TSTP Solution File: SYN013-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 23:53:10 EDT 2022
% Result : Unsatisfiable 0.15s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n007.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Sep 5 00:48:05 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.15/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.31 Usage: tptp [options] [-file:]file
% 0.15/0.31 -h, -? prints this message.
% 0.15/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.31 -m, -model generate model.
% 0.15/0.31 -p, -proof generate proof.
% 0.15/0.31 -c, -core generate unsat core of named formulas.
% 0.15/0.31 -st, -statistics display statistics.
% 0.15/0.31 -t:timeout set timeout (in second).
% 0.15/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.31 -<param>:<value> configuration parameter and value.
% 0.15/0.31 -o:<output-file> file to place output in.
% 0.15/0.37 % SZS status Unsatisfiable
% 0.15/0.37 % SZS output start Proof
% 0.15/0.37 tff(element_type, type, (
% 0.15/0.37 element: ( $i * $i ) > $o)).
% 0.15/0.37 tff(n_type, type, (
% 0.15/0.37 n: $i)).
% 0.15/0.37 tff(k_type, type, (
% 0.15/0.37 k: $i)).
% 0.15/0.37 tff(f_type, type, (
% 0.15/0.37 f: $i > $i)).
% 0.15/0.37 tff(m_type, type, (
% 0.15/0.37 m: $i)).
% 0.15/0.37 tff(g_type, type, (
% 0.15/0.37 g: $i > $i)).
% 0.15/0.37 tff(1,plain,
% 0.15/0.37 ((k = n) <=> (n = k)),
% 0.15/0.37 inference(commutativity,[status(thm)],[])).
% 0.15/0.37 tff(2,plain,
% 0.15/0.37 ((n = k) <=> (k = n)),
% 0.15/0.37 inference(symmetry,[status(thm)],[1])).
% 0.15/0.37 tff(3,plain,
% 0.15/0.37 ((~(n = k)) <=> (~(k = n))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.15/0.37 tff(4,plain,
% 0.15/0.37 ((~(n = k)) <=> (~(n = k))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(5,axiom,(~(n = k)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_2')).
% 0.15/0.37 tff(6,plain,
% 0.15/0.37 (~(n = k)),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.15/0.37 tff(7,plain,
% 0.15/0.37 (~(k = n)),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.15/0.37 tff(8,assumption,(~element(k, n)), introduced(assumption)).
% 0.15/0.37 tff(9,plain,
% 0.15/0.37 (^[Y: $i] : refl(((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(10,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.15/0.37 tff(11,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(12,plain,
% 0.15/0.37 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(13,plain,
% 0.15/0.37 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.15/0.37 tff(14,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_10')).
% 0.15/0.37 tff(15,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.15/0.37 tff(16,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.15/0.37 tff(17,plain,(
% 0.15/0.37 ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.15/0.37 inference(skolemize,[status(sab)],[16])).
% 0.15/0.37 tff(18,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.15/0.37 tff(19,plain,
% 0.15/0.37 (((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (element(k, n) | (k = n) | (~(g(k) = k)))) <=> ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | element(k, n) | (k = n) | (~(g(k) = k)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(20,plain,
% 0.15/0.37 (((k = n) | element(k, n) | (~(g(k) = k))) <=> (element(k, n) | (k = n) | (~(g(k) = k)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(21,plain,
% 0.15/0.37 (((~![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)))) | (element(k, n) | (k = n) | (~(g(k) = k))))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.15/0.37 tff(22,plain,
% 0.15/0.37 (((~![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)))) | element(k, n) | (k = n) | (~(g(k) = k)))),
% 0.15/0.37 inference(transitivity,[status(thm)],[21, 19])).
% 0.15/0.37 tff(23,plain,
% 0.15/0.37 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((k = n) | element(k, n) | (~(g(k) = k)))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(24,plain,
% 0.15/0.37 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | element(k, n) | (k = n) | (~(g(k) = k))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.15/0.37 tff(25,plain,
% 0.15/0.37 (~(g(k) = k)),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[24, 18, 8, 7])).
