%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN015-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:37:58 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN015-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:25:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(element_type, type, (
% 0.13/0.39 element: ( $i * $i ) > $o)).
% 0.13/0.39 tff(k_type, type, (
% 0.13/0.39 k: $i)).
% 0.13/0.39 tff(f_type, type, (
% 0.13/0.39 f: $i > $i)).
% 0.13/0.39 tff(n_type, type, (
% 0.13/0.39 n: $i)).
% 0.13/0.39 tff(m_type, type, (
% 0.13/0.39 m: $i)).
% 0.13/0.39 tff(g_type, type, (
% 0.13/0.39 g: $i > $i)).
% 0.13/0.39 tff(j_type, type, (
% 0.13/0.39 j: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((k = m) <=> (m = k)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((m = k) <=> (k = m)),
% 0.13/0.39 inference(symmetry,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~(m = k)) <=> (~(k = m))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[2])).
% 0.13/0.39 tff(4,assumption,(~(m = k)), introduced(assumption)).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~(k = m)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 ((k = n) <=> (n = k)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 ((n = k) <=> (k = n)),
% 0.13/0.39 inference(symmetry,[status(thm)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~(n = k)) <=> (~(k = n))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[7])).
% 0.13/0.39 tff(9,assumption,(n = k), introduced(assumption)).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((m = n) <=> (m = k)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~(m = n)) <=> (~(m = k))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((~(m = n)) <=> (~(m = n))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,axiom,(~(m = n)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_1')).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~(m = n)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~(m = k)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~(k = m)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 3])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ((j = k) <=> (k = j)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((j = n) <=> (j = k)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ((j = n) <=> (k = j)),
% 0.13/0.39 inference(transitivity,[status(thm)],[18, 17])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((k = j) <=> (j = n)),
% 0.13/0.39 inference(symmetry,[status(thm)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~(k = j)) <=> (~(j = n))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.39 tff(22,assumption,(k = j), introduced(assumption)).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (j = k),
% 0.13/0.39 inference(symmetry,[status(thm)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((m = j) <=> (m = k)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[23])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((m = k) <=> (m = j)),
% 0.13/0.39 inference(symmetry,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~(m = k)) <=> (~(m = j))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~(m = j)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 26])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (element(m, j) <=> element(m, k)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[23])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (element(m, k) <=> element(m, j)),
% 0.13/0.39 inference(symmetry,[status(thm)],[28])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 ((element(m, k) | (m = k)) <=> (element(m, k) | (m = k))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![Y: $i] : (element(m, k) | (m = k)) <=> (element(m, k) | (m = k))),
% 0.13/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> ![Y: $i] : (element(m, k) | (m = k))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> (element(m, k) | (m = k))),
% 0.13/0.39 inference(transitivity,[status(thm)],[32, 31])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k)) <=> (element(m, k) | (m = k))),
% 0.13/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.13/0.39 tff(37,axiom,(![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_14')).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (element(m, k) | (m = k)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (element(m, k) | (m = k)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (element(m, k) | (m = k)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 30])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (element(m, k) | (m = k)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (element(m, k) | (m = k)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 30])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (element(m, k)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[42, 4])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (element(m, j)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 29])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (^[Y: $i] : refl(((Y = k) | (Y = j) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (^[Y: $i] : rewrite((((Y = j) | (Y = k)) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.13/0.39 tff(50,axiom,(![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_3')).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.39 tff(53,plain,(
% 0.13/0.39 ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[52])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (((~![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) | (m = j) | (~element(m, j)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (m = j) | (~element(m, j)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (m = k) | (m = j) | (~element(m, j))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ((m = j) | (~element(m, j))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[57, 54, 4])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[58, 44, 27])).
% 0.13/0.39 tff(60,plain,((~(k = j)) | (m = k)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (~(k = j)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[60, 15])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 (~(j = n)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[61, 21])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (k = n),
% 0.13/0.39 inference(symmetry,[status(thm)],[9])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (element(j, n) <=> element(j, k)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 (element(j, k) <=> element(j, n)),
% 0.13/0.39 inference(symmetry,[status(thm)],[64])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 ((~element(j, k)) <=> (~element(j, n))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[65])).
% 0.13/0.39 tff(67,assumption,(~element(j, k)), introduced(assumption)).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 (~element(j, n)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (^[Y: $i] : refl(((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.22/0.39 tff(71,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(72,plain,
% 0.22/0.39 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(73,plain,
% 0.22/0.39 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.22/0.39 tff(74,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_10')).
% 0.22/0.39 tff(75,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.22/0.39 tff(76,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.22/0.39 tff(77,plain,(
% 0.22/0.39 ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.22/0.39 inference(skolemize,[status(sab)],[76])).
% 0.22/0.39 tff(78,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.22/0.39 tff(79,plain,
% 0.22/0.39 (((~![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)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(80,plain,
% 0.22/0.39 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((j = n) | element(j, n) | (~(g(j) = j)))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(81,plain,
% 0.22/0.39 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (j = n) | element(j, n) | (~(g(j) = j))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.22/0.39 tff(82,plain,
% 0.22/0.39 ((j = n) | element(j, n) | (~(g(j) = j))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.22/0.39 tff(83,plain,
% 0.22/0.39 (~(g(j) = j)),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[82, 68, 62])).
