%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN014-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN014-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:26:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(k_type, type, (
% 0.19/0.38 k: $i)).
% 0.19/0.38 tff(f_type, type, (
% 0.19/0.38 f: $i > $i)).
% 0.19/0.38 tff(n_type, type, (
% 0.19/0.38 n: $i)).
% 0.19/0.38 tff(m_type, type, (
% 0.19/0.38 m: $i)).
% 0.19/0.38 tff(element_type, type, (
% 0.19/0.38 element: ( $i * $i ) > $o)).
% 0.19/0.38 tff(j_type, type, (
% 0.19/0.38 j: $i)).
% 0.19/0.38 tff(g_type, type, (
% 0.19/0.38 g: $i > $i)).
% 0.19/0.38 tff(1,assumption,(n = k), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((k = m) <=> (m = k)),
% 0.19/0.38 inference(commutativity,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 ((m = k) <=> (k = m)),
% 0.19/0.38 inference(symmetry,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 ((~(m = k)) <=> (~(k = m))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 ((m = n) <=> (m = k)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 ((~(m = n)) <=> (~(m = k))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 ((~(m = n)) <=> (~(m = n))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(8,axiom,(~(m = n)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_1')).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (~(m = n)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~(m = k)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (~(k = m)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 ((j = k) <=> (k = j)),
% 0.19/0.38 inference(commutativity,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((j = n) <=> (j = k)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((j = n) <=> (k = j)),
% 0.19/0.38 inference(transitivity,[status(thm)],[13, 12])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((k = j) <=> (j = n)),
% 0.19/0.38 inference(symmetry,[status(thm)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ((~(k = j)) <=> (~(j = n))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.38 tff(17,assumption,(k = j), introduced(assumption)).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (j = k),
% 0.19/0.38 inference(symmetry,[status(thm)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ((m = j) <=> (m = k)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((m = k) <=> (m = j)),
% 0.19/0.38 inference(symmetry,[status(thm)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ((~(m = k)) <=> (~(m = j))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.38 tff(22,assumption,(~(m = k)), introduced(assumption)).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (~(m = j)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (element(m, j) <=> element(m, k)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (element(m, k) <=> element(m, j)),
% 0.19/0.38 inference(symmetry,[status(thm)],[24])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (((m = k) | element(m, k)) <=> ((m = k) | element(m, k))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 ((element(m, k) | (m = k)) <=> ((m = k) | element(m, k))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![Y: $i] : (element(m, k) | (m = k)) <=> (element(m, k) | (m = k))),
% 0.19/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> ![Y: $i] : (element(m, k) | (m = k))),
% 0.19/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> (element(m, k) | (m = k))),
% 0.19/0.38 inference(transitivity,[status(thm)],[29, 28])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k)) <=> ((m = k) | element(m, k))),
% 0.19/0.38 inference(transitivity,[status(thm)],[30, 27])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | (~(Y = m)) | element(Y, k))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k)) <=> ((m = k) | element(m, k))),
% 0.19/0.38 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.38 tff(35,axiom,(![Y: $i] : (((Y = k) | (~(Y = m))) | element(Y, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_15')).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ((m = k) | element(m, k)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 ((m = k) | element(m, k)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (element(m, k)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[37, 22])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (element(m, j)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[38, 25])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (^[Y: $i] : refl(((Y = k) | (Y = j) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (^[Y: $i] : rewrite((((Y = j) | (Y = k)) | (~element(Y, j))) <=> ((Y = k) | (Y = j) | (~element(Y, j))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j))) <=> ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.38 tff(45,axiom,(![Y: $i] : (((Y = j) | (Y = k)) | (~element(Y, j)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_4')).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.38 tff(48,plain,(
% 0.19/0.38 ![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[47])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (((~![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((m = k) | (m = j) | (~element(m, j)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (m = k) | (m = j) | (~element(m, j))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 ((m = j) | (~element(m, j))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 22, 49])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[53, 39, 23])).
