 0.20/0.44 ((~element(m, k)) | (m = k)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[183, 40, 177, 159, 4, 167])).
% 0.20/0.44 tff(185,plain,
% 0.20/0.44 (~element(m, k)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[184, 158])).
% 0.20/0.44 tff(186,plain,
% 0.20/0.44 (^[Y: $i] : refl(((Y = k) | (~(Y = m)) | element(Y, k)) <=> ((Y = k) | (~(Y = m)) | element(Y, k)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(187,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.44 tff(188,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(189,plain,
% 0.20/0.44 (^[Y: $i] : trans(monotonicity(rewrite(((Y = k) | (~(Y = m))) <=> ((Y = k) | (~(Y = m)))), ((((Y = k) | (~(Y = m))) | element(Y, k)) <=> (((Y = k) | (~(Y = m))) | element(Y, k)))), rewrite((((Y = k) | (~(Y = m))) | element(Y, k)) <=> ((Y = k) | (~(Y = m)) | element(Y, k))), ((((Y = k) | (~(Y = m))) | element(Y, k)) <=> ((Y = k) | (~(Y = m)) | element(Y, k))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(190,plain,
% 0.20/0.44 (![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.44 tff(191,axiom,(![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_14')).
% 0.20/0.44 tff(192,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.44 tff(193,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.44 tff(194,plain,(
% 0.20/0.44 ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.20/0.44 inference(skolemize,[status(sab)],[193])).
% 0.20/0.44 tff(195,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.44 tff(196,plain,
% 0.20/0.44 (((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | (element(m, k) | (m = k))) <=> ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | element(m, k) | (m = k))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(197,plain,
% 0.20/0.44 (((m = k) | $false | element(m, k)) <=> (element(m, k) | (m = k))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(198,plain,
% 0.20/0.44 ((m = m) <=> $true),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(199,plain,
% 0.20/0.44 ((~(m = m)) <=> (~$true)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[198])).
% 0.20/0.44 tff(200,plain,
% 0.20/0.44 ((~(m = m)) <=> $false),
% 0.20/0.44 inference(transitivity,[status(thm)],[199, 17])).
% 0.20/0.44 tff(201,plain,
% 0.20/0.44 (((m = k) | (~(m = m)) | element(m, k)) <=> ((m = k) | $false | element(m, k))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[200])).
% 0.20/0.44 tff(202,plain,
% 0.20/0.44 (((m = k) | (~(m = m)) | element(m, k)) <=> (element(m, k) | (m = k))),
% 0.20/0.44 inference(transitivity,[status(thm)],[201, 197])).
% 0.20/0.45 tff(203,plain,
% 0.20/0.45 (((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | ((m = k) | (~(m = m)) | element(m, k))) <=> ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | (element(m, k) | (m = k)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 (((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | ((m = k) | (~(m = m)) | element(m, k))) <=> ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | element(m, k) | (m = k))),
% 0.20/0.45 inference(transitivity,[status(thm)],[203, 196])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | ((m = k) | (~(m = m)) | element(m, k))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | element(m, k) | (m = k)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[206, 195, 185, 158])).
% 0.20/0.45 tff(208,plain,((k = m) | (~element(k, n)) | (k = n) | (n = k)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(209,plain,
% 0.20/0.45 (~element(k, n)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[208, 4, 3, 153])).
% 0.20/0.45 tff(210,plain,
% 0.20/0.45 (^[Y: $i] : refl(((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(211,plain,
% 0.20/0.45 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[210])).
% 0.20/0.45 tff(212,plain,
% 0.20/0.45 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(213,plain,
% 0.20/0.45 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(214,plain,
% 0.20/0.45 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.45 tff(215,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_9')).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.45 tff(217,plain,
% 0.20/0.45 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.20/0.45 tff(218,plain,(
% 0.20/0.45 ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.45 inference(skolemize,[status(sab)],[217])).
% 0.20/0.45 tff(219,plain,
% 0.20/0.45 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[218, 211])).
