TSTP Solution File: SYN014-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 01:13:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(k_type, type, (
% 0.13/0.40 k: $i)).
% 0.13/0.40 tff(f_type, type, (
% 0.13/0.40 f: $i > $i)).
% 0.13/0.40 tff(n_type, type, (
% 0.13/0.40 n: $i)).
% 0.13/0.40 tff(m_type, type, (
% 0.13/0.40 m: $i)).
% 0.13/0.40 tff(element_type, type, (
% 0.13/0.40 element: ( $i * $i ) > $o)).
% 0.13/0.40 tff(j_type, type, (
% 0.13/0.40 j: $i)).
% 0.13/0.40 tff(g_type, type, (
% 0.13/0.40 g: $i > $i)).
% 0.13/0.40 tff(1,assumption,(~(m = k)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (((n = k) | (m = k)) <=> ((n = k) | (m = k))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,axiom,((n = k) | (m = k)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_2')).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((n = k) | (m = k)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (n = k),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[11, 1])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 ((j = k) <=> (k = j)),
% 0.13/0.40 inference(commutativity,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((j = n) <=> (j = k)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[12])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 ((j = n) <=> (k = j)),
% 0.13/0.40 inference(transitivity,[status(thm)],[14, 13])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((k = j) <=> (j = n)),
% 0.13/0.40 inference(symmetry,[status(thm)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~(k = j)) <=> (~(j = n))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.13/0.40 tff(18,assumption,(k = j), introduced(assumption)).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (j = k),
% 0.13/0.40 inference(symmetry,[status(thm)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (element(m, j) <=> element(m, k)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (element(m, k) <=> element(m, j)),
% 0.13/0.40 inference(symmetry,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (^[Y: $i] : refl(((Y = k) | (~(Y = m)) | element(Y, k)) <=> ((Y = k) | (~(Y = m)) | element(Y, k)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.40 tff(27,axiom,(![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_15')).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.40 tff(30,plain,(
% 0.13/0.40 ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.40 inference(skolemize,[status(sab)],[29])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | ((m = k) | element(m, k))) <=> ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | (m = k) | element(m, k))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.20/0.40 (((m = k) | $false | element(m, k)) <=> ((m = k) | element(m, k))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~$true) <=> $false),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((m = m) <=> $true),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((~(m = m)) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~(m = m)) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (((m = k) | (~(m = m)) | element(m, k)) <=> ((m = k) | $false | element(m, k))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (((m = k) | (~(m = m)) | element(m, k)) <=> ((m = k) | element(m, k))),
% 0.20/0.40 inference(transitivity,[status(thm)],[38, 33])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (((~![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))) | ((m = k) | element(m, k)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![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))) | (m = k) | element(m, k))),
% 0.20/0.41 inference(transitivity,[status(thm)],[40, 32])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | ((m = k) | (~(m = m)) | element(m, k))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))) | (m = k) | element(m, k)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((m = k) | element(m, k)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 31])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (element(m, k)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[44, 1])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (element(m, j)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 21])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((m = j) <=> (m = k)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((m = k) <=> (m = j)),
% 0.20/0.41 inference(symmetry,[status(thm)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~(m = k)) <=> (~(m = j))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (~(m = j)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[1, 49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (^[Y: $i] : refl(((Y = k) | (Y = j) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (^[Y: $i] : rewrite((((Y = j) | (Y = k)) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.41 tff(56,axiom,(![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_4')).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.41 tff(59,plain,(
% 0.20/0.41 ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[58])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (((~![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (((m = k) | (m = j) | (~element(m, j))) <=> ((m = k) | (~element(m, j)) | (m = j))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (((~![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))),
% 0.20/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (m = j) | (~element(m, j)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (m = k) | (~element(m, j)) | (m = j)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~element(m, j)) | (m = j)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 1, 60])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 50, 46])).
% 0.20/0.41 tff(69,plain,((~(k = j)) | (m = k)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (~(k = j)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 1])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (~(j = n)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[70, 17])).