% 0.22/0.39 tff(84,plain,
% 0.22/0.39 (^[Y: $i] : refl(((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(85,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[84])).
% 0.22/0.39 tff(86,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(87,plain,
% 0.22/0.39 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(88,plain,
% 0.22/0.39 (![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[87])).
% 0.22/0.39 tff(89,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_12')).
% 0.22/0.39 tff(90,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.22/0.39 tff(91,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.22/0.39 tff(92,plain,(
% 0.22/0.39 ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.22/0.39 inference(skolemize,[status(sab)],[91])).
% 0.22/0.39 tff(93,plain,
% 0.22/0.39 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.22/0.39 tff(94,plain,
% 0.22/0.39 (((~![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))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(95,plain,
% 0.22/0.39 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((j = n) | element(j, n) | element(g(j), j))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(96,plain,
% 0.22/0.39 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (j = n) | element(j, n) | element(g(j), j)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.22/0.40 tff(97,plain,
% 0.22/0.40 ((j = n) | element(j, n) | element(g(j), j)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.22/0.40 tff(98,plain,
% 0.22/0.40 (element(g(j), j)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[97, 68, 62])).
% 0.22/0.40 tff(99,plain,
% 0.22/0.40 (((~![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))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(100,plain,
% 0.22/0.40 (((g(j) = k) | (g(j) = j) | (~element(g(j), j))) <=> ((g(j) = j) | (~element(g(j), j)) | (g(j) = k))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(101,plain,
% 0.22/0.40 (((~![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)))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[100])).
% 0.22/0.40 tff(102,plain,
% 0.22/0.40 (((~![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))),
% 0.22/0.40 inference(transitivity,[status(thm)],[101, 99])).
% 0.22/0.40 tff(103,plain,
% 0.22/0.40 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = k) | (g(j) = j) | (~element(g(j), j)))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(104,plain,
% 0.22/0.40 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (g(j) = j) | (~element(g(j), j)) | (g(j) = k)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.22/0.40 tff(105,plain,
% 0.22/0.40 (g(j) = k),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[104, 54, 98, 83])).
% 0.22/0.40 tff(106,plain,
% 0.22/0.40 (g(j) = n),
% 0.22/0.40 inference(transitivity,[status(thm)],[105, 63])).
% 0.22/0.40 tff(107,plain,
% 0.22/0.40 (^[Y: $i] : refl(((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(108,plain,
% 0.22/0.40 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[107])).
% 0.22/0.40 tff(109,plain,
% 0.22/0.40 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(110,plain,
% 0.22/0.40 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(111,plain,
% 0.22/0.40 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[110])).
% 0.22/0.40 tff(112,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_9')).
% 0.22/0.40 tff(113,plain,
% 0.22/0.40 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.22/0.40 tff(114,plain,
% 0.22/0.40 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.22/0.40 tff(115,plain,(
% 0.22/0.40 ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.22/0.40 inference(skolemize,[status(sab)],[114])).
% 0.22/0.40 tff(116,plain,
% 0.22/0.40 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.22/0.40 tff(117,plain,
% 0.22/0.40 (((~![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))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(118,plain,
% 0.22/0.40 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(j) = n)) | (j = n) | element(j, n))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(119,plain,
% 0.22/0.40 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(j) = n)) | (j = n) | element(j, n)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.22/0.40 tff(120,plain,
% 0.22/0.40 ((~(g(j) = n)) | (j = n) | element(j, n)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.22/0.40 tff(121,plain,
% 0.22/0.40 (~(g(j) = n)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[120, 68, 62])).
% 0.22/0.40 tff(122,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[121, 106])).
% 0.22/0.40 tff(123,plain,(element(j, k) | (~(n = k))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.40 tff(124,plain,
% 0.22/0.40 (element(j, k)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[123, 9])).
% 0.22/0.40 tff(125,plain,
% 0.22/0.40 ((k = j) <=> (j = k)),
% 0.22/0.40 inference(symmetry,[status(thm)],[17])).
% 0.22/0.40 tff(126,plain,
% 0.22/0.40 ((~(k = j)) <=> (~(j = k))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[125])).
% 0.22/0.40 tff(127,plain,
% 0.22/0.40 (~(j = k)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[61, 126])).
% 0.22/0.40 tff(128,plain,
% 0.22/0.40 (^[Y: $i] : refl(((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(129,plain,
% 0.22/0.40 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.22/0.40 tff(130,plain,
% 0.22/0.40 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(131,plain,
% 0.22/0.40 (^[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)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(132,plain,
% 0.22/0.40 (![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[131])).
% 0.22/0.40 tff(133,axiom,(![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_16')).
% 0.22/0.40 tff(134,plain,
% 0.22/0.40 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.22/0.40 tff(135,plain,
% 0.22/0.40 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.22/0.40 tff(136,plain,(
% 0.22/0.40 ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[135])).
% 0.22/0.40 tff(137,plain,
% 0.22/0.40 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.22/0.40 tff(138,plain,
% 0.22/0.40 (((~![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))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(139,plain,
% 0.22/0.40 (((j = k) | (j = m) | (j = n) | (~element(j, k))) <=> ((j = k) | (j = m) | (~element(j, k)) | (j = n))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(140,plain,
% 0.22/0.40 (((~![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)))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[139])).