% 0.15/0.37 tff(26,plain,
% 0.15/0.37 (^[Y: $i] : refl(((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(27,plain,
% 0.15/0.37 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.15/0.37 tff(28,plain,
% 0.15/0.37 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(29,plain,
% 0.15/0.37 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(30,plain,
% 0.15/0.37 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.15/0.37 tff(31,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_9')).
% 0.15/0.37 tff(32,plain,
% 0.15/0.37 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.15/0.37 tff(33,plain,
% 0.15/0.37 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.15/0.37 tff(34,plain,(
% 0.15/0.37 ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.15/0.37 inference(skolemize,[status(sab)],[33])).
% 0.15/0.37 tff(35,plain,
% 0.15/0.37 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.15/0.37 tff(36,plain,
% 0.15/0.37 (((~![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))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(37,plain,
% 0.15/0.37 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(k) = n)) | (k = n) | element(k, n))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(38,plain,
% 0.15/0.37 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(k) = n)) | (k = n) | element(k, n)),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.15/0.37 tff(39,plain,
% 0.15/0.37 (~(g(k) = n)),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[38, 35, 8, 7])).
% 0.15/0.37 tff(40,plain,
% 0.15/0.37 (^[Y: $i] : refl(((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(41,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[40])).
% 0.15/0.37 tff(42,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(43,plain,
% 0.15/0.37 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(44,plain,
% 0.15/0.37 (![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.15/0.37 tff(45,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_12')).
% 0.15/0.37 tff(46,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.15/0.37 tff(47,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.15/0.37 tff(48,plain,(
% 0.15/0.37 ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.15/0.37 inference(skolemize,[status(sab)],[47])).
% 0.15/0.37 tff(49,plain,
% 0.15/0.37 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.15/0.37 tff(50,plain,
% 0.15/0.37 (((~![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))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(51,plain,
% 0.15/0.37 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((k = n) | element(k, n) | element(g(k), k))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(52,plain,
% 0.15/0.37 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (k = n) | element(k, n) | element(g(k), k)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.17/0.38 tff(53,plain,
% 0.17/0.38 (element(g(k), k)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[52, 49, 8, 7])).
% 0.17/0.38 tff(54,plain,
% 0.17/0.38 (^[Y: $i] : refl(((Y = m) | (Y = n) | (Y = k) | (~element(Y, k))) <=> ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(55,plain,
% 0.17/0.38 (![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k))) <=> ![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.17/0.38 tff(56,plain,
% 0.17/0.38 (![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k))) <=> ![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(57,plain,
% 0.17/0.38 (^[Y: $i] : trans(monotonicity(rewrite((((Y = k) | (Y = m)) | (Y = n)) <=> ((Y = m) | (Y = n) | (Y = k))), (((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> (((Y = m) | (Y = n) | (Y = k)) | (~element(Y, k))))), rewrite((((Y = m) | (Y = n) | (Y = k)) | (~element(Y, k))) <=> ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))), (((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(58,plain,
% 0.17/0.38 (![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> ![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.17/0.38 tff(59,axiom,(![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_16')).
% 0.17/0.38 tff(60,plain,
% 0.17/0.38 (![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.17/0.38 tff(61,plain,
% 0.17/0.38 (![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.17/0.38 tff(62,plain,(
% 0.17/0.38 ![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))),
% 0.17/0.38 inference(skolemize,[status(sab)],[61])).
% 0.17/0.38 tff(63,plain,
% 0.17/0.38 (![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.17/0.38 tff(64,plain,
% 0.17/0.38 (((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | (g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(65,plain,
% 0.17/0.38 (((g(k) = m) | (g(k) = n) | (g(k) = k) | (~element(g(k), k))) <=> ((g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(66,plain,
% 0.17/0.38 (((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((g(k) = m) | (g(k) = n) | (g(k) = k) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k))))),
% 0.17/0.38 inference(monotonicity,[status(thm)],[65])).
% 0.17/0.38 tff(67,plain,
% 0.17/0.38 (((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((g(k) = m) | (g(k) = n) | (g(k) = k) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | (g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))),
% 0.17/0.38 inference(transitivity,[status(thm)],[66, 64])).