% 0.20/0.41 tff(72,assumption,(n = k), introduced(assumption)).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (k = n),
% 0.20/0.41 inference(symmetry,[status(thm)],[72])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ((j = n) <=> (j = k)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((j = n) <=> (k = j)),
% 0.20/0.41 inference(transitivity,[status(thm)],[74, 13])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 ((k = j) <=> (j = n)),
% 0.20/0.41 inference(symmetry,[status(thm)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 ((~(k = j)) <=> (~(j = n))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.41 tff(78,assumption,(~(k = j)), introduced(assumption)).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (~(j = n)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (element(j, n) <=> element(j, k)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (element(j, k) <=> element(j, n)),
% 0.20/0.41 inference(symmetry,[status(thm)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 ((~element(j, k)) <=> (~element(j, n))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.41 tff(83,assumption,(~element(j, k)), introduced(assumption)).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (~element(j, n)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (^[Y: $i] : refl(((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.41 tff(90,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_11')).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.41 tff(93,plain,(
% 0.20/0.41 ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[92])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((j = n) | element(j, n) | (~(g(j) = j)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (j = n) | element(j, n) | (~(g(j) = j))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ((j = n) | element(j, n) | (~(g(j) = j))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (~(g(j) = j)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 84, 79])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (^[Y: $i] : refl(((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.41 tff(105,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_13')).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.41 tff(108,plain,(
% 0.20/0.41 ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.41 inference(skolemize,[status(sab)],[107])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (((~![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((j = n) | element(j, n) | element(g(j), j))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (j = n) | element(j, n) | element(g(j), j)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ((j = n) | element(j, n) | element(g(j), j)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[112, 109])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (element(g(j), j)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 84, 79])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (((~![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((g(j) = k) | (g(j) = j) | (~element(g(j), j))) <=> ((g(j) = j) | (~element(g(j), j)) | (g(j) = k))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (((~![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))),
% 0.20/0.41 inference(transitivity,[status(thm)],[117, 115])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = k) | (g(j) = j) | (~element(g(j), j)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (g(j) = j) | (~element(g(j), j)) | (g(j) = k)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (g(j) = k),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[120, 60, 114, 99])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (g(j) = n),
% 0.20/0.42 inference(transitivity,[status(thm)],[121, 73])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (^[Y: $i] : refl(((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.42 tff(128,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_10')).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.42 tff(131,plain,(
% 0.20/0.42 ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.42 inference(skolemize,[status(sab)],[130])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(j) = n)) | (j = n) | element(j, n))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(j) = n)) | (j = n) | element(j, n)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~(g(j) = n)) | (j = n) | element(j, n)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (~(g(j) = n)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 84, 79])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[137, 122])).
% 0.20/0.42 tff(139,plain,(element(j, k) | (~(n = k)) | (k = j)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 (element(j, k)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[139, 12, 70])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 ((k = j) <=> (j = k)),
% 0.20/0.42 inference(symmetry,[status(thm)],[13])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 ((~(k = j)) <=> (~(j = k))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (~(j = k)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 142])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (^[Y: $i] : refl(((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[144])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 (![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.42 tff(149,axiom,(![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_17')).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.20/0.42 tff(152,plain,(
% 0.20/0.42 ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[151])).