% 0.22/0.40 tff(141,plain,
% 0.22/0.40 (((~![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))),
% 0.22/0.40 inference(transitivity,[status(thm)],[140, 138])).
% 0.22/0.40 tff(142,plain,
% 0.22/0.40 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((j = k) | (j = m) | (j = n) | (~element(j, k)))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(143,plain,
% 0.22/0.40 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (j = k) | (j = m) | (~element(j, k)) | (j = n)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.22/0.41 tff(144,plain,
% 0.22/0.41 ((j = m) | (j = n)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[143, 137, 127, 124])).
% 0.22/0.41 tff(145,plain,
% 0.22/0.41 (j = m),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[144, 62])).
% 0.22/0.41 tff(146,plain,
% 0.22/0.41 (element(k, j) <=> element(k, m)),
% 0.22/0.41 inference(monotonicity,[status(thm)],[145])).
% 0.22/0.41 tff(147,plain,
% 0.22/0.41 (((k = j) | element(k, j)) <=> ((k = j) | element(k, j))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(148,plain,
% 0.22/0.41 (![Y: $i] : ((k = j) | element(k, j)) <=> ((k = j) | element(k, j))),
% 0.22/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.41 tff(149,plain,
% 0.22/0.41 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j)) <=> ![Y: $i] : ((k = j) | element(k, j))),
% 0.22/0.41 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.41 tff(150,plain,
% 0.22/0.41 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j)) <=> ((k = j) | element(k, j))),
% 0.22/0.41 inference(transitivity,[status(thm)],[149, 148])).
% 0.22/0.41 tff(151,plain,
% 0.22/0.41 (^[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))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(152,plain,
% 0.22/0.41 (![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j)) <=> ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[151])).
% 0.22/0.41 tff(153,plain,
% 0.22/0.41 (![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j)) <=> ((k = j) | element(k, j))),
% 0.22/0.41 inference(transitivity,[status(thm)],[152, 150])).
% 0.22/0.41 tff(154,axiom,(![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_2')).
% 0.22/0.41 tff(155,plain,
% 0.22/0.41 ((k = j) | element(k, j)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.41 tff(156,plain,
% 0.22/0.41 ((k = j) | element(k, j)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[155, 147])).
% 0.22/0.41 tff(157,plain,
% 0.22/0.41 (element(k, j)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[156, 61])).
% 0.22/0.41 tff(158,plain,
% 0.22/0.41 (element(k, m)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[157, 146])).
% 0.22/0.41 tff(159,plain,
% 0.22/0.41 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(160,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[159])).
% 0.22/0.41 tff(161,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(162,plain,
% 0.22/0.41 (^[Y: $i] : trans(monotonicity(rewrite(((Y = m) | (~element(Y, m))) <=> ((~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> (((~element(Y, m)) | (Y = m)) | (~(f(Y) = Y))))), rewrite((((~element(Y, m)) | (Y = m)) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(163,plain,
% 0.22/0.41 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[162])).
% 0.22/0.41 tff(164,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_5')).
% 0.22/0.41 tff(165,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.22/0.41 tff(166,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.22/0.41 tff(167,plain,(
% 0.22/0.41 ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[166])).
% 0.22/0.41 tff(168,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.22/0.41 tff(169,plain,
% 0.22/0.41 (((~![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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(170,plain,
% 0.22/0.41 (((~element(k, m)) | (k = m) | (~(f(k) = k))) <=> ((k = m) | (~element(k, m)) | (~(f(k) = k)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(171,plain,
% 0.22/0.41 (((~![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))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[170])).
% 0.22/0.41 tff(172,plain,
% 0.22/0.41 (((~![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)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[171, 169])).
% 0.22/0.41 tff(173,plain,
% 0.22/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(k, m)) | (k = m) | (~(f(k) = k)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(174,plain,
% 0.22/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (k = m) | (~element(k, m)) | (~(f(k) = k))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.22/0.41 tff(175,plain,
% 0.22/0.41 (~(f(k) = k)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[174, 168, 158, 16])).
% 0.22/0.41 tff(176,plain,
% 0.22/0.41 (^[Y: $i] : refl(((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(177,plain,
% 0.22/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[176])).
% 0.22/0.41 tff(178,plain,
% 0.22/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(179,plain,
% 0.22/0.41 (^[Y: $i] : trans(monotonicity(rewrite(((Y = m) | (~element(Y, m))) <=> ((~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> (((~element(Y, m)) | (Y = m)) | (~(f(Y) = m))))), rewrite((((~element(Y, m)) | (Y = m)) | (~(f(Y) = m))) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))), ((((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(180,plain,
% 0.22/0.41 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[179])).
% 0.22/0.41 tff(181,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_4')).
% 0.22/0.41 tff(182,plain,
% 0.22/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.22/0.41 tff(183,plain,
% 0.22/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.22/0.41 tff(184,plain,(
% 0.22/0.41 ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.41 inference(skolemize,[status(sab)],[183])).
% 0.22/0.41 tff(185,plain,
% 0.22/0.41 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.22/0.41 tff(186,plain,
% 0.22/0.41 (((~![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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(187,plain,
% 0.22/0.41 (((~(f(k) = m)) | (~element(k, m)) | (k = m)) <=> ((k = m) | (~element(k, m)) | (~(f(k) = m)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(188,plain,
% 0.22/0.41 (((~![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))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[187])).