% 0.19/0.38 tff(55,plain,((~(k = j)) | (m = k)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (~(k = j)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[55, 10])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (~(j = n)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[56, 16])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (k = n),
% 0.19/0.38 inference(symmetry,[status(thm)],[1])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (element(j, n) <=> element(j, k)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (element(j, k) <=> element(j, n)),
% 0.19/0.38 inference(symmetry,[status(thm)],[59])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 ((~element(j, k)) <=> (~element(j, n))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.38 tff(62,assumption,(~element(j, k)), introduced(assumption)).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (~element(j, n)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (^[Y: $i] : refl(((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ((Y = n) | element(Y, n) | (~(g(Y) = Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y))) <=> ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.38 tff(69,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_11')).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.38 tff(72,plain,(
% 0.19/0.38 ![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[71])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (((~![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | ((j = n) | element(j, n) | (~(g(j) = j)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 ((~![Y: $i] : ((Y = n) | element(Y, n) | (~(g(Y) = Y)))) | (j = n) | element(j, n) | (~(g(j) = j))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 ((j = n) | element(j, n) | (~(g(j) = j))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (~(g(j) = j)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[77, 63, 57])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (^[Y: $i] : refl(((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ((Y = n) | element(Y, n) | element(g(Y), Y)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y)) <=> ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.38 tff(84,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | element(g(Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_13')).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.19/0.38 tff(87,plain,(
% 0.19/0.38 ![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.19/0.38 inference(skolemize,[status(sab)],[86])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 (![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 (((~![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))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(90,plain,
% 0.19/0.38 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | ((j = n) | element(j, n) | element(g(j), j))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 ((~![Y: $i] : ((Y = n) | element(Y, n) | element(g(Y), Y))) | (j = n) | element(j, n) | element(g(j), j)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 ((j = n) | element(j, n) | element(g(j), j)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.19/0.38 tff(93,plain,
% 0.19/0.38 (element(g(j), j)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[92, 63, 57])).
% 0.19/0.38 tff(94,plain,
% 0.19/0.39 (((~![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (((g(j) = k) | (g(j) = j) | (~element(g(j), j))) <=> ((g(j) = j) | (~element(g(j), j)) | (g(j) = k))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (((~![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))),
% 0.19/0.39 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | ((g(j) = k) | (g(j) = j) | (~element(g(j), j)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~![Y: $i] : ((Y = k) | (Y = j) | (~element(Y, j)))) | (g(j) = j) | (~element(g(j), j)) | (g(j) = k)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (g(j) = k),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 49, 93, 78])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (g(j) = n),
% 0.19/0.39 inference(transitivity,[status(thm)],[100, 58])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (^[Y: $i] : refl(((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n)) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (^[Y: $i] : rewrite((((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ((~(g(Y) = n)) | (Y = n) | element(Y, n)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n))) <=> ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.39 tff(107,axiom,(![Y: $i] : (((Y = n) | element(Y, n)) | (~(g(Y) = n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_10')).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.39 tff(110,plain,(
% 0.19/0.39 ![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.19/0.39 inference(skolemize,[status(sab)],[109])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 (((~![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | ((~(g(j) = n)) | (j = n) | element(j, n))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 ((~![Y: $i] : ((~(g(Y) = n)) | (Y = n) | element(Y, n))) | (~(g(j) = n)) | (j = n) | element(j, n)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 ((~(g(j) = n)) | (j = n) | element(j, n)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 (~(g(j) = n)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[115, 63, 57])).
% 0.19/0.39 tff(117,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[116, 101])).
% 0.19/0.39 tff(118,plain,(element(j, k) | (~(n = k))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(119,plain,
% 0.19/0.39 (element(j, k)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[118, 1])).
% 0.19/0.39 tff(120,plain,
% 0.19/0.39 ((k = j) <=> (j = k)),
% 0.19/0.39 inference(symmetry,[status(thm)],[12])).
% 0.19/0.39 tff(121,plain,
% 0.19/0.39 ((~(k = j)) <=> (~(j = k))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[120])).
% 0.19/0.39 tff(122,plain,
% 0.19/0.39 (~(j = k)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[56, 121])).
% 0.19/0.39 tff(123,plain,
% 0.19/0.39 (^[Y: $i] : refl(((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(124,plain,
% 0.19/0.39 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.39 tff(125,plain,
% 0.19/0.39 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(126,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(127,plain,
% 0.19/0.39 (![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k))) <=> ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.39 tff(128,axiom,(![Y: $i] : ((((Y = k) | (Y = m)) | (Y = n)) | (~element(Y, k)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_17')).
% 0.19/0.39 tff(129,plain,
% 0.19/0.39 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.39 tff(130,plain,
% 0.19/0.39 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.39 tff(131,plain,(
% 0.19/0.39 ![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[130])).