% 0.20/0.42 tff(153,plain,
% 0.20/0.42 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((j = k) | (j = m) | (~element(j, k)) | (j = n))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (j = k) | (j = m) | (~element(j, k)) | (j = n))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 (((j = k) | (j = m) | (j = n) | (~element(j, k))) <=> ((j = k) | (j = m) | (~element(j, k)) | (j = n))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((j = k) | (j = m) | (j = n) | (~element(j, k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((j = k) | (j = m) | (~element(j, k)) | (j = n)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.42 tff(157,plain,
% 0.20/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((j = k) | (j = m) | (j = n) | (~element(j, k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (j = k) | (j = m) | (~element(j, k)) | (j = n))),
% 0.20/0.42 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((j = k) | (j = m) | (j = n) | (~element(j, k)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (j = k) | (j = m) | (~element(j, k)) | (j = n)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 ((j = m) | (j = n)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[159, 153, 143, 140])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 (j = m),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[160, 71])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 (element(k, j) <=> element(k, m)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.42 tff(163,plain,
% 0.20/0.42 (^[Y: $i] : refl((element(Y, j) | (~(Y = k)) | (Y = j)) <=> (element(Y, j) | (~(Y = k)) | (Y = j)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(164,plain,
% 0.20/0.42 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j)) <=> ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.42 tff(165,plain,
% 0.20/0.42 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j)) <=> ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(166,plain,
% 0.20/0.42 (^[Y: $i] : trans(monotonicity(rewrite(((Y = j) | (~(Y = k))) <=> ((~(Y = k)) | (Y = j))), ((((Y = j) | (~(Y = k))) | element(Y, j)) <=> (((~(Y = k)) | (Y = j)) | element(Y, j)))), rewrite((((~(Y = k)) | (Y = j)) | element(Y, j)) <=> (element(Y, j) | (~(Y = k)) | (Y = j))), ((((Y = j) | (~(Y = k))) | element(Y, j)) <=> (element(Y, j) | (~(Y = k)) | (Y = j))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(167,plain,
% 0.20/0.42 (![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j)) <=> ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.42 tff(168,axiom,(![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_3')).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.20/0.43 tff(171,plain,(
% 0.20/0.43 ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.43 inference(skolemize,[status(sab)],[170])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 ((element(k, j) | $false | (k = j)) <=> ((k = j) | element(k, j))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 ((k = k) <=> $true),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 ((~(k = k)) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 ((~(k = k)) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[176, 34])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 ((element(k, j) | (~(k = k)) | (k = j)) <=> (element(k, j) | $false | (k = j))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 ((element(k, j) | (~(k = k)) | (k = j)) <=> ((k = j) | element(k, j))),
% 0.20/0.43 inference(transitivity,[status(thm)],[178, 174])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(transitivity,[status(thm)],[180, 173])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 ((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (element(k, j) | (~(k = k)) | (k = j))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 ((~![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))) | (k = j) | element(k, j)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 ((k = j) | element(k, j)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[183, 172])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 (element(k, j)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[184, 70])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (element(k, m)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[185, 162])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 ((k = m) <=> (m = k)),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 ((m = k) <=> (k = m)),
% 0.20/0.43 inference(symmetry,[status(thm)],[187])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 ((~(m = k)) <=> (~(k = m))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[188])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 (~(k = m)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[1, 189])).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(194,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(195,plain,
% 0.20/0.43 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[194])).
% 0.20/0.43 tff(196,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_6')).
% 0.20/0.43 tff(197,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.20/0.43 tff(199,plain,(
% 0.20/0.43 ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[198])).
% 0.20/0.43 tff(200,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((k = m) | (~element(k, m)) | (~(f(k) = k)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (k = m) | (~element(k, m)) | (~(f(k) = k)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 (((~element(k, m)) | (k = m) | (~(f(k) = k))) <=> ((k = m) | (~element(k, m)) | (~(f(k) = k)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(203,plain,
% 0.20/0.43 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(k, m)) | (k = m) | (~(f(k) = k)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((k = m) | (~element(k, m)) | (~(f(k) = k))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.43 tff(204,plain,
% 0.20/0.43 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(k, m)) | (k = m) | (~(f(k) = k)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (k = m) | (~element(k, m)) | (~(f(k) = k)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[203, 201])).
% 0.20/0.43 tff(205,plain,
% 0.20/0.43 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(k, m)) | (k = m) | (~(f(k) = k)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(206,plain,
% 0.20/0.43 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (k = m) | (~element(k, m)) | (~(f(k) = k))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.43 tff(207,plain,
% 0.20/0.43 (~(f(k) = k)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[206, 200, 190, 186])).