% 0.22/0.41 tff(189,plain,
% 0.22/0.41 (((~![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)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[188, 186])).
% 0.22/0.41 tff(190,plain,
% 0.22/0.41 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(k) = m)) | (~element(k, m)) | (k = m))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(191,plain,
% 0.22/0.41 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | (~(f(k) = m))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.22/0.41 tff(192,plain,
% 0.22/0.41 (~(f(k) = m)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[191, 185, 158, 16])).
% 0.22/0.41 tff(193,plain,
% 0.22/0.41 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ((~element(Y, m)) | (Y = m) | element(f(Y), Y)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(194,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[193])).
% 0.22/0.41 tff(195,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(196,plain,
% 0.22/0.41 (^[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))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(197,plain,
% 0.22/0.41 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[196])).
% 0.22/0.41 tff(198,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_7')).
% 0.22/0.41 tff(199,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.22/0.41 tff(200,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.22/0.41 tff(201,plain,(
% 0.22/0.41 ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.22/0.41 inference(skolemize,[status(sab)],[200])).
% 0.22/0.41 tff(202,plain,
% 0.22/0.41 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.22/0.41 tff(203,plain,
% 0.22/0.41 (((~![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))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(204,plain,
% 0.22/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(k, m)) | (k = m) | element(f(k), k))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(205,plain,
% 0.22/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(k, m)) | (k = m) | element(f(k), k)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.22/0.41 tff(206,plain,
% 0.22/0.41 (element(f(k), k)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[205, 202, 158, 16])).
% 0.22/0.41 tff(207,plain,
% 0.22/0.41 (((~![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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(208,plain,
% 0.22/0.41 (((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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(209,plain,
% 0.22/0.41 (((~![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))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[208])).
% 0.22/0.42 tff(210,plain,
% 0.22/0.42 (((~![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)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[209, 207])).
% 0.22/0.42 tff(211,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(k) = k) | (f(k) = m) | (f(k) = n) | (~element(f(k), k)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(212,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.22/0.42 tff(213,plain,
% 0.22/0.42 (f(k) = n),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[212, 137, 206, 192, 175])).
% 0.22/0.42 tff(214,plain,
% 0.22/0.42 (f(k) = k),
% 0.22/0.42 inference(transitivity,[status(thm)],[213, 9])).
% 0.22/0.42 tff(215,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[175, 214])).
% 0.22/0.42 tff(216,plain,(~(n = k)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(217,plain,
% 0.22/0.42 (~(k = n)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[216, 8])).
% 0.22/0.42 tff(218,assumption,(~element(k, n)), introduced(assumption)).
% 0.22/0.42 tff(219,plain,
% 0.22/0.42 (((~![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)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(220,plain,
% 0.22/0.42 (((k = n) | element(k, n) | (~(g(k) = k))) <=> (element(k, n) | (k = n) | (~(g(k) = k)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(221,plain,
% 0.22/0.42 (((~![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))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[220])).
% 0.22/0.42 tff(222,plain,
% 0.22/0.42 (((~![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)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[221, 219])).
% 0.22/0.42 tff(223,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((k = n) | element(k, n) | (~(g(k) = k)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(224,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | element(k, n) | (k = n) | (~(g(k) = k))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.22/0.42 tff(225,plain,
% 0.22/0.42 (~(g(k) = k)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[224, 78, 218, 217])).
% 0.22/0.42 tff(226,plain,
% 0.22/0.42 (((~![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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(227,plain,
% 0.22/0.42 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(k) = n)) | (k = n) | element(k, n))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(228,plain,
% 0.22/0.42 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(k) = n)) | (k = n) | element(k, n)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.22/0.42 tff(229,plain,
% 0.22/0.42 (~(g(k) = n)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[228, 116, 218, 217])).
% 0.22/0.42 tff(230,plain,
% 0.22/0.42 (((~![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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(231,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((k = n) | element(k, n) | element(g(k), k))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(232,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (k = n) | element(k, n) | element(g(k), k)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.22/0.42 tff(233,plain,
% 0.22/0.42 (element(g(k), k)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[232, 93, 218, 217])).
% 0.22/0.42 tff(234,plain,
% 0.22/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(235,plain,
% 0.22/0.42 (((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k))) <=> ((g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(236,plain,
% 0.22/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[235])).
% 0.22/0.42 tff(237,plain,
% 0.22/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[236, 234])).
% 0.22/0.42 tff(238,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((g(k) = k) | (g(k) = m) | (g(k) = n) | (~element(g(k), k)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(239,plain,
% 0.22/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (g(k) = n) | (g(k) = k) | (g(k) = m) | (~element(g(k), k))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.22/0.42 tff(240,plain,
% 0.22/0.42 (g(k) = m),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[239, 137, 233, 229, 225])).
% 0.22/0.42 tff(241,plain,
% 0.22/0.42 (element(k, g(k)) <=> element(k, m)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[240])).
% 0.22/0.42 tff(242,plain,
% 0.22/0.42 (^[Y: $i] : refl((element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> (element(Y, g(Y)) | (Y = n) | element(Y, n)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(243,plain,
% 0.22/0.42 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[242])).