% 0.19/0.39 tff(132,plain,
% 0.19/0.39 (![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.39 tff(133,plain,
% 0.19/0.39 (((~![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(134,plain,
% 0.19/0.39 (((j = k) | (j = m) | (j = n) | (~element(j, k))) <=> ((j = k) | (j = m) | (~element(j, k)) | (j = n))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(135,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.39 tff(136,plain,
% 0.19/0.39 (((~![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))),
% 0.19/0.39 inference(transitivity,[status(thm)],[135, 133])).
% 0.19/0.39 tff(137,plain,
% 0.19/0.39 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((j = k) | (j = m) | (j = n) | (~element(j, k)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(138,plain,
% 0.19/0.39 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (j = k) | (j = m) | (~element(j, k)) | (j = n)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.39 tff(139,plain,
% 0.19/0.39 ((j = m) | (j = n)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[138, 132, 122, 119])).
% 0.19/0.39 tff(140,plain,
% 0.19/0.39 (j = m),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[139, 57])).
% 0.19/0.39 tff(141,plain,
% 0.19/0.39 (element(k, j) <=> element(k, m)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.39 tff(142,plain,
% 0.19/0.39 (((k = j) | element(k, j)) <=> ((k = j) | element(k, j))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(143,plain,
% 0.19/0.39 (![Y: $i] : ((k = j) | element(k, j)) <=> ((k = j) | element(k, j))),
% 0.19/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.39 tff(144,plain,
% 0.19/0.39 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j)) <=> ![Y: $i] : ((k = j) | element(k, j))),
% 0.19/0.39 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.39 tff(145,plain,
% 0.19/0.39 (![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j)) <=> ((k = j) | element(k, j))),
% 0.19/0.39 inference(transitivity,[status(thm)],[144, 143])).
% 0.19/0.39 tff(146,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(147,plain,
% 0.19/0.39 (![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j)) <=> ![Y: $i] : (element(Y, j) | (~(Y = k)) | (Y = j))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.39 tff(148,plain,
% 0.19/0.39 (![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j)) <=> ((k = j) | element(k, j))),
% 0.19/0.39 inference(transitivity,[status(thm)],[147, 145])).
% 0.19/0.39 tff(149,axiom,(![Y: $i] : (((Y = j) | (~(Y = k))) | element(Y, j))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_3')).
% 0.19/0.39 tff(150,plain,
% 0.19/0.39 ((k = j) | element(k, j)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.39 tff(151,plain,
% 0.19/0.39 ((k = j) | element(k, j)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[150, 142])).
% 0.19/0.39 tff(152,plain,
% 0.19/0.39 (element(k, j)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[151, 56])).
% 0.19/0.39 tff(153,plain,
% 0.19/0.39 (element(k, m)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[152, 141])).
% 0.19/0.39 tff(154,plain,
% 0.19/0.39 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(155,plain,
% 0.19/0.39 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.39 tff(156,plain,
% 0.19/0.39 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(157,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(158,plain,
% 0.19/0.39 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y))) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.39 tff(159,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_6')).
% 0.19/0.39 tff(160,plain,
% 0.19/0.39 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.39 tff(161,plain,
% 0.19/0.39 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.19/0.39 tff(162,plain,(
% 0.19/0.39 ![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[161])).
% 0.19/0.39 tff(163,plain,
% 0.19/0.39 (![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.19/0.39 tff(164,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(165,plain,
% 0.19/0.39 (((~element(k, m)) | (k = m) | (~(f(k) = k))) <=> ((k = m) | (~element(k, m)) | (~(f(k) = k)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(166,plain,
% 0.19/0.40 (((~![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))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.40 tff(167,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[166, 164])).
% 0.19/0.40 tff(168,plain,
% 0.19/0.40 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(k, m)) | (k = m) | (~(f(k) = k)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(169,plain,
% 0.19/0.40 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (k = m) | (~element(k, m)) | (~(f(k) = k))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.40 tff(170,plain,
% 0.19/0.40 (~(f(k) = k)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[169, 163, 153, 11])).
% 0.19/0.40 tff(171,plain,
% 0.19/0.40 (^[Y: $i] : refl(((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(172,plain,
% 0.19/0.40 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[171])).
% 0.19/0.40 tff(173,plain,
% 0.19/0.40 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(174,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(175,plain,
% 0.19/0.40 (![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m))) <=> ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[174])).