% 0.17/0.38 tff(68,plain,
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% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(69,plain,
% 0.17/0.38 ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | (g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
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% 0.17/0.38 (g(k) = m),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[69, 63, 53, 39, 25])).
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% 0.17/0.38 (element(k, g(k)) <=> element(k, m)),
% 0.17/0.38 inference(monotonicity,[status(thm)],[70])).
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% 0.17/0.38 (^[Y: $i] : refl((element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> (element(Y, g(Y)) | (Y = n) | element(Y, n)))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(73,plain,
% 0.17/0.38 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[72])).
% 0.17/0.38 tff(74,plain,
% 0.17/0.38 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(75,plain,
% 0.17/0.38 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | element(Y, g(Y))) <=> (element(Y, g(Y)) | (Y = n) | element(Y, n)))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(76,plain,
% 0.17/0.38 (![Y: $i] : (((Y = n) | element(Y, n)) | element(Y, g(Y))) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.17/0.38 tff(77,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(Y, g(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_11')).
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% 0.17/0.38 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[77, 76])).
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% 0.17/0.38 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.17/0.38 tff(80,plain,(
% 0.17/0.38 ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.17/0.38 inference(skolemize,[status(sab)],[79])).
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% 0.17/0.38 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[80, 73])).
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% 0.17/0.38 inference(rewrite,[status(thm)],[])).
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% 0.17/0.38 ((element(k, g(k)) | (k = n) | element(k, n)) <=> (element(k, n) | (k = n) | element(k, g(k)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(84,plain,
% 0.17/0.38 (((~![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))) | (element(k, g(k)) | (k = n) | element(k, n))) <=> ((~![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))) | (element(k, n) | (k = n) | element(k, g(k))))),
% 0.17/0.38 inference(monotonicity,[status(thm)],[83])).
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% 0.17/0.38 inference(transitivity,[status(thm)],[84, 82])).
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% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
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% 0.17/0.38 ((~![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))) | element(k, n) | (k = n) | element(k, g(k))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[86, 85])).
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% 0.17/0.38 inference(unit_resolution,[status(thm)],[87, 81, 8, 7])).
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% 0.17/0.38 inference(modus_ponens,[status(thm)],[88, 71])).
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% 0.17/0.38 inference(bind,[status(th)],[])).
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% 0.17/0.38 inference(quant_intro,[status(thm)],[90])).
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% 0.17/0.38 inference(rewrite,[status(thm)],[])).
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% 0.17/0.38 inference(bind,[status(th)],[])).
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% 0.17/0.38 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[93])).
% 0.17/0.38 tff(95,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_5')).
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% 0.17/0.38 inference(modus_ponens,[status(thm)],[95, 94])).
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% 0.17/0.38 inference(modus_ponens,[status(thm)],[96, 92])).
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% 0.17/0.38 ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.17/0.38 inference(skolemize,[status(sab)],[97])).
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% 0.17/0.38 inference(modus_ponens,[status(thm)],[98, 91])).
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% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(101,axiom,(~(k = m)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_3')).
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% 0.17/0.38 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.17/0.38 tff(103,plain,
% 0.17/0.38 (((~![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)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(104,plain,
% 0.17/0.38 (((~element(k, m)) | (k = m) | (~(f(k) = k))) <=> ((k = m) | (~element(k, m)) | (~(f(k) = k)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(105,plain,
% 0.17/0.38 (((~![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))))),
% 0.17/0.38 inference(monotonicity,[status(thm)],[104])).
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% 0.17/0.38 (((~![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)))),
% 0.17/0.38 inference(transitivity,[status(thm)],[105, 103])).
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% 0.17/0.38 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(k, m)) | (k = m) | (~(f(k) = k)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(108,plain,
% 0.17/0.38 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (k = m) | (~element(k, m)) | (~(f(k) = k))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[107, 106])).
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% 0.17/0.38 inference(unit_resolution,[status(thm)],[108, 102, 99, 89])).
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% 0.17/0.38 (^[Y: $i] : refl(((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)))),
% 0.17/0.38 inference(bind,[status(th)],[])).
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% 0.17/0.38 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[110])).
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% 0.17/0.38 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
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% 0.17/0.38 inference(bind,[status(th)],[])).