% 0.22/0.42 tff(244,plain,
% 0.22/0.42 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(245,plain,
% 0.22/0.42 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | element(Y, g(Y))) <=> (element(Y, g(Y)) | (Y = n) | element(Y, n)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(246,plain,
% 0.22/0.42 (![Y: $i] : (((Y = n) | element(Y, n)) | element(Y, g(Y))) <=> ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[245])).
% 0.22/0.42 tff(247,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(Y, g(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_11')).
% 0.22/0.42 tff(248,plain,
% 0.22/0.42 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.22/0.42 tff(249,plain,
% 0.22/0.42 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.22/0.42 tff(250,plain,(
% 0.22/0.42 ![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.22/0.42 inference(skolemize,[status(sab)],[249])).
% 0.22/0.42 tff(251,plain,
% 0.22/0.42 (![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.22/0.42 tff(252,plain,
% 0.22/0.42 (((~![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))) | (element(k, n) | (k = n) | element(k, g(k)))) <=> ((~![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))) | element(k, n) | (k = n) | element(k, g(k)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(253,plain,
% 0.22/0.42 ((element(k, g(k)) | (k = n) | element(k, n)) <=> (element(k, n) | (k = n) | element(k, g(k)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(254,plain,
% 0.22/0.42 (((~![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))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[253])).
% 0.22/0.42 tff(255,plain,
% 0.22/0.42 (((~![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)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[254, 252])).
% 0.22/0.42 tff(256,plain,
% 0.22/0.42 ((~![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))) | (element(k, g(k)) | (k = n) | element(k, n))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(257,plain,
% 0.22/0.42 ((~![Y: $i] : (element(Y, g(Y)) | (Y = n) | element(Y, n))) | element(k, n) | (k = n) | element(k, g(k))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.22/0.42 tff(258,plain,
% 0.22/0.42 (element(k, g(k))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[257, 251, 218, 217])).
% 0.22/0.42 tff(259,plain,
% 0.22/0.42 (element(k, m)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[258, 241])).
% 0.22/0.42 tff(260,plain,
% 0.22/0.42 ((k = m) | (~(f(k) = k))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[174, 168, 259])).
% 0.22/0.42 tff(261,plain,
% 0.22/0.42 (~(f(k) = k)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[260, 5])).
% 0.22/0.42 tff(262,plain,
% 0.22/0.42 ((k = m) | (~(f(k) = m))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[191, 185, 259])).
% 0.22/0.42 tff(263,plain,
% 0.22/0.42 (~(f(k) = m)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[262, 5])).
% 0.22/0.42 tff(264,plain,
% 0.22/0.42 ((k = m) | element(f(k), k)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[205, 202, 259])).
% 0.22/0.42 tff(265,plain,
% 0.22/0.42 (element(f(k), k)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[264, 5])).
% 0.22/0.42 tff(266,plain,
% 0.22/0.42 (f(k) = n),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[212, 137, 265, 263, 261])).
% 0.22/0.42 tff(267,plain,
% 0.22/0.42 (element(k, f(k)) <=> element(k, n)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[266])).
% 0.22/0.42 tff(268,plain,
% 0.22/0.42 (element(k, n) <=> element(k, f(k))),
% 0.22/0.42 inference(symmetry,[status(thm)],[267])).
% 0.22/0.42 tff(269,plain,
% 0.22/0.42 ((~element(k, n)) <=> (~element(k, f(k)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[268])).
% 0.22/0.42 tff(270,plain,
% 0.22/0.42 (~element(k, f(k))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[218, 269])).
% 0.22/0.43 tff(271,plain,
% 0.22/0.43 (^[Y: $i] : refl((element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(272,plain,
% 0.22/0.43 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[271])).
% 0.22/0.43 tff(273,plain,
% 0.22/0.43 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(274,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(275,plain,
% 0.22/0.43 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y))) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[274])).
% 0.22/0.43 tff(276,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_6')).
% 0.22/0.43 tff(277,plain,
% 0.22/0.43 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.22/0.43 tff(278,plain,
% 0.22/0.43 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.22/0.43 tff(279,plain,(
% 0.22/0.43 ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.43 inference(skolemize,[status(sab)],[278])).
% 0.22/0.43 tff(280,plain,
% 0.22/0.43 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.22/0.43 tff(281,plain,
% 0.22/0.43 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((k = m) | element(k, f(k)) | (~element(k, m)))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (k = m) | element(k, f(k)) | (~element(k, m)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(282,plain,
% 0.22/0.43 ((element(k, f(k)) | (~element(k, m)) | (k = m)) <=> ((k = m) | element(k, f(k)) | (~element(k, m)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(283,plain,
% 0.22/0.43 (((~![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, f(k)) | (~element(k, m))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[282])).
% 0.22/0.43 tff(284,plain,
% 0.22/0.43 (((~![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, f(k)) | (~element(k, m)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[283, 281])).
% 0.22/0.43 tff(285,plain,
% 0.22/0.43 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(k, f(k)) | (~element(k, m)) | (k = m))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(286,plain,
% 0.22/0.43 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (k = m) | element(k, f(k)) | (~element(k, m))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.22/0.43 tff(287,plain,
% 0.22/0.43 ((k = m) | element(k, f(k))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[286, 280, 259])).
% 0.22/0.43 tff(288,plain,
% 0.22/0.43 (element(k, f(k))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[287, 5])).
% 0.22/0.43 tff(289,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[288, 270])).