% 0.20/0.45 tff(220,plain,
% 0.20/0.45 (((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(k) = n)) | (k = n) | element(k, n))) <=> ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(k) = n)) | (k = n) | element(k, n))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(221,plain,
% 0.20/0.45 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(k) = n)) | (k = n) | element(k, n))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(222,plain,
% 0.20/0.45 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(k) = n)) | (k = n) | element(k, n)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.20/0.45 tff(223,plain,
% 0.20/0.45 ((~(g(k) = n)) | (k = n) | element(k, n)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[222, 219])).
% 0.20/0.45 tff(224,plain,
% 0.20/0.45 (~(g(k) = n)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[223, 209, 4])).
% 0.20/0.45 tff(225,plain,
% 0.20/0.45 (^[Y: $i] : refl(((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(226,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[225])).
% 0.20/0.45 tff(227,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(228,plain,
% 0.20/0.45 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(229,plain,
% 0.20/0.45 (![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[228])).
% 0.20/0.45 tff(230,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_12')).
% 0.20/0.45 tff(231,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.45 tff(232,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.20/0.45 tff(233,plain,(
% 0.20/0.45 ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.45 inference(skolemize,[status(sab)],[232])).
% 0.20/0.45 tff(234,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.20/0.45 tff(235,plain,
% 0.20/0.45 (((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((k = n) | element(k, n) | element(g(k), k))) <=> ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (k = n) | element(k, n) | element(g(k), k))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(236,plain,
% 0.20/0.45 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((k = n) | element(k, n) | element(g(k), k))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(237,plain,
% 0.20/0.45 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (k = n) | element(k, n) | element(g(k), k)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.45 tff(238,plain,
% 0.20/0.45 ((k = n) | element(k, n) | element(g(k), k)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[237, 234])).
% 0.20/0.45 tff(239,plain,
% 0.20/0.45 (element(g(k), k)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[238, 209, 4])).
% 0.20/0.45 tff(240,plain,
% 0.20/0.45 (^[Y: $i] : refl(((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(241,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[240])).
% 0.20/0.45 tff(242,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(243,plain,
% 0.20/0.45 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(244,plain,
% 0.20/0.45 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[243])).
% 0.20/0.45 tff(245,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_10')).
% 0.20/0.45 tff(246,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.45 tff(247,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.20/0.45 tff(248,plain,(
% 0.20/0.45 ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[247])).
% 0.20/0.45 tff(249,plain,
% 0.20/0.45 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.20/0.45 tff(250,plain,
% 0.20/0.45 (((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((~(g(k) = k)) | element(k, n) | (k = n))) <=> ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (~(g(k) = k)) | element(k, n) | (k = n))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(251,plain,
% 0.20/0.45 (((k = n) | element(k, n) | (~(g(k) = k))) <=> ((~(g(k) = k)) | element(k, n) | (k = n))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(252,plain,
% 0.20/0.45 (((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((k = n) | element(k, n) | (~(g(k) = k)))) <=> ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((~(g(k) = k)) | element(k, n) | (k = n)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[251])).
% 0.20/0.45 tff(253,plain,
% 0.20/0.45 (((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((k = n) | element(k, n) | (~(g(k) = k)))) <=> ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (~(g(k) = k)) | element(k, n) | (k = n))),
% 0.20/0.46 inference(transitivity,[status(thm)],[252, 250])).
% 0.20/0.46 tff(254,plain,
% 0.20/0.46 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((k = n) | element(k, n) | (~(g(k) = k)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(255,plain,
% 0.20/0.46 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (~(g(k) = k)) | element(k, n) | (k = n)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.20/0.46 tff(256,plain,
% 0.20/0.46 ((~(g(k) = k)) | element(k, n) | (k = n)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[255, 249])).
% 0.20/0.46 tff(257,plain,
% 0.20/0.46 (~(g(k) = k)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[256, 209, 4])).
% 0.20/0.46 tff(258,plain,
% 0.20/0.46 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = n) | (~element(g(k), k)) | (g(k) = m))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (g(k) = k) | (g(k) = n) | (~element(g(k), k)) | (g(k) = m))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(259,plain,
% 0.20/0.46 (((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k))) <=> ((g(k) = k) | (g(k) = n) | (~element(g(k), k)) | (g(k) = m))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(260,plain,
% 0.20/0.46 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = n) | (~element(g(k), k)) | (g(k) = m)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[259])).