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% 0.17/0.38 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[113])).
% 0.17/0.38 tff(115,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_4')).
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% 0.17/0.39 inference(modus_ponens,[status(thm)],[118, 111])).
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% 0.17/0.39 inference(rewrite,[status(thm)],[])).
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% 0.17/0.39 inference(rewrite,[status(thm)],[])).
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% 0.17/0.39 (((~![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))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[121])).
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% 0.17/0.39 inference(modus_ponens,[status(thm)],[124, 123])).
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% 0.17/0.39 inference(unit_resolution,[status(thm)],[125, 102, 119, 89])).
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% 0.17/0.39 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
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% 0.17/0.39 inference(bind,[status(th)],[])).
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% 0.17/0.39 inference(quant_intro,[status(thm)],[130])).
% 0.17/0.39 tff(132,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_7')).
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% 0.17/0.39 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(k, m)) | (k = m) | element(f(k), k)),
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% 0.17/0.39 inference(unit_resolution,[status(thm)],[139, 102, 136, 89])).
% 0.17/0.39 tff(141,plain,
% 0.17/0.39 (((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))) <=> ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(142,plain,
% 0.17/0.39 (((f(k) = m) | (f(k) = n) | (f(k) = k) | (~element(f(k), k))) <=> ((f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(143,plain,
% 0.17/0.39 (((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((f(k) = m) | (f(k) = n) | (f(k) = k) | (~element(f(k), k)))) <=> ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[142])).
% 0.17/0.39 tff(144,plain,
% 0.17/0.39 (((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((f(k) = m) | (f(k) = n) | (f(k) = k) | (~element(f(k), k)))) <=> ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[143, 141])).
% 0.17/0.39 tff(145,plain,
% 0.17/0.39 ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | ((f(k) = m) | (f(k) = n) | (f(k) = k) | (~element(f(k), k)))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(146,plain,
% 0.17/0.39 ((~![Y: $i] : ((Y = m) | (Y = n) | (Y = k) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.17/0.39 tff(147,plain,
% 0.17/0.39 (f(k) = n),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[146, 63, 140, 126, 109])).
% 0.17/0.39 tff(148,plain,
% 0.17/0.39 (element(k, f(k)) <=> element(k, n)),
% 0.17/0.39 inference(monotonicity,[status(thm)],[147])).
% 0.17/0.39 tff(149,plain,
% 0.17/0.39 (element(k, n) <=> element(k, f(k))),
% 0.17/0.39 inference(symmetry,[status(thm)],[148])).
% 0.17/0.39 tff(150,plain,
% 0.17/0.39 ((~element(k, n)) <=> (~element(k, f(k)))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[149])).
% 0.17/0.39 tff(151,plain,
% 0.17/0.39 (~element(k, f(k))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[8, 150])).
% 0.17/0.39 tff(152,plain,
% 0.17/0.39 (^[Y: $i] : refl((element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(153,plain,
% 0.17/0.39 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[152])).
% 0.17/0.39 tff(154,plain,
% 0.17/0.39 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(155,plain,
% 0.17/0.39 (^[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))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(156,plain,
% 0.17/0.39 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y))) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[155])).
% 0.17/0.39 tff(157,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_6')).
% 0.17/0.39 tff(158,plain,
% 0.17/0.39 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.17/0.39 tff(159,plain,
% 0.17/0.39 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.17/0.39 tff(160,plain,(
% 0.17/0.39 ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.39 inference(skolemize,[status(sab)],[159])).
% 0.17/0.39 tff(161,plain,
% 0.17/0.39 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.17/0.40 tff(162,plain,
% 0.17/0.40 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((k = m) | (~element(k, m)) | element(k, f(k)))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | element(k, f(k)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(163,plain,
% 0.17/0.40 ((element(k, f(k)) | (~element(k, m)) | (k = m)) <=> ((k = m) | (~element(k, m)) | element(k, f(k)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(164,plain,
% 0.17/0.40 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(k, f(k)) | (~element(k, m)) | (k = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((k = m) | (~element(k, m)) | element(k, f(k))))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[163])).