% 0.22/0.43 tff(290,plain,(element(k, n) | (m = k)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(291,plain,
% 0.22/0.43 (element(k, n)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[290, 4])).
% 0.22/0.43 tff(292,plain,
% 0.22/0.43 (^[V: $i, Y: $i] : refl(((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(293,plain,
% 0.22/0.43 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[292])).
% 0.22/0.43 tff(294,plain,
% 0.22/0.43 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(295,plain,
% 0.22/0.43 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Y = n) | (~element(Y, n))) <=> ((Y = n) | (~element(Y, n)))), ((((Y = n) | (~element(Y, n))) | (V = n)) <=> (((Y = n) | (~element(Y, n))) | (V = n)))), rewrite((((Y = n) | (~element(Y, n))) | (V = n)) <=> ((Y = n) | (V = n) | (~element(Y, n)))), ((((Y = n) | (~element(Y, n))) | (V = n)) <=> ((Y = n) | (V = n) | (~element(Y, n))))), (((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) <=> (((Y = n) | (V = n) | (~element(Y, n))) | (V = Y)))), rewrite((((Y = n) | (V = n) | (~element(Y, n))) | (V = Y)) <=> ((Y = n) | (V = Y) | (V = n) | (~element(Y, n)))), (((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) <=> ((Y = n) | (V = Y) | (V = n) | (~element(Y, n))))), ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) <=> (((Y = n) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(Y, V))))), rewrite((((Y = n) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(Y, V))) <=> ((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n)))), ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) <=> ((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))))), (((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> (((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(V, Y))))), rewrite((((Y = n) | (~element(Y, V)) | (V = Y) | (V = n) | (~element(Y, n))) | (~element(V, Y))) <=> ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))), (((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(296,plain,
% 0.22/0.43 (![V: $i, Y: $i] : ((((((Y = n) | (~element(Y, n))) | (V = n)) | (V = Y)) | (~element(Y, V))) | (~element(V, Y))) <=> ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[295])).
% 0.22/0.43 tff(297,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')).
% 0.22/0.43 tff(298,plain,
% 0.22/0.43 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.22/0.43 tff(299,plain,
% 0.22/0.43 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.22/0.43 tff(300,plain,(
% 0.22/0.43 ![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[299])).
% 0.22/0.43 tff(301,plain,
% 0.22/0.43 (![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.22/0.43 tff(302,plain,
% 0.22/0.43 (((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((m = n) | (m = k) | (~element(k, n)) | (~element(k, m)) | (k = n) | (~element(m, k)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (m = k) | (~element(k, n)) | (~element(k, m)) | (k = n) | (~element(m, k)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(303,plain,
% 0.22/0.43 (((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n))) <=> ((m = n) | (m = k) | (~element(k, n)) | (~element(k, m)) | (k = n) | (~element(m, k)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(304,plain,
% 0.22/0.43 (((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((m = n) | (m = k) | (~element(k, n)) | (~element(k, m)) | (k = n) | (~element(m, k))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[303])).
% 0.22/0.43 tff(305,plain,
% 0.22/0.43 (((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n)))) <=> ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (m = k) | (~element(k, n)) | (~element(k, m)) | (k = n) | (~element(m, k)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[304, 302])).
% 0.22/0.43 tff(306,plain,
% 0.22/0.43 ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | ((k = n) | (~element(k, m)) | (~element(m, k)) | (m = k) | (m = n) | (~element(k, n)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(307,plain,
% 0.22/0.43 ((~![V: $i, Y: $i] : ((Y = n) | (~element(Y, V)) | (~element(V, Y)) | (V = Y) | (V = n) | (~element(Y, n)))) | (m = n) | (m = k) | (~element(k, n)) | (~element(k, m)) | (k = n) | (~element(m, k))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.22/0.43 tff(308,plain,
% 0.22/0.43 ((~element(k, n)) | (~element(k, m))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[307, 14, 301, 43, 4, 217])).
% 0.22/0.43 tff(309,plain,
% 0.22/0.43 (~element(k, m)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[308, 291])).
% 0.22/0.43 tff(310,plain,
% 0.22/0.43 ((n = m) <=> (m = n)),
% 0.22/0.43 inference(commutativity,[status(thm)],[])).
% 0.22/0.44 tff(311,plain,
% 0.22/0.44 ((m = n) <=> (n = m)),
% 0.22/0.44 inference(symmetry,[status(thm)],[310])).
% 0.22/0.44 tff(312,plain,
% 0.22/0.44 ((~(m = n)) <=> (~(n = m))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[311])).
% 0.22/0.44 tff(313,plain,
% 0.22/0.44 (~(n = m)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[14, 312])).
% 0.22/0.44 tff(314,plain,
% 0.22/0.44 (((n = k) | element(n, k)) <=> ((n = k) | element(n, k))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(315,plain,
% 0.22/0.44 (![Y: $i] : ((n = k) | element(n, k)) <=> ((n = k) | element(n, k))),
% 0.22/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.44 tff(316,plain,
% 0.22/0.44 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ![Y: $i] : ((n = k) | element(n, k))),
% 0.22/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.44 tff(317,plain,
% 0.22/0.44 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ((n = k) | element(n, k))),
% 0.22/0.44 inference(transitivity,[status(thm)],[316, 315])).
% 0.22/0.44 tff(318,plain,
% 0.22/0.44 (^[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)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(319,plain,
% 0.22/0.44 (![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[318])).