% 0.20/0.46 tff(261,plain,
% 0.20/0.46 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (g(k) = k) | (g(k) = n) | (~element(g(k), k)) | (g(k) = m))),
% 0.20/0.46 inference(transitivity,[status(thm)],[260, 258])).
% 0.20/0.46 tff(262,plain,
% 0.20/0.46 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k)))),
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% 0.20/0.46 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (g(k) = k) | (g(k) = n) | (~element(g(k), k)) | (g(k) = m)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[262, 261])).
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% 0.20/0.46 inference(unit_resolution,[status(thm)],[263, 143, 257, 239, 224])).
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% 0.20/0.46 (element(k, g(k)) <=> element(k, m)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[264])).
% 0.20/0.46 tff(266,assumption,(~element(k, g(k))), introduced(assumption)).
% 0.20/0.46 tff(267,plain,
% 0.20/0.46 (^[Y: $i] : refl((element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> (element(Y, g(Y)) | (Y = n) | element(Y, n)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(268,plain,
% 0.20/0.46 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[267])).
% 0.20/0.46 tff(269,plain,
% 0.20/0.46 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
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% 0.20/0.46 inference(bind,[status(th)],[])).
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% 0.20/0.46 tff(272,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(Y, g(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_11')).
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
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% 0.20/0.46 inference(monotonicity,[status(thm)],[278])).
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
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% 0.20/0.46 inference(transitivity,[status(thm)],[302, 300])).
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% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(355,plain,
% 0.20/0.47 (![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j)) <=> ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[354])).
% 0.20/0.47 tff(356,axiom,(![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_2')).
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% 0.20/0.47 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.20/0.47 tff(358,plain,
% 0.20/0.47 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[357, 353])).
% 0.20/0.47 tff(359,plain,(
% 0.20/0.47 ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.47 inference(skolemize,[status(sab)],[358])).
% 0.20/0.47 tff(360,plain,
% 0.20/0.47 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[359, 352])).
% 0.20/0.47 tff(361,plain,
% 0.20/0.47 (((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | ((k = j) | element(k, j))) <=> ((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (k = j) | element(k, j))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(362,plain,
% 0.20/0.47 ((element(k, j) | $false | (k = j)) <=> ((k = j) | element(k, j))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(363,plain,
% 0.20/0.47 ((k = k) <=> $true),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(364,plain,
% 0.20/0.47 ((~(k = k)) <=> (~$true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.47 tff(365,plain,
% 0.20/0.47 ((~(k = k)) <=> $false),
% 0.20/0.47 inference(transitivity,[status(thm)],[364, 17])).
% 0.20/0.47 tff(366,plain,
% 0.20/0.47 ((element(k, j) | (~(k = k)) | (k = j)) <=> (element(k, j) | $false | (k = j))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[365])).
% 0.20/0.47 tff(367,plain,
% 0.20/0.47 ((element(k, j) | (~(k = k)) | (k = j)) <=> ((k = j) | element(k, j))),
% 0.20/0.47 inference(transitivity,[status(thm)],[366, 362])).
% 0.20/0.47 tff(368,plain,
% 0.20/0.47 (((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (element(k, j) | (~(k = k)) | (k = j))) <=> ((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | ((k = j) | element(k, j)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.47 tff(369,plain,
% 0.20/0.47 (((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (element(k, j) | (~(k = k)) | (k = j))) <=> ((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (k = j) | element(k, j))),
% 0.20/0.47 inference(transitivity,[status(thm)],[368, 361])).
% 0.20/0.47 tff(370,plain,
% 0.20/0.47 ((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (element(k, j) | (~(k = k)) | (k = j))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(371,plain,
% 0.20/0.47 ((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (k = j) | element(k, j)),
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% 0.20/0.47 tff(372,plain,
% 0.20/0.47 ((k = j) | element(k, j)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[371, 360])).