% 0.20/0.43 tff(208,plain,
% 0.20/0.43 (^[Y: $i] : refl(((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(209,plain,
% 0.20/0.43 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[208])).
% 0.20/0.43 tff(210,plain,
% 0.20/0.43 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(211,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(212,plain,
% 0.20/0.43 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.43 tff(213,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_5')).
% 0.20/0.43 tff(214,plain,
% 0.20/0.43 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.43 tff(215,plain,
% 0.20/0.43 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.20/0.43 tff(216,plain,(
% 0.20/0.43 ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.43 inference(skolemize,[status(sab)],[215])).
% 0.20/0.43 tff(217,plain,
% 0.20/0.43 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.20/0.43 tff(218,plain,
% 0.20/0.43 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((k = m) | (~element(k, m)) | (~(f(k) = m)))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | (~(f(k) = m)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(219,plain,
% 0.20/0.43 (((~(f(k) = m)) | (~element(k, m)) | (k = m)) <=> ((k = m) | (~element(k, m)) | (~(f(k) = m)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(220,plain,
% 0.20/0.43 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(k) = m)) | (~element(k, m)) | (k = m))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((k = m) | (~element(k, m)) | (~(f(k) = m))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[219])).
% 0.20/0.43 tff(221,plain,
% 0.20/0.43 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(k) = m)) | (~element(k, m)) | (k = m))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | (~(f(k) = m)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[220, 218])).
% 0.20/0.43 tff(222,plain,
% 0.20/0.43 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(k) = m)) | (~element(k, m)) | (k = m))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(223,plain,
% 0.20/0.43 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | (~(f(k) = m))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.43 tff(224,plain,
% 0.20/0.43 (~(f(k) = m)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[223, 217, 190, 186])).
% 0.20/0.43 tff(225,plain,
% 0.20/0.43 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ((~element(Y, m)) | (Y = m) | element(f(Y), Y)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(226,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[225])).
% 0.20/0.43 tff(227,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(228,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(229,plain,
% 0.20/0.43 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[228])).
% 0.20/0.43 tff(230,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_8')).
% 0.20/0.43 tff(231,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.43 tff(232,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.20/0.43 tff(233,plain,(
% 0.20/0.43 ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.43 inference(skolemize,[status(sab)],[232])).
% 0.20/0.43 tff(234,plain,
% 0.20/0.43 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.20/0.43 tff(235,plain,
% 0.20/0.43 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(k, m)) | (k = m) | element(f(k), k))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(k, m)) | (k = m) | element(f(k), k))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(236,plain,
% 0.20/0.43 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(k, m)) | (k = m) | element(f(k), k))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(237,plain,
% 0.20/0.43 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(k, m)) | (k = m) | element(f(k), k)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.44 tff(238,plain,
% 0.20/0.44 (element(f(k), k)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[237, 234, 190, 186])).
% 0.20/0.44 tff(239,plain,
% 0.20/0.44 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(240,plain,
% 0.20/0.44 (((f(k) = k) | (f(k) = m) | (f(k) = n) | (~element(f(k), k))) <=> ((f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(241,plain,
% 0.20/0.44 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(k) = k) | (f(k) = m) | (f(k) = n) | (~element(f(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[240])).
% 0.20/0.44 tff(242,plain,
% 0.20/0.44 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(k) = k) | (f(k) = m) | (f(k) = n) | (~element(f(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[241, 239])).
% 0.20/0.44 tff(243,plain,
% 0.20/0.44 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(k) = k) | (f(k) = m) | (f(k) = n) | (~element(f(k), k)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(244,plain,
% 0.20/0.44 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.20/0.44 tff(245,plain,
% 0.20/0.44 (f(k) = n),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[244, 153, 238, 224, 207])).
% 0.20/0.44 tff(246,plain,
% 0.20/0.44 (f(k) = k),
% 0.20/0.44 inference(transitivity,[status(thm)],[245, 12])).