% 0.19/0.40 tff(176,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | (~(f(Y) = m)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_5')).
% 0.19/0.40 tff(177,plain,
% 0.19/0.40 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.40 tff(178,plain,
% 0.19/0.40 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.19/0.40 tff(179,plain,(
% 0.19/0.40 ![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.40 inference(skolemize,[status(sab)],[178])).
% 0.19/0.40 tff(180,plain,
% 0.19/0.40 (![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.19/0.40 tff(181,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(182,plain,
% 0.19/0.40 (((~(f(k) = m)) | (~element(k, m)) | (k = m)) <=> ((k = m) | (~element(k, m)) | (~(f(k) = m)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(183,plain,
% 0.19/0.40 (((~![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))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.40 tff(184,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[183, 181])).
% 0.19/0.40 tff(185,plain,
% 0.19/0.40 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(k) = m)) | (~element(k, m)) | (k = m))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(186,plain,
% 0.19/0.40 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (k = m) | (~element(k, m)) | (~(f(k) = m))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.40 tff(187,plain,
% 0.19/0.40 (~(f(k) = m)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[186, 180, 153, 11])).
% 0.19/0.40 tff(188,plain,
% 0.19/0.40 (^[Y: $i] : refl(((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ((~element(Y, m)) | (Y = m) | element(f(Y), Y)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(189,plain,
% 0.19/0.40 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[188])).
% 0.19/0.40 tff(190,plain,
% 0.19/0.40 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(191,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(192,plain,
% 0.19/0.40 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y)) <=> ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[191])).
% 0.19/0.40 tff(193,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(f(Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_8')).
% 0.19/0.40 tff(194,plain,
% 0.19/0.40 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.40 tff(195,plain,
% 0.19/0.40 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.19/0.40 tff(196,plain,(
% 0.19/0.40 ![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.19/0.40 inference(skolemize,[status(sab)],[195])).
% 0.19/0.40 tff(197,plain,
% 0.19/0.40 (![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.19/0.40 tff(198,plain,
% 0.19/0.40 (((~![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(199,plain,
% 0.19/0.40 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(k, m)) | (k = m) | element(f(k), k))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(200,plain,
% 0.19/0.40 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(k, m)) | (k = m) | element(f(k), k)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.40 tff(201,plain,
% 0.19/0.40 (element(f(k), k)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[200, 197, 153, 11])).
% 0.19/0.40 tff(202,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(203,plain,
% 0.19/0.40 (((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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(204,plain,
% 0.19/0.40 (((~![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))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[203])).
% 0.19/0.40 tff(205,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[204, 202])).
% 0.19/0.41 tff(206,plain,
% 0.19/0.41 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(k) = k) | (f(k) = m) | (f(k) = n) | (~element(f(k), k)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(207,plain,
% 0.19/0.41 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(k) = m) | (f(k) = k) | (f(k) = n) | (~element(f(k), k))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.19/0.41 tff(208,plain,
% 0.19/0.41 (f(k) = n),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[207, 132, 201, 187, 170])).
% 0.19/0.41 tff(209,plain,
% 0.19/0.41 (f(k) = k),
% 0.19/0.41 inference(transitivity,[status(thm)],[208, 1])).
% 0.19/0.41 tff(210,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[170, 209])).
% 0.19/0.41 tff(211,plain,(~(n = k)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(212,plain,
% 0.19/0.41 (((n = k) | (m = k)) <=> ((n = k) | (m = k))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(213,axiom,((n = k) | (m = k)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_2')).
% 0.19/0.41 tff(214,plain,
% 0.19/0.41 ((n = k) | (m = k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.41 tff(215,plain,
% 0.19/0.41 ((n = k) | (m = k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[214, 212])).
% 0.19/0.41 tff(216,plain,
% 0.19/0.41 ((n = k) | (m = k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.19/0.41 tff(217,plain,
% 0.19/0.41 ((n = k) | (m = k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.19/0.41 tff(218,plain,
% 0.19/0.41 ((n = k) | (m = k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[217, 212])).
% 0.19/0.41 tff(219,plain,
% 0.19/0.41 (m = k),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[218, 211])).
% 0.19/0.41 tff(220,plain,
% 0.19/0.41 (k = m),
% 0.19/0.41 inference(symmetry,[status(thm)],[219])).