% 0.17/0.40 tff(165,plain,
% 0.17/0.40 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(k, f(k)) | (~element(k, m)) | (k = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | element(k, f(k)))),
% 0.17/0.40 inference(transitivity,[status(thm)],[164, 162])).
% 0.17/0.40 tff(166,plain,
% 0.17/0.40 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(k, f(k)) | (~element(k, m)) | (k = m))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(167,plain,
% 0.17/0.40 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | element(k, f(k))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.17/0.40 tff(168,plain,
% 0.17/0.40 (element(k, f(k))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[167, 102, 161, 89])).
% 0.17/0.40 tff(169,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[168, 151])).
% 0.17/0.40 tff(170,plain,(element(k, n)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.40 tff(171,plain,
% 0.17/0.40 ((n = m) <=> (m = n)),
% 0.17/0.40 inference(commutativity,[status(thm)],[])).
% 0.17/0.40 tff(172,plain,
% 0.17/0.40 ((m = n) <=> (n = m)),
% 0.17/0.40 inference(symmetry,[status(thm)],[171])).
% 0.17/0.40 tff(173,plain,
% 0.17/0.40 ((~(m = n)) <=> (~(n = m))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[172])).
% 0.17/0.40 tff(174,plain,
% 0.17/0.40 ((~(m = n)) <=> (~(m = n))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(175,axiom,(~(m = n)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_1')).
% 0.17/0.40 tff(176,plain,
% 0.17/0.40 (~(m = n)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.17/0.40 tff(177,plain,
% 0.17/0.40 (~(n = m)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.17/0.40 tff(178,plain,
% 0.17/0.40 (^[Y: $i] : refl(((~(Y = n)) | element(Y, k) | (Y = k)) <=> ((~(Y = n)) | element(Y, k) | (Y = k)))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(179,plain,
% 0.17/0.40 (![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k)) <=> ![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[178])).
% 0.17/0.40 tff(180,plain,
% 0.17/0.40 (![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k)) <=> ![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(181,plain,
% 0.17/0.40 (^[Y: $i] : trans(monotonicity(rewrite(((Y = k) | (~(Y = n))) <=> ((~(Y = n)) | (Y = k))), ((((Y = k) | (~(Y = n))) | element(Y, k)) <=> (((~(Y = n)) | (Y = k)) | element(Y, k)))), rewrite((((~(Y = n)) | (Y = k)) | element(Y, k)) <=> ((~(Y = n)) | element(Y, k) | (Y = k))), ((((Y = k) | (~(Y = n))) | element(Y, k)) <=> ((~(Y = n)) | element(Y, k) | (Y = k))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(182,plain,
% 0.17/0.40 (![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k)) <=> ![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[181])).
% 0.17/0.40 tff(183,axiom,(![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_15')).
% 0.17/0.40 tff(184,plain,
% 0.17/0.40 (![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.17/0.40 tff(185,plain,
% 0.17/0.40 (![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.17/0.40 tff(186,plain,(
% 0.17/0.40 ![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))),
% 0.17/0.40 inference(skolemize,[status(sab)],[185])).
% 0.17/0.40 tff(187,plain,
% 0.17/0.40 (![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.17/0.40 tff(188,plain,
% 0.17/0.40 (((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | ((n = k) | element(n, k))) <=> ((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | (n = k) | element(n, k))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(189,plain,
% 0.17/0.40 (($false | element(n, k) | (n = k)) <=> ((n = k) | element(n, k))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(190,plain,
% 0.17/0.40 ((~$true) <=> $false),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(191,plain,
% 0.17/0.40 ((n = n) <=> $true),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(192,plain,
% 0.17/0.40 ((~(n = n)) <=> (~$true)),
% 0.17/0.40 inference(monotonicity,[status(thm)],[191])).
% 0.17/0.40 tff(193,plain,
% 0.17/0.40 ((~(n = n)) <=> $false),
% 0.17/0.40 inference(transitivity,[status(thm)],[192, 190])).
% 0.17/0.40 tff(194,plain,
% 0.17/0.40 (((~(n = n)) | element(n, k) | (n = k)) <=> ($false | element(n, k) | (n = k))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[193])).