% 0.20/0.44 tff(247,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[207, 246])).
% 0.20/0.44 tff(248,plain,(m = k), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(249,plain,
% 0.20/0.44 (k = m),
% 0.20/0.44 inference(symmetry,[status(thm)],[248])).
% 0.20/0.44 tff(250,plain,
% 0.20/0.44 ((f(n) = k) <=> (f(n) = m)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[249])).
% 0.20/0.44 tff(251,plain,
% 0.20/0.44 ((f(n) = m) <=> (f(n) = k)),
% 0.20/0.44 inference(symmetry,[status(thm)],[250])).
% 0.20/0.44 tff(252,plain,
% 0.20/0.44 ((~(f(n) = m)) <=> (~(f(n) = k))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[251])).
% 0.20/0.44 tff(253,plain,
% 0.20/0.44 (element(n, m) <=> element(n, k)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.44 tff(254,plain,
% 0.20/0.44 (element(n, k) <=> element(n, m)),
% 0.20/0.44 inference(symmetry,[status(thm)],[253])).
% 0.20/0.44 tff(255,plain,
% 0.20/0.44 ((k = n) <=> (n = k)),
% 0.20/0.44 inference(commutativity,[status(thm)],[])).
% 0.20/0.44 tff(256,plain,
% 0.20/0.44 ((m = n) <=> (k = n)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.44 tff(257,plain,
% 0.20/0.44 ((m = n) <=> (n = k)),
% 0.20/0.44 inference(transitivity,[status(thm)],[256, 255])).
% 0.20/0.44 tff(258,plain,
% 0.20/0.44 ((~(m = n)) <=> (~(n = k))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[257])).
% 0.20/0.44 tff(259,plain,
% 0.20/0.44 ((~(m = n)) <=> (~(m = n))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(260,axiom,(~(m = n)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_1')).
% 0.20/0.44 tff(261,plain,
% 0.20/0.44 (~(m = n)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.20/0.44 tff(262,plain,
% 0.20/0.44 (~(n = k)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[261, 258])).
% 0.20/0.44 tff(263,plain,
% 0.20/0.44 (^[Y: $i] : refl(((Y = k) | element(Y, k) | (~(Y = n))) <=> ((Y = k) | element(Y, k) | (~(Y = n))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(264,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[263])).
% 0.20/0.44 tff(265,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(266,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(267,plain,
% 0.20/0.44 (![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[266])).
% 0.20/0.44 tff(268,axiom,(![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_16')).
% 0.20/0.44 tff(269,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.44 tff(270,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.20/0.44 tff(271,plain,(
% 0.20/0.44 ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[270])).
% 0.20/0.44 tff(272,plain,
% 0.20/0.44 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.20/0.44 tff(273,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(274,plain,
% 0.20/0.44 (((n = k) | element(n, k) | $false) <=> ((n = k) | element(n, k))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(275,plain,
% 0.20/0.44 ((n = n) <=> $true),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(276,plain,
% 0.20/0.44 ((~(n = n)) <=> (~$true)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[275])).
% 0.20/0.44 tff(277,plain,
% 0.20/0.44 ((~(n = n)) <=> $false),
% 0.20/0.44 inference(transitivity,[status(thm)],[276, 34])).
% 0.20/0.44 tff(278,plain,
% 0.20/0.44 (((n = k) | element(n, k) | (~(n = n))) <=> ((n = k) | element(n, k) | $false)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[277])).
% 0.20/0.44 tff(279,plain,
% 0.20/0.44 (((n = k) | element(n, k) | (~(n = n))) <=> ((n = k) | element(n, k))),
% 0.20/0.44 inference(transitivity,[status(thm)],[278, 274])).
% 0.20/0.44 tff(280,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[279])).
% 0.20/0.44 tff(281,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(transitivity,[status(thm)],[280, 273])).