% 0.19/0.41 tff(221,plain,
% 0.19/0.41 ((f(n) = k) <=> (f(n) = m)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[220])).
% 0.19/0.41 tff(222,plain,
% 0.19/0.41 ((f(n) = m) <=> (f(n) = k)),
% 0.19/0.41 inference(symmetry,[status(thm)],[221])).
% 0.19/0.41 tff(223,plain,
% 0.19/0.41 ((~(f(n) = m)) <=> (~(f(n) = k))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[222])).
% 0.19/0.41 tff(224,plain,
% 0.19/0.41 (element(n, m) <=> element(n, k)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.41 tff(225,plain,
% 0.19/0.41 (element(n, k) <=> element(n, m)),
% 0.19/0.41 inference(symmetry,[status(thm)],[224])).
% 0.19/0.41 tff(226,plain,
% 0.19/0.41 (((n = k) | element(n, k)) <=> ((n = k) | element(n, k))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(227,plain,
% 0.19/0.41 (![Y: $i] : ((n = k) | element(n, k)) <=> ((n = k) | element(n, k))),
% 0.19/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.41 tff(228,plain,
% 0.19/0.41 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ![Y: $i] : ((n = k) | element(n, k))),
% 0.19/0.41 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.41 tff(229,plain,
% 0.19/0.41 (![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n))) <=> ((n = k) | element(n, k))),
% 0.19/0.41 inference(transitivity,[status(thm)],[228, 227])).
% 0.19/0.41 tff(230,plain,
% 0.19/0.41 (^[Y: $i] : trans(monotonicity(rewrite(((Y = k) | (~(Y = n))) <=> ((Y = k) | (~(Y = n)))), ((((Y = k) | (~(Y = n))) | element(Y, k)) <=> (((Y = k) | (~(Y = n))) | element(Y, k)))), rewrite((((Y = k) | (~(Y = n))) | element(Y, k)) <=> ((Y = k) | element(Y, k) | (~(Y = n)))), ((((Y = k) | (~(Y = n))) | element(Y, k)) <=> ((Y = k) | element(Y, k) | (~(Y = n)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(231,plain,
% 0.19/0.41 (![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k)) <=> ![Y: $i] : ((Y = k) | element(Y, k) | (~(Y = n)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[230])).
% 0.19/0.41 tff(232,plain,
% 0.19/0.41 (![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k)) <=> ((n = k) | element(n, k))),
% 0.19/0.41 inference(transitivity,[status(thm)],[231, 229])).
% 0.19/0.41 tff(233,axiom,(![Y: $i] : (((Y = k) | (~(Y = n))) | element(Y, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_16')).
% 0.19/0.41 tff(234,plain,
% 0.19/0.41 ((n = k) | element(n, k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.19/0.41 tff(235,plain,
% 0.19/0.41 ((n = k) | element(n, k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[234, 226])).
% 0.19/0.41 tff(236,plain,
% 0.19/0.41 (element(n, k)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[235, 211])).
% 0.19/0.41 tff(237,plain,
% 0.19/0.41 (element(n, m)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[236, 225])).
% 0.19/0.41 tff(238,plain,
% 0.19/0.41 ((n = m) <=> (n = k)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.41 tff(239,plain,
% 0.19/0.41 ((n = k) <=> (n = m)),
% 0.19/0.41 inference(symmetry,[status(thm)],[238])).
% 0.19/0.41 tff(240,plain,
% 0.19/0.41 ((~(n = k)) <=> (~(n = m))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[239])).
% 0.19/0.41 tff(241,plain,
% 0.19/0.41 (~(n = m)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[211, 240])).
% 0.19/0.41 tff(242,plain,
% 0.19/0.41 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~element(n, m)) | (n = m) | (~(f(n) = m)))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | (~(f(n) = m)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(243,plain,
% 0.19/0.41 (((~(f(n) = m)) | (~element(n, m)) | (n = m)) <=> ((~element(n, m)) | (n = m) | (~(f(n) = m)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(244,plain,
% 0.19/0.41 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~element(n, m)) | (n = m) | (~(f(n) = m))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[243])).
% 0.19/0.41 tff(245,plain,
% 0.19/0.41 (((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | (~(f(n) = m)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[244, 242])).