% 0.17/0.40 tff(195,plain,
% 0.17/0.40 (((~(n = n)) | element(n, k) | (n = k)) <=> ((n = k) | element(n, k))),
% 0.17/0.40 inference(transitivity,[status(thm)],[194, 189])).
% 0.17/0.40 tff(196,plain,
% 0.17/0.40 (((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | ((~(n = n)) | element(n, k) | (n = k))) <=> ((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | ((n = k) | element(n, k)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[195])).
% 0.17/0.40 tff(197,plain,
% 0.17/0.40 (((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | ((~(n = n)) | element(n, k) | (n = k))) <=> ((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | (n = k) | element(n, k))),
% 0.17/0.40 inference(transitivity,[status(thm)],[196, 188])).
% 0.17/0.40 tff(198,plain,
% 0.17/0.40 ((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | ((~(n = n)) | element(n, k) | (n = k))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(199,plain,
% 0.17/0.40 ((~![Y: $i] : ((~(Y = n)) | element(Y, k) | (Y = k))) | (n = k) | element(n, k)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.17/0.40 tff(200,plain,
% 0.17/0.40 (element(n, k)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[199, 6, 187])).
% 0.17/0.40 tff(201,plain,
% 0.17/0.40 (^[V: $i, Y: $i] : refl((element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m)) <=> (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m)))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(202,plain,
% 0.17/0.40 (![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m)) <=> ![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[201])).
% 0.17/0.40 tff(203,plain,
% 0.17/0.40 (![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m)) <=> ![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(204,plain,
% 0.17/0.40 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((Y = m) | element(Y, m)) | (V = m)) <=> (element(Y, m) | (Y = m) | (V = m))), (((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) <=> ((element(Y, m) | (Y = m) | (V = m)) | (V = Y)))), rewrite(((element(Y, m) | (Y = m) | (V = m)) | (V = Y)) <=> (element(Y, m) | (Y = m) | (V = Y) | (V = m))), (((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) <=> (element(Y, m) | (Y = m) | (V = Y) | (V = m)))), ((((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) | (~element(Y, V))) <=> ((element(Y, m) | (Y = m) | (V = Y) | (V = m)) | (~element(Y, V))))), rewrite(((element(Y, m) | (Y = m) | (V = Y) | (V = m)) | (~element(Y, V))) <=> (element(Y, m) | (Y = m) | (~element(Y, V)) | (V = Y) | (V = m))), ((((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) | (~element(Y, V))) <=> (element(Y, m) | (Y = m) | (~element(Y, V)) | (V = Y) | (V = m)))), (((((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> ((element(Y, m) | (Y = m) | (~element(Y, V)) | (V = Y) | (V = m)) | (~element(V, Y))))), rewrite(((element(Y, m) | (Y = m) | (~element(Y, V)) | (V = Y) | (V = m)) | (~element(V, Y))) <=> (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))), (((((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(205,plain,
% 0.17/0.40 (![V: $i, Y: $i] : ((((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> ![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[204])).
% 0.17/0.40 tff(206,axiom,(![V: $i, Y: $i] : ((((((Y = m) | element(Y, m)) | (V = m)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_8')).
% 0.17/0.40 tff(207,plain,
% 0.17/0.40 (![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.17/0.40 tff(208,plain,
% 0.17/0.40 (![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.17/0.40 tff(209,plain,(
% 0.17/0.40 ![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))),
% 0.17/0.40 inference(skolemize,[status(sab)],[208])).
% 0.17/0.40 tff(210,plain,
% 0.17/0.40 (![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.17/0.40 tff(211,plain,
% 0.17/0.40 (((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | ((n = k) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)) | element(k, m))) <=> ((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | (n = k) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)) | element(k, m))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(212,plain,
% 0.17/0.40 ((element(k, m) | (k = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | (n = m)) <=> ((n = k) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)) | element(k, m))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(213,plain,
% 0.17/0.40 (((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | (element(k, m) | (k = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | (n = m))) <=> ((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | ((n = k) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)) | element(k, m)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[212])).