% 0.22/0.44 tff(320,plain,
% 0.22/0.44 (![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k)) <=> ((n = k) | element(n, k))),
% 0.22/0.44 inference(transitivity,[status(thm)],[319, 317])).
% 0.22/0.44 tff(321,axiom,(![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_15')).
% 0.22/0.44 tff(322,plain,
% 0.22/0.44 ((n = k) | element(n, k)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.22/0.44 tff(323,plain,
% 0.22/0.44 ((n = k) | element(n, k)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[322, 314])).
% 0.22/0.44 tff(324,plain,
% 0.22/0.44 (element(n, k)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[323, 216])).
% 0.22/0.44 tff(325,plain,
% 0.22/0.44 (^[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)))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(326,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[325])).
% 0.22/0.44 tff(327,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(328,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(329,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[328])).
% 0.22/0.44 tff(330,axiom,(![Y: $i, V1: $i] : ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_8')).
% 0.22/0.44 tff(331,plain,
% 0.22/0.44 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.22/0.44 tff(332,plain,
% 0.22/0.44 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.22/0.44 tff(333,plain,(
% 0.22/0.44 ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.22/0.44 inference(skolemize,[status(sab)],[332])).
% 0.22/0.44 tff(334,plain,
% 0.22/0.44 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.22/0.44 tff(335,plain,
% 0.22/0.44 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = k) | element(k, m) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = k) | element(k, m) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(336,plain,
% 0.22/0.44 (((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m)) <=> ((n = k) | element(k, m) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(337,plain,
% 0.22/0.44 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = k) | element(k, m) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.44 tff(338,plain,
% 0.22/0.44 (((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m))) <=> ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = k) | element(k, m) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[337, 335])).
% 0.22/0.44 tff(339,plain,
% 0.22/0.44 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | ((n = m) | (~element(n, k)) | (~element(k, n)) | (n = k) | element(k, m) | (k = m))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(340,plain,
% 0.22/0.44 ((~![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))) | (n = k) | element(k, m) | (k = m) | (n = m) | (~element(k, n)) | (~element(n, k))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.22/0.44 tff(341,plain,
% 0.22/0.44 (element(k, m) | (k = m) | (n = m) | (~element(k, n))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[340, 334, 216, 324])).
% 0.22/0.44 tff(342,plain,
% 0.22/0.44 (element(k, m) | (k = m) | (~element(k, n))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[341, 313])).
% 0.22/0.44 tff(343,plain,
% 0.22/0.44 (k = m),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[342, 309, 291])).
% 0.22/0.44 tff(344,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[343, 5])).
% 0.22/0.44 tff(345,plain,(m = k), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(346,plain,
% 0.22/0.44 (k = m),
% 0.22/0.44 inference(symmetry,[status(thm)],[345])).
% 0.22/0.44 tff(347,plain,
% 0.22/0.44 (element(f(n), k) <=> element(f(n), m)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[346])).
% 0.22/0.44 tff(348,plain,
% 0.22/0.44 (element(f(n), m) <=> element(f(n), k)),
% 0.22/0.44 inference(symmetry,[status(thm)],[347])).
% 0.22/0.44 tff(349,plain,
% 0.22/0.44 ((n = f(n)) <=> (f(n) = n)),
% 0.22/0.44 inference(commutativity,[status(thm)],[])).
% 0.22/0.44 tff(350,plain,
% 0.22/0.44 ((f(n) = n) <=> (n = f(n))),
% 0.22/0.44 inference(symmetry,[status(thm)],[349])).
% 0.22/0.44 tff(351,plain,
% 0.22/0.44 ((~(f(n) = n)) <=> (~(n = f(n)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[350])).
% 0.22/0.44 tff(352,plain,
% 0.22/0.44 (element(n, m) <=> element(n, k)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[345])).
% 0.22/0.44 tff(353,plain,
% 0.22/0.44 (element(n, k) <=> element(n, m)),
% 0.22/0.44 inference(symmetry,[status(thm)],[352])).
% 0.22/0.44 tff(354,plain,
% 0.22/0.44 (element(n, m)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[324, 353])).
% 0.22/0.45 tff(355,plain,
% 0.22/0.45 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((n = m) | (~element(n, m)) | (~(f(n) = n)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (n = m) | (~element(n, m)) | (~(f(n) = n)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(356,plain,
% 0.22/0.45 (((~element(n, m)) | (n = m) | (~(f(n) = n))) <=> ((n = m) | (~element(n, m)) | (~(f(n) = n)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(357,plain,
% 0.22/0.45 (((~![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)))) | ((n = m) | (~element(n, m)) | (~(f(n) = n))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[356])).
% 0.22/0.45 tff(358,plain,
% 0.22/0.45 (((~![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)))) | (n = m) | (~element(n, m)) | (~(f(n) = n)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[357, 355])).
% 0.22/0.45 tff(359,plain,
% 0.22/0.45 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(n, m)) | (n = m) | (~(f(n) = n)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(360,plain,
% 0.22/0.45 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (n = m) | (~element(n, m)) | (~(f(n) = n))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.22/0.45 tff(361,plain,
% 0.22/0.45 (~(f(n) = n)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[360, 168, 354, 313])).