% 0.19/0.41 tff(246,plain,
% 0.19/0.41 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | ((~(f(n) = m)) | (~element(n, m)) | (n = m))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(247,plain,
% 0.19/0.41 ((~![Y: $i] : ((~(f(Y) = m)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | (~(f(n) = m))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.19/0.41 tff(248,plain,
% 0.19/0.41 ((~element(n, m)) | (n = m) | (~(f(n) = m))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[247, 180])).
% 0.19/0.41 tff(249,plain,
% 0.19/0.41 (~(f(n) = m)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[248, 241, 237])).
% 0.19/0.41 tff(250,plain,
% 0.19/0.41 (~(f(n) = k)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[249, 223])).
% 0.19/0.41 tff(251,plain,
% 0.19/0.41 (element(f(n), k) <=> element(f(n), m)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[220])).
% 0.19/0.41 tff(252,plain,
% 0.19/0.41 (element(f(n), m) <=> element(f(n), k)),
% 0.19/0.41 inference(symmetry,[status(thm)],[251])).
% 0.19/0.41 tff(253,plain,
% 0.19/0.41 ((n = f(n)) <=> (f(n) = n)),
% 0.19/0.41 inference(commutativity,[status(thm)],[])).
% 0.19/0.41 tff(254,plain,
% 0.19/0.41 ((f(n) = n) <=> (n = f(n))),
% 0.19/0.41 inference(symmetry,[status(thm)],[253])).
% 0.19/0.41 tff(255,plain,
% 0.19/0.41 ((~(f(n) = n)) <=> (~(n = f(n)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[254])).
% 0.19/0.41 tff(256,plain,
% 0.19/0.41 (((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(n, m)) | (n = m) | (~(f(n) = n)))) <=> ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (~element(n, m)) | (n = m) | (~(f(n) = n)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(257,plain,
% 0.19/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | ((~element(n, m)) | (n = m) | (~(f(n) = n)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(258,plain,
% 0.19/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | (~(f(Y) = Y)))) | (~element(n, m)) | (n = m) | (~(f(n) = n))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.19/0.41 tff(259,plain,
% 0.19/0.41 ((~element(n, m)) | (n = m) | (~(f(n) = n))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[258, 163])).
% 0.19/0.41 tff(260,plain,
% 0.19/0.41 (~(f(n) = n)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[259, 241, 237])).
% 0.19/0.41 tff(261,plain,
% 0.19/0.41 (~(n = f(n))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[260, 255])).
% 0.19/0.41 tff(262,plain,
% 0.19/0.41 (^[Y: $i] : refl((element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(263,plain,
% 0.19/0.41 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[262])).
% 0.19/0.41 tff(264,plain,
% 0.19/0.41 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m)) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(265,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(266,plain,
% 0.19/0.41 (![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y))) <=> ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[265])).
% 0.19/0.41 tff(267,axiom,(![Y: $i] : (((Y = m) | (~element(Y, m))) | element(Y, f(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_7')).
% 0.19/0.41 tff(268,plain,
% 0.19/0.41 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.41 tff(269,plain,
% 0.19/0.41 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.19/0.41 tff(270,plain,(
% 0.19/0.41 ![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.41 inference(skolemize,[status(sab)],[269])).
% 0.19/0.41 tff(271,plain,
% 0.19/0.41 (![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[270, 263])).
% 0.19/0.41 tff(272,plain,
% 0.19/0.41 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((~element(n, m)) | (n = m) | element(n, f(n)))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | element(n, f(n)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(273,plain,
% 0.19/0.41 ((element(n, f(n)) | (~element(n, m)) | (n = m)) <=> ((~element(n, m)) | (n = m) | element(n, f(n)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(274,plain,
% 0.19/0.41 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | ((~element(n, m)) | (n = m) | element(n, f(n))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[273])).
% 0.19/0.41 tff(275,plain,
% 0.19/0.41 (((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))) <=> ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | element(n, f(n)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[274, 272])).
% 0.19/0.41 tff(276,plain,
% 0.19/0.41 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (element(n, f(n)) | (~element(n, m)) | (n = m))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(277,plain,
% 0.19/0.41 ((~![Y: $i] : (element(Y, f(Y)) | (~element(Y, m)) | (Y = m))) | (~element(n, m)) | (n = m) | element(n, f(n))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.19/0.41 tff(278,plain,
% 0.19/0.41 ((~element(n, m)) | (n = m) | element(n, f(n))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[277, 271])).