% 0.20/0.47 tff(373,plain,
% 0.20/0.47 (element(k, j)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[372, 341])).
% 0.20/0.47 tff(374,assumption,(j = m), introduced(assumption)).
% 0.20/0.47 tff(375,plain,
% 0.20/0.47 (element(k, j) <=> element(k, m)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[374])).
% 0.20/0.47 tff(376,plain,
% 0.20/0.47 (element(k, m) <=> element(k, j)),
% 0.20/0.47 inference(symmetry,[status(thm)],[375])).
% 0.20/0.47 tff(377,plain,
% 0.20/0.47 ((~element(k, m)) <=> (~element(k, j))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[376])).
% 0.20/0.47 tff(378,assumption,(element(k, m)), introduced(assumption)).
% 0.20/0.47 tff(379,plain,
% 0.20/0.47 ((m = n) <=> (m = k)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[334])).
% 0.20/0.47 tff(380,plain,
% 0.20/0.47 ((m = n) <=> (k = m)),
% 0.20/0.47 inference(transitivity,[status(thm)],[379, 154])).
% 0.20/0.47 tff(381,plain,
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% 0.20/0.47 tff(382,plain,
% 0.20/0.47 (~(k = m)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[40, 381])).
% 0.20/0.47 tff(383,plain,
% 0.20/0.47 (~(f(k) = k)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[298, 54, 382, 378])).
% 0.20/0.47 tff(384,plain,
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% 0.20/0.47 inference(unit_resolution,[status(thm)],[305, 72, 382, 378])).
% 0.20/0.47 tff(385,plain,
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% 0.20/0.47 inference(unit_resolution,[status(thm)],[309, 106, 382, 378])).
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% 0.20/0.47 inference(unit_resolution,[status(thm)],[316, 143, 385, 384, 383])).
% 0.20/0.47 tff(387,plain,
% 0.20/0.47 (f(k) = k),
% 0.20/0.47 inference(transitivity,[status(thm)],[386, 334])).
% 0.20/0.47 tff(388,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[383, 387])).
% 0.20/0.47 tff(389,plain,(~element(k, m)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(390,plain,
% 0.20/0.47 (~element(k, j)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[389, 377])).
% 0.20/0.47 tff(391,assumption,(element(k, j)), introduced(assumption)).
% 0.20/0.47 tff(392,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.20/0.47 tff(393,plain,((~(j = m)) | (~element(k, j))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(394,plain,
% 0.20/0.47 (~(j = m)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[393, 373])).
% 0.20/0.47 tff(395,plain,
% 0.20/0.47 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((k = m) | element(k, m) | (~element(k, j)) | (~element(j, k)) | (j = m) | (j = k))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (k = m) | element(k, m) | (~element(k, j)) | (~element(j, k)) | (j = m) | (j = k))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(396,plain,
% 0.20/0.47 (((j = m) | (~element(j, k)) | (~element(k, j)) | (j = k) | element(k, m) | (k = m)) <=> ((k = m) | element(k, m) | (~element(k, j)) | (~element(j, k)) | (j = m) | (j = k))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(397,plain,
% 0.20/0.47 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((j = m) | (~element(j, k)) | (~element(k, j)) | (j = k) | element(k, m) | (k = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((k = m) | element(k, m) | (~element(k, j)) | (~element(j, k)) | (j = m) | (j = k)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[396])).
% 0.20/0.47 tff(398,plain,
% 0.20/0.47 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((j = m) | (~element(j, k)) | (~element(k, j)) | (j = k) | element(k, m) | (k = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (k = m) | element(k, m) | (~element(k, j)) | (~element(j, k)) | (j = m) | (j = k))),
% 0.20/0.47 inference(transitivity,[status(thm)],[397, 395])).
% 0.20/0.47 tff(399,plain,
% 0.20/0.47 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((j = m) | (~element(j, k)) | (~element(k, j)) | (j = k) | element(k, m) | (k = m))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(400,plain,
% 0.20/0.47 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (k = m) | element(k, m) | (~element(k, j)) | (~element(j, k)) | (j = m) | (j = k)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.20/0.47 tff(401,plain,
% 0.20/0.47 ((~element(j, k)) | (j = m) | (j = k)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[400, 120, 382, 373, 389])).