% 0.20/0.44 tff(282,plain,
% 0.20/0.44 ((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | ((n = k) | element(n, k) | (~(n = n)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(283,plain,
% 0.20/0.44 ((~![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))) | (n = k) | element(n, k)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.20/0.44 tff(284,plain,
% 0.20/0.44 ((n = k) | element(n, k)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[283, 272])).
% 0.20/0.44 tff(285,plain,
% 0.20/0.44 (element(n, k)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[284, 262])).
% 0.20/0.44 tff(286,plain,
% 0.20/0.44 (element(n, m)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[285, 254])).
% 0.20/0.44 tff(287,plain,
% 0.20/0.44 ((n = m) <=> (n = k)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.44 tff(288,plain,
% 0.20/0.44 ((n = k) <=> (n = m)),
% 0.20/0.44 inference(symmetry,[status(thm)],[287])).
% 0.20/0.44 tff(289,plain,
% 0.20/0.44 ((~(n = k)) <=> (~(n = m))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[288])).
% 0.20/0.44 tff(290,plain,
% 0.20/0.44 (~(n = m)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[262, 289])).
% 0.20/0.44 tff(291,plain,
% 0.20/0.44 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~element(n, m)) | (n = m) | (~(f(n) = m)))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | (~(f(n) = m)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(292,plain,
% 0.20/0.44 (((~(f(n) = m)) | (~element(n, m)) | (n = m)) <=> ((~element(n, m)) | (n = m) | (~(f(n) = m)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(293,plain,
% 0.20/0.44 (((~![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))) | ((~element(n, m)) | (n = m) | (~(f(n) = m))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[292])).
% 0.20/0.45 tff(294,plain,
% 0.20/0.45 (((~![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))) | (~element(n, m)) | (n = m) | (~(f(n) = m)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[293, 291])).
% 0.20/0.45 tff(295,plain,
% 0.20/0.45 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(296,plain,
% 0.20/0.45 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | (~(f(n) = m))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.45 tff(297,plain,
% 0.20/0.45 ((~element(n, m)) | (n = m) | (~(f(n) = m))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[296, 217])).
% 0.20/0.45 tff(298,plain,
% 0.20/0.45 (~(f(n) = m)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[297, 290, 286])).
% 0.20/0.45 tff(299,plain,
% 0.20/0.45 (~(f(n) = k)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[298, 252])).
% 0.20/0.45 tff(300,plain,
% 0.20/0.45 (element(f(n), k) <=> element(f(n), m)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[249])).
% 0.20/0.45 tff(301,plain,
% 0.20/0.45 (element(f(n), m) <=> element(f(n), k)),
% 0.20/0.45 inference(symmetry,[status(thm)],[300])).
% 0.20/0.45 tff(302,plain,
% 0.20/0.45 ((n = f(n)) <=> (f(n) = n)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(303,plain,
% 0.20/0.45 ((f(n) = n) <=> (n = f(n))),
% 0.20/0.45 inference(symmetry,[status(thm)],[302])).
% 0.20/0.45 tff(304,plain,
% 0.20/0.45 ((~(f(n) = n)) <=> (~(n = f(n)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[303])).
% 0.20/0.45 tff(305,plain,
% 0.20/0.45 (((~![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)))) | (~element(n, m)) | (n = m) | (~(f(n) = n)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(306,plain,
% 0.20/0.45 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(n, m)) | (n = m) | (~(f(n) = n)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(307,plain,
% 0.20/0.45 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (~element(n, m)) | (n = m) | (~(f(n) = n))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.45 tff(308,plain,
% 0.20/0.45 ((~element(n, m)) | (n = m) | (~(f(n) = n))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[307, 200])).
% 0.20/0.45 tff(309,plain,
% 0.20/0.45 (~(f(n) = n)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[308, 290, 286])).
% 0.20/0.45 tff(310,plain,
% 0.20/0.45 (~(n = f(n))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[309, 304])).