% 0.19/0.41 tff(279,plain,
% 0.19/0.41 (element(n, f(n))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[278, 241, 237])).
% 0.19/0.41 tff(280,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(281,plain,
% 0.19/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | ((~element(n, m)) | (n = m) | element(f(n), n))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(282,plain,
% 0.19/0.41 ((~![Y: $i] : ((~element(Y, m)) | (Y = m) | element(f(Y), Y))) | (~element(n, m)) | (n = m) | element(f(n), n)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.41 tff(283,plain,
% 0.19/0.41 ((~element(n, m)) | (n = m) | element(f(n), n)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[282, 197])).
% 0.19/0.41 tff(284,plain,
% 0.19/0.41 (element(f(n), n)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[283, 241, 237])).
% 0.19/0.41 tff(285,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(286,plain,
% 0.19/0.41 (![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))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[285])).
% 0.19/0.42 tff(287,plain,
% 0.19/0.42 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) <=> ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(288,plain,
% 0.19/0.42 (^[Y: $i, V1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((Y = m) | element(Y, m)) | (V1 = m)) <=> ((V1 = m) | element(Y, m) | (Y = m))), (((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) <=> (((V1 = m) | element(Y, m) | (Y = m)) | (V1 = Y)))), rewrite((((V1 = m) | element(Y, m) | (Y = m)) | (V1 = Y)) <=> ((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m))), (((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) <=> ((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m)))), ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) <=> (((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(Y, V1))))), rewrite((((V1 = m) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(Y, V1))) <=> ((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))), ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) <=> ((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)))), (((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y))) <=> (((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(V1, Y))))), rewrite((((V1 = m) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m)) | (~element(V1, Y))) <=> ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))), (((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y))) <=> ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(289,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[288])).
% 0.19/0.42 tff(290,axiom,(![Y: $i, V1: $i] : ((((((Y = m) | element(Y, m)) | (V1 = m)) | (V1 = Y)) | (~element(Y, V1))) | (~element(V1, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_9')).
% 0.19/0.42 tff(291,plain,
% 0.19/0.42 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.19/0.42 tff(292,plain,
% 0.19/0.42 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.19/0.42 tff(293,plain,(
% 0.19/0.42 ![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.19/0.42 inference(skolemize,[status(sab)],[292])).
% 0.19/0.42 tff(294,plain,
% 0.19/0.42 (![Y: $i, V1: $i] : ((V1 = m) | (~element(V1, Y)) | (~element(Y, V1)) | (V1 = Y) | element(Y, m) | (Y = m))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.19/0.42 tff(295,plain,
% 0.19/0.42 (((~![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(296,plain,
% 0.19/0.42 (((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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(297,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[296])).
% 0.19/0.42 tff(298,plain,
% 0.19/0.42 (((~![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))),
% 0.19/0.42 inference(transitivity,[status(thm)],[297, 295])).
% 0.19/0.42 tff(299,plain,
% 0.19/0.42 ((~![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))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(300,plain,
% 0.19/0.42 ((~![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)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.19/0.42 tff(301,plain,
% 0.19/0.42 ((n = f(n)) | element(f(n), m)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[300, 294, 241, 284, 279, 249])).
% 0.19/0.42 tff(302,plain,
% 0.19/0.42 (element(f(n), m)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[301, 261])).
% 0.19/0.42 tff(303,plain,
% 0.19/0.42 (element(f(n), k)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[302, 252])).
% 0.19/0.42 tff(304,plain,
% 0.19/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(305,plain,
% 0.19/0.42 (((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k))) <=> ((f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(306,plain,
% 0.19/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[305])).
% 0.19/0.42 tff(307,plain,
% 0.19/0.42 (((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))) <=> ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[306, 304])).
% 0.19/0.42 tff(308,plain,
% 0.19/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | ((f(n) = k) | (f(n) = m) | (f(n) = n) | (~element(f(n), k)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(309,plain,
% 0.19/0.42 ((~![Y: $i] : ((Y = k) | (Y = m) | (Y = n) | (~element(Y, k)))) | (f(n) = m) | (f(n) = n) | (f(n) = k) | (~element(f(n), k))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.19/0.42 tff(310,plain,
% 0.19/0.42 ((f(n) = k) | (~element(f(n), k))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[309, 132, 249, 260])).
% 0.19/0.42 tff(311,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[310, 303, 250])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------