% 0.17/0.40 tff(214,plain,
% 0.17/0.40 (((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | (element(k, m) | (k = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | (n = m))) <=> ((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | (n = k) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)) | element(k, m))),
% 0.17/0.40 inference(transitivity,[status(thm)],[213, 211])).
% 0.17/0.40 tff(215,plain,
% 0.17/0.40 ((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | (element(k, m) | (k = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | (n = m))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(216,plain,
% 0.17/0.40 ((~![V: $i, Y: $i] : (element(Y, m) | (Y = m) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = m))) | (n = k) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)) | element(k, m)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.17/0.40 tff(217,plain,
% 0.17/0.40 ((n = m) | (~element(k, n)) | element(k, m)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[216, 6, 102, 210, 200])).
% 0.17/0.40 tff(218,plain,
% 0.17/0.40 ((~element(k, n)) | element(k, m)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[217, 177])).
% 0.17/0.40 tff(219,plain,
% 0.17/0.40 (element(k, m)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[218, 170])).
% 0.17/0.40 tff(220,plain,
% 0.17/0.40 ((m = k) <=> (k = m)),
% 0.17/0.40 inference(commutativity,[status(thm)],[])).
% 0.17/0.40 tff(221,plain,
% 0.17/0.40 ((k = m) <=> (m = k)),
% 0.17/0.40 inference(symmetry,[status(thm)],[220])).
% 0.17/0.41 tff(222,plain,
% 0.17/0.41 ((~(k = m)) <=> (~(m = k))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[221])).
% 0.17/0.41 tff(223,plain,
% 0.17/0.41 (~(m = k)),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[102, 222])).
% 0.17/0.41 tff(224,plain,
% 0.17/0.41 (^[Y: $i] : refl(((~(Y = m)) | element(Y, k) | (Y = k)) <=> ((~(Y = m)) | element(Y, k) | (Y = k)))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(225,plain,
% 0.17/0.41 (![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k)) <=> ![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[224])).
% 0.17/0.41 tff(226,plain,
% 0.17/0.41 (![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k)) <=> ![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(227,plain,
% 0.17/0.41 (^[Y: $i] : trans(monotonicity(rewrite(((Y = k) | (~(Y = m))) <=> ((~(Y = m)) | (Y = k))), ((((Y = k) | (~(Y = m))) | element(Y, k)) <=> (((~(Y = m)) | (Y = k)) | element(Y, k)))), rewrite((((~(Y = m)) | (Y = k)) | element(Y, k)) <=> ((~(Y = m)) | element(Y, k) | (Y = k))), ((((Y = k) | (~(Y = m))) | element(Y, k)) <=> ((~(Y = m)) | element(Y, k) | (Y = k))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(228,plain,
% 0.17/0.41 (![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k)) <=> ![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[227])).
% 0.17/0.41 tff(229,axiom,(![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_14')).
% 0.17/0.41 tff(230,plain,
% 0.17/0.41 (![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.17/0.41 tff(231,plain,
% 0.17/0.41 (![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.17/0.41 tff(232,plain,(
% 0.17/0.41 ![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))),
% 0.17/0.41 inference(skolemize,[status(sab)],[231])).
% 0.17/0.41 tff(233,plain,
% 0.17/0.41 (![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.17/0.41 tff(234,plain,
% 0.17/0.41 (((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | (element(m, k) | (m = k))) <=> ((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | element(m, k) | (m = k))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(235,plain,
% 0.17/0.41 (($false | element(m, k) | (m = k)) <=> (element(m, k) | (m = k))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(236,plain,
% 0.17/0.41 ((m = m) <=> $true),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(237,plain,
% 0.17/0.41 ((~(m = m)) <=> (~$true)),
% 0.17/0.41 inference(monotonicity,[status(thm)],[236])).
% 0.17/0.41 tff(238,plain,
% 0.17/0.41 ((~(m = m)) <=> $false),
% 0.17/0.41 inference(transitivity,[status(thm)],[237, 190])).
% 0.17/0.41 tff(239,plain,
% 0.17/0.41 (((~(m = m)) | element(m, k) | (m = k)) <=> ($false | element(m, k) | (m = k))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[238])).