% 0.20/0.45 tff(311,plain,
% 0.20/0.45 (^[Y: $i] : refl((element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(312,plain,
% 0.20/0.45 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[311])).
% 0.20/0.45 tff(313,plain,
% 0.20/0.45 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(314,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(315,plain,
% 0.20/0.45 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y))) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[314])).
% 0.20/0.45 tff(316,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_7')).
% 0.20/0.45 tff(317,plain,
% 0.20/0.45 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.20/0.45 tff(318,plain,
% 0.20/0.45 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[317, 313])).
% 0.20/0.45 tff(319,plain,(
% 0.20/0.46 ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.46 inference(skolemize,[status(sab)],[318])).
% 0.20/0.46 tff(320,plain,
% 0.20/0.46 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[319, 312])).
% 0.20/0.46 tff(321,plain,
% 0.20/0.46 (((~![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))) | element(n, f(n)) | (~element(n, m)) | (n = m))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(322,plain,
% 0.20/0.46 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(323,plain,
% 0.20/0.46 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | element(n, f(n)) | (~element(n, m)) | (n = m)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.20/0.46 tff(324,plain,
% 0.20/0.46 (element(n, f(n)) | (~element(n, m)) | (n = m)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[323, 320])).
% 0.20/0.46 tff(325,plain,
% 0.20/0.46 (element(n, f(n))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[324, 290, 286])).
% 0.20/0.46 tff(326,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(327,plain,
% 0.20/0.46 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(n, m)) | (n = m) | element(f(n), n))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(328,plain,
% 0.20/0.46 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(n, m)) | (n = m) | element(f(n), n)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.20/0.46 tff(329,plain,
% 0.20/0.46 ((~element(n, m)) | (n = m) | element(f(n), n)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[328, 234])).
% 0.20/0.46 tff(330,plain,
% 0.20/0.46 (element(f(n), n)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[329, 290, 286])).
% 0.20/0.46 tff(331,plain,
% 0.20/0.46 (^[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)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(332,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[331])).
% 0.20/0.46 tff(333,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(334,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(335,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[334])).
% 0.20/0.46 tff(336,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_9')).
% 0.20/0.46 tff(337,plain,
% 0.20/0.46 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.20/0.46 tff(338,plain,
% 0.20/0.46 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.20/0.46 tff(339,plain,(
% 0.20/0.46 ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.46 inference(skolemize,[status(sab)],[338])).
% 0.20/0.46 tff(340,plain,
% 0.20/0.46 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[339, 332])).
% 0.20/0.46 tff(341,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(342,plain,
% 0.20/0.46 (((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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(343,plain,
% 0.20/0.46 (((~![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)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[342])).
% 0.20/0.46 tff(344,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(transitivity,[status(thm)],[343, 341])).
% 0.20/0.46 tff(345,plain,
% 0.20/0.46 ((~![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))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(346,plain,
% 0.20/0.46 ((~![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)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.20/0.46 tff(347,plain,
% 0.20/0.46 ((n = f(n)) | element(f(n), m)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[346, 340, 290, 330, 325, 298])).
% 0.20/0.46 tff(348,plain,
% 0.20/0.46 (element(f(n), m)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[347, 310])).
% 0.20/0.47 tff(349,plain,
% 0.20/0.47 (element(f(n), k)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[348, 301])).
% 0.20/0.47 tff(350,plain,
% 0.20/0.47 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(351,plain,
% 0.20/0.47 (((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k))) <=> ((f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(352,plain,
% 0.20/0.47 (((~![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)))) | ((f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[351])).
% 0.20/0.47 tff(353,plain,
% 0.20/0.47 (((~![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)))) | (f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[352, 350])).
% 0.20/0.47 tff(354,plain,
% 0.20/0.47 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(355,plain,
% 0.20/0.47 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.20/0.47 tff(356,plain,
% 0.20/0.47 ((f(n) = k) | (~element(f(n), k))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[355, 153, 298, 309])).
% 0.20/0.47 tff(357,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[356, 349, 299])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------