% 0.20/0.47 tff(402,plain,
% 0.20/0.47 (~element(j, k)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[401, 394, 350])).
% 0.20/0.47 tff(403,plain,
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% 0.20/0.47 inference(modus_ponens,[status(thm)],[402, 345])).
% 0.20/0.47 tff(404,plain,
% 0.20/0.47 (((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((j = n) | element(j, n) | (~(g(j) = j)))) <=> ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (j = n) | element(j, n) | (~(g(j) = j)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(405,plain,
% 0.20/0.47 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((j = n) | element(j, n) | (~(g(j) = j)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(406,plain,
% 0.20/0.47 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (j = n) | element(j, n) | (~(g(j) = j))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.20/0.47 tff(407,plain,
% 0.20/0.47 ((j = n) | element(j, n) | (~(g(j) = j))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[406, 249])).
% 0.20/0.48 tff(408,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[407, 403, 342])).
% 0.20/0.48 tff(409,plain,
% 0.20/0.48 (((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((j = n) | element(j, n) | element(g(j), j))) <=> ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (j = n) | element(j, n) | element(g(j), j))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(410,plain,
% 0.20/0.48 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((j = n) | element(j, n) | element(g(j), j))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(411,plain,
% 0.20/0.48 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (j = n) | element(j, n) | element(g(j), j)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.20/0.48 tff(412,plain,
% 0.20/0.48 ((j = n) | element(j, n) | element(g(j), j)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[411, 234])).
% 0.20/0.48 tff(413,plain,
% 0.20/0.48 (element(g(j), j)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[412, 403, 342])).
% 0.20/0.48 tff(414,plain,
% 0.20/0.48 (^[Y: $i] : refl(((Y = k) | (Y = j) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(415,plain,
% 0.20/0.48 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[414])).
% 0.20/0.48 tff(416,plain,
% 0.20/0.48 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(417,plain,
% 0.20/0.48 (^[Y: $i] : rewrite((((Y = j) | (Y = k)) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(418,plain,
% 0.20/0.48 (![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[417])).
% 0.20/0.48 tff(419,axiom,(![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_3')).
% 0.20/0.48 tff(420,plain,
% 0.20/0.48 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.20/0.48 tff(421,plain,
% 0.20/0.48 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[420, 416])).
% 0.20/0.48 tff(422,plain,(
% 0.20/0.48 ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[421])).
% 0.20/0.48 tff(423,plain,
% 0.20/0.48 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[422, 415])).
% 0.20/0.48 tff(424,plain,
% 0.20/0.48 (((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = j) | (~element(g(j), j)) | (g(j) = k))) <=> ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (g(j) = j) | (~element(g(j), j)) | (g(j) = k))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(425,plain,
% 0.20/0.48 (((g(j) = k) | (g(j) = j) | (~element(g(j), j))) <=> ((g(j) = j) | (~element(g(j), j)) | (g(j) = k))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(426,plain,
% 0.20/0.48 (((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = k) | (g(j) = j) | (~element(g(j), j)))) <=> ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = j) | (~element(g(j), j)) | (g(j) = k)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[425])).
% 0.20/0.48 tff(427,plain,
% 0.20/0.48 (((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = k) | (g(j) = j) | (~element(g(j), j)))) <=> ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (g(j) = j) | (~element(g(j), j)) | (g(j) = k))),
% 0.20/0.48 inference(transitivity,[status(thm)],[426, 424])).
% 0.20/0.48 tff(428,plain,
% 0.20/0.48 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = k) | (g(j) = j) | (~element(g(j), j)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(429,plain,
% 0.20/0.48 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (g(j) = j) | (~element(g(j), j)) | (g(j) = k)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.20/0.48 tff(430,plain,
% 0.20/0.48 (g(j) = k),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[429, 423, 413, 408])).
% 0.20/0.48 tff(431,plain,
% 0.20/0.48 (g(j) = n),
% 0.20/0.48 inference(transitivity,[status(thm)],[430, 335])).