% 0.22/0.45 tff(362,plain,
% 0.22/0.45 (~(n = f(n))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[361, 351])).
% 0.22/0.45 tff(363,plain,
% 0.22/0.45 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((n = m) | (~element(n, m)) | (~(f(n) = m)))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | (~(f(n) = m)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(364,plain,
% 0.22/0.45 (((~(f(n) = m)) | (~element(n, m)) | (n = m)) <=> ((n = m) | (~element(n, m)) | (~(f(n) = m)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(365,plain,
% 0.22/0.45 (((~![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))) | ((n = m) | (~element(n, m)) | (~(f(n) = m))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[364])).
% 0.22/0.45 tff(366,plain,
% 0.22/0.45 (((~![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))) | (n = m) | (~element(n, m)) | (~(f(n) = m)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[365, 363])).
% 0.22/0.45 tff(367,plain,
% 0.22/0.45 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(368,plain,
% 0.22/0.45 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (n = m) | (~element(n, m)) | (~(f(n) = m))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.22/0.45 tff(369,plain,
% 0.22/0.45 (~(f(n) = m)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[368, 185, 354, 313])).
% 0.22/0.45 tff(370,plain,
% 0.22/0.45 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((n = m) | element(n, f(n)) | (~element(n, m)))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (n = m) | element(n, f(n)) | (~element(n, m)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(371,plain,
% 0.22/0.45 ((element(n, f(n)) | (~element(n, m)) | (n = m)) <=> ((n = m) | element(n, f(n)) | (~element(n, m)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(372,plain,
% 0.22/0.45 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((n = m) | element(n, f(n)) | (~element(n, m))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[371])).
% 0.22/0.45 tff(373,plain,
% 0.22/0.45 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (n = m) | element(n, f(n)) | (~element(n, m)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[372, 370])).
% 0.22/0.45 tff(374,plain,
% 0.22/0.45 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(375,plain,
% 0.22/0.45 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (n = m) | element(n, f(n)) | (~element(n, m))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.22/0.45 tff(376,plain,
% 0.22/0.45 (element(n, f(n))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[375, 280, 354, 313])).
% 0.22/0.45 tff(377,plain,
% 0.22/0.45 (((~![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))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(378,plain,
% 0.22/0.45 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(n, m)) | (n = m) | element(f(n), n))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(379,plain,
% 0.22/0.45 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(n, m)) | (n = m) | element(f(n), n)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.22/0.45 tff(380,plain,
% 0.22/0.45 (element(f(n), n)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[379, 202, 354, 313])).
% 0.22/0.45 tff(381,plain,
% 0.22/0.45 (((~![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))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(382,plain,
% 0.22/0.45 (((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))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(383,plain,
% 0.22/0.45 (((~![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)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[382])).
% 0.22/0.45 tff(384,plain,
% 0.22/0.45 (((~![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))),
% 0.22/0.45 inference(transitivity,[status(thm)],[383, 381])).
% 0.22/0.46 tff(385,plain,
% 0.22/0.46 ((~![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))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(386,plain,
% 0.22/0.46 ((~![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)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.22/0.46 tff(387,plain,
% 0.22/0.46 ((n = f(n)) | element(f(n), m)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[386, 334, 313, 380, 376, 369])).
% 0.22/0.46 tff(388,plain,
% 0.22/0.46 (element(f(n), m)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[387, 362])).
% 0.22/0.46 tff(389,plain,
% 0.22/0.46 (element(f(n), k)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[388, 348])).
% 0.22/0.46 tff(390,plain,
% 0.22/0.46 ((f(n) = k) <=> (f(n) = m)),
% 0.22/0.46 inference(monotonicity,[status(thm)],[346])).
% 0.22/0.46 tff(391,plain,
% 0.22/0.46 ((f(n) = m) <=> (f(n) = k)),
% 0.22/0.46 inference(symmetry,[status(thm)],[390])).
% 0.22/0.46 tff(392,plain,
% 0.22/0.46 ((~(f(n) = m)) <=> (~(f(n) = k))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[391])).
% 0.22/0.46 tff(393,plain,
% 0.22/0.46 (~(f(n) = k)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[369, 392])).
% 0.22/0.46 tff(394,plain,
% 0.22/0.46 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = m) | (f(n) = n) | (~element(f(n), k)) | (f(n) = k))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)) | (f(n) = k))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(395,plain,
% 0.22/0.46 (((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k))) <=> ((f(n) = m) | (f(n) = n) | (~element(f(n), k)) | (f(n) = k))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(396,plain,
% 0.22/0.46 (((~![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) | (~element(f(n), k)) | (f(n) = k)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[395])).
% 0.22/0.46 tff(397,plain,
% 0.22/0.46 (((~![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) | (~element(f(n), k)) | (f(n) = k))),
% 0.22/0.46 inference(transitivity,[status(thm)],[396, 394])).
% 0.22/0.46 tff(398,plain,
% 0.22/0.46 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(399,plain,
% 0.22/0.46 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)) | (f(n) = k)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.22/0.46 tff(400,plain,
% 0.22/0.46 ((~element(f(n), k)) | (f(n) = k)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[399, 137, 369, 361])).
% 0.22/0.46 tff(401,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[400, 393, 389])).
% 0.22/0.46 % SZS output end Proof
% 0.22/0.46 % E exiting
%------------------------------------------------------------------------------