% 0.17/0.41 tff(240,plain,
% 0.17/0.41 (((~(m = m)) | element(m, k) | (m = k)) <=> (element(m, k) | (m = k))),
% 0.17/0.41 inference(transitivity,[status(thm)],[239, 235])).
% 0.17/0.41 tff(241,plain,
% 0.17/0.41 (((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | ((~(m = m)) | element(m, k) | (m = k))) <=> ((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | (element(m, k) | (m = k)))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[240])).
% 0.17/0.41 tff(242,plain,
% 0.17/0.41 (((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | ((~(m = m)) | element(m, k) | (m = k))) <=> ((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | element(m, k) | (m = k))),
% 0.17/0.41 inference(transitivity,[status(thm)],[241, 234])).
% 0.17/0.41 tff(243,plain,
% 0.17/0.41 ((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | ((~(m = m)) | element(m, k) | (m = k))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(244,plain,
% 0.17/0.41 ((~![Y: $i] : ((~(Y = m)) | element(Y, k) | (Y = k))) | element(m, k) | (m = k)),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.17/0.41 tff(245,plain,
% 0.17/0.41 (element(m, k) | (m = k)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[244, 233])).
% 0.17/0.41 tff(246,plain,
% 0.17/0.41 (element(m, k)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[245, 223])).
% 0.17/0.41 tff(247,plain,
% 0.17/0.41 (^[V: $i, Y: $i] : refl(((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(248,plain,
% 0.17/0.41 (![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[247])).
% 0.17/0.41 tff(249,plain,
% 0.17/0.41 (![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(250,plain,
% 0.17/0.41 (^[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(V, Y)) | (~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(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(251,plain,
% 0.17/0.41 (![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(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[250])).
% 0.17/0.41 tff(252,axiom,(![V: $i, Y: $i] : ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_13')).
% 0.17/0.41 tff(253,plain,
% 0.17/0.41 (![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.17/0.41 tff(254,plain,
% 0.17/0.41 (![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.17/0.41 tff(255,plain,(
% 0.17/0.41 ![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.17/0.41 inference(skolemize,[status(sab)],[254])).
% 0.17/0.41 tff(256,plain,
% 0.17/0.41 (![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.17/0.41 tff(257,plain,
% 0.17/0.41 (((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((m = n) | (m = k) | (~element(k, n)) | (k = n) | (~element(k, m)) | (~element(m, k)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (m = k) | (~element(k, n)) | (k = n) | (~element(k, m)) | (~element(m, k)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(258,plain,
% 0.17/0.42 (((k = n) | (~element(m, k)) | (~element(k, m)) | (m = k) | (m = n) | (~element(k, n))) <=> ((m = n) | (m = k) | (~element(k, n)) | (k = n) | (~element(k, m)) | (~element(m, k)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(259,plain,
% 0.17/0.42 (((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(m, k)) | (~element(k, m)) | (m = k) | (m = n) | (~element(k, n)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((m = n) | (m = k) | (~element(k, n)) | (k = n) | (~element(k, m)) | (~element(m, k))))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[258])).
% 0.17/0.42 tff(260,plain,
% 0.17/0.42 (((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(m, k)) | (~element(k, m)) | (m = k) | (m = n) | (~element(k, n)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (m = k) | (~element(k, n)) | (k = n) | (~element(k, m)) | (~element(m, k)))),
% 0.17/0.42 inference(transitivity,[status(thm)],[259, 257])).
% 0.17/0.42 tff(261,plain,
% 0.17/0.42 ((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(m, k)) | (~element(k, m)) | (m = k) | (m = n) | (~element(k, n)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(262,plain,
% 0.17/0.42 ((~![V: $i, Y: $i] : ((Y = n) | (~element(V, Y)) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (m = k) | (~element(k, n)) | (k = n) | (~element(k, m)) | (~element(m, k))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.17/0.42 tff(263,plain,
% 0.17/0.42 ((~element(k, n)) | (~element(k, m))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[262, 176, 256, 246, 223, 7])).
% 0.17/0.42 tff(264,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[263, 219, 170])).
% 0.17/0.42 % SZS output end Proof
%------------------------------------------------------------------------------