% 0.20/0.48 tff(432,plain,
% 0.20/0.48 (((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(j) = n)) | (j = n) | element(j, n))) <=> ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(j) = n)) | (j = n) | element(j, n))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(433,plain,
% 0.20/0.48 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(j) = n)) | (j = n) | element(j, n))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(434,plain,
% 0.20/0.48 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(j) = n)) | (j = n) | element(j, n)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.20/0.48 tff(435,plain,
% 0.20/0.48 ((~(g(j) = n)) | (j = n) | element(j, n)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[434, 219])).
% 0.20/0.48 tff(436,plain,
% 0.20/0.48 (~(g(j) = n)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[435, 403, 342])).
% 0.20/0.48 tff(437,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[436, 431])).
% 0.20/0.48 tff(438,plain,(k = j), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(439,plain,
% 0.20/0.48 (j = k),
% 0.20/0.48 inference(symmetry,[status(thm)],[438])).
% 0.20/0.48 tff(440,plain,
% 0.20/0.48 (element(m, j) <=> element(m, k)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[439])).
% 0.20/0.48 tff(441,plain,
% 0.20/0.48 (element(m, k) <=> element(m, j)),
% 0.20/0.48 inference(symmetry,[status(thm)],[440])).
% 0.20/0.48 tff(442,plain,
% 0.20/0.48 ((m = n) <=> (m = k)),
% 0.20/0.48 inference(transitivity,[status(thm)],[380, 155])).
% 0.20/0.48 tff(443,plain,
% 0.20/0.48 ((~(m = n)) <=> (~(m = k))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[442])).
% 0.20/0.48 tff(444,plain,
% 0.20/0.48 (~(m = k)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[40, 443])).
% 0.20/0.48 tff(445,plain,
% 0.20/0.48 (element(m, k) | (m = k)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[206, 195])).
% 0.20/0.48 tff(446,plain,
% 0.20/0.48 (element(m, k)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[445, 444])).
% 0.20/0.48 tff(447,plain,
% 0.20/0.48 (element(m, j)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[446, 441])).
% 0.20/0.48 tff(448,plain,
% 0.20/0.48 ((m = j) <=> (m = k)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[439])).
% 0.20/0.48 tff(449,plain,
% 0.20/0.48 ((m = j) <=> (k = m)),
% 0.20/0.48 inference(transitivity,[status(thm)],[448, 154])).
% 0.20/0.48 tff(450,plain,
% 0.20/0.48 ((k = m) <=> (m = j)),
% 0.20/0.48 inference(symmetry,[status(thm)],[449])).
% 0.20/0.48 tff(451,plain,
% 0.20/0.48 ((~(k = m)) <=> (~(m = j))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[450])).
% 0.20/0.48 tff(452,plain,
% 0.20/0.48 (~(m = j)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[382, 451])).
% 0.20/0.48 tff(453,plain,
% 0.20/0.48 (((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (~element(m, j)) | (m = j))) <=> ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (m = k) | (~element(m, j)) | (m = j))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(454,plain,
% 0.20/0.48 (((m = k) | (m = j) | (~element(m, j))) <=> ((m = k) | (~element(m, j)) | (m = j))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(455,plain,
% 0.20/0.48 (((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (m = j) | (~element(m, j)))) <=> ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (~element(m, j)) | (m = j)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[454])).
% 0.20/0.48 tff(456,plain,
% 0.20/0.48 (((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (m = j) | (~element(m, j)))) <=> ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (m = k) | (~element(m, j)) | (m = j))),
% 0.20/0.48 inference(transitivity,[status(thm)],[455, 453])).
% 0.20/0.48 tff(457,plain,
% 0.20/0.48 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (m = j) | (~element(m, j)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(458,plain,
% 0.20/0.48 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (m = k) | (~element(m, j)) | (m = j)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.20/0.48 tff(459,plain,
% 0.20/0.48 ((~element(m, j)) | (m = j)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[458, 423, 444])).
% 0.20/0.48 tff(460,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[459, 452, 447])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------