%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN015-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN015-2 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 12:25:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(equalish_type, type, (
% 0.21/0.38 equalish: ( $i * $i ) > $o)).
% 0.21/0.38 tff(k_type, type, (
% 0.21/0.38 k: $i)).
% 0.21/0.38 tff(f_type, type, (
% 0.21/0.38 f: $i > $i)).
% 0.21/0.38 tff(n_type, type, (
% 0.21/0.38 n: $i)).
% 0.21/0.38 tff(element_type, type, (
% 0.21/0.38 element: ( $i * $i ) > $o)).
% 0.21/0.38 tff(m_type, type, (
% 0.21/0.38 m: $i)).
% 0.21/0.38 tff(1,assumption,(~element(f(n), k)), introduced(assumption)).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (equalish(m, k) <=> equalish(m, k)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(3,axiom,(equalish(m, k)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_23')).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (equalish(m, k)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (^[Y: $i, X: $i] : refl(((~equalish(X, Y)) | equalish(Y, X)) <=> ((~equalish(X, Y)) | equalish(Y, X)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X)) <=> ![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X)) <=> ![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(8,axiom,(![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetryish')).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.38 tff(10,plain,(
% 0.21/0.38 ![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))),
% 0.21/0.38 inference(skolemize,[status(sab)],[9])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | ((~equalish(m, k)) | equalish(k, m))) <=> ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | (~equalish(m, k)) | equalish(k, m))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | ((~equalish(m, k)) | equalish(k, m))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | (~equalish(m, k)) | equalish(k, m)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (equalish(k, m)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 0.21/0.38 tff(16,assumption,(~equalish(n, n)), introduced(assumption)).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (^[X: $i] : refl(equalish(X, X) <=> equalish(X, X))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (![X: $i] : equalish(X, X) <=> ![X: $i] : equalish(X, X)),
% 0.21/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (![X: $i] : equalish(X, X) <=> ![X: $i] : equalish(X, X)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(20,axiom,(![X: $i] : equalish(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivityish')).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (![X: $i] : equalish(X, X)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.38 tff(22,plain,(
% 0.21/0.38 ![X: $i] : equalish(X, X)),
% 0.21/0.38 inference(skolemize,[status(sab)],[21])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (![X: $i] : equalish(X, X)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 ((~![X: $i] : equalish(X, X)) | equalish(n, n)),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[24, 23, 16])).
% 0.21/0.38 tff(26,plain,(equalish(n, n)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 ((~equalish(n, k)) <=> (~equalish(n, k))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(28,axiom,(~equalish(n, k)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_20')).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (~equalish(n, k)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (^[A: $i] : refl((equalish(A, k) | element(A, k) | (~equalish(A, n))) <=> (equalish(A, k) | element(A, k) | (~equalish(A, n))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n))) <=> ![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n))) <=> ![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (^[A: $i] : rewrite((((~equalish(A, n)) | element(A, k)) | equalish(A, k)) <=> (equalish(A, k) | element(A, k) | (~equalish(A, n))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (![A: $i] : (((~equalish(A, n)) | element(A, k)) | equalish(A, k)) <=> ![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.39 tff(35,axiom,(![A: $i] : (((~equalish(A, n)) | element(A, k)) | equalish(A, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_16')).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.39 tff(38,plain,(
% 0.21/0.39 ![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[37])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (((~![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))) | (equalish(n, k) | element(n, k) | (~equalish(n, n)))) <=> ((~![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))) | equalish(n, k) | element(n, k) | (~equalish(n, n)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 ((~![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))) | (equalish(n, k) | element(n, k) | (~equalish(n, n)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 ((~![A: $i] : (equalish(A, k) | element(A, k) | (~equalish(A, n)))) | equalish(n, k) | element(n, k) | (~equalish(n, n))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (element(n, k) | (~equalish(n, n))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (element(n, k)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[43, 26])).
% 0.21/0.39 tff(45,assumption,(~element(n, m)), introduced(assumption)).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (^[B: $i, A: $i, C: $i] : refl(((~equalish(A, B)) | element(C, B) | (~element(C, A))) <=> ((~equalish(A, B)) | element(C, B) | (~element(C, A))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A))) <=> ![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A))) <=> ![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~equalish(A, B)) | (~element(C, A))) <=> ((~equalish(A, B)) | (~element(C, A)))), ((((~equalish(A, B)) | (~element(C, A))) | element(C, B)) <=> (((~equalish(A, B)) | (~element(C, A))) | element(C, B)))), rewrite((((~equalish(A, B)) | (~element(C, A))) | element(C, B)) <=> ((~equalish(A, B)) | element(C, B) | (~element(C, A)))), ((((~equalish(A, B)) | (~element(C, A))) | element(C, B)) <=> ((~equalish(A, B)) | element(C, B) | (~element(C, A)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : (((~equalish(A, B)) | (~element(C, A))) | element(C, B)) <=> ![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.39 tff(51,axiom,(![B: $i, A: $i, C: $i] : (((~equalish(A, B)) | (~element(C, A))) | element(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_substitutionish1')).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.39 tff(54,plain,(
% 0.21/0.39 ![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[53])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | (element(n, m) | (~element(n, k)) | (~equalish(k, m)))) <=> ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | element(n, m) | (~element(n, k)) | (~equalish(k, m)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (((~equalish(k, m)) | element(n, m) | (~element(n, k))) <=> (element(n, m) | (~element(n, k)) | (~equalish(k, m)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(k, m)) | element(n, m) | (~element(n, k)))) <=> ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | (element(n, m) | (~element(n, k)) | (~equalish(k, m))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(k, m)) | element(n, m) | (~element(n, k)))) <=> ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | element(n, m) | (~element(n, k)) | (~equalish(k, m)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[58, 56])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(k, m)) | element(n, m) | (~element(n, k)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | element(n, m) | (~element(n, k)) | (~equalish(k, m))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[61, 55, 45, 44, 15])).
% 0.21/0.39 tff(63,plain,(element(n, m)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 ((~equalish(m, n)) <=> (~equalish(m, n))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(65,axiom,(~equalish(m, n)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_19')).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 (~equalish(m, n)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 (((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | ((~equalish(n, m)) | equalish(m, n))) <=> ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | (~equalish(n, m)) | equalish(m, n))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(68,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | ((~equalish(n, m)) | equalish(m, n))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | (~equalish(n, m)) | equalish(m, n)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.39 tff(70,plain,
% 0.21/0.39 (~equalish(n, m)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[69, 11, 66])).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 (^[A: $i] : refl((equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A))) <=> (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A))) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A))) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 (^[A: $i] : trans(monotonicity(rewrite(((~equalish(f(A), A)) | (~element(A, m))) <=> ((~element(A, m)) | (~equalish(f(A), A)))), ((((~equalish(f(A), A)) | (~element(A, m))) | equalish(A, m)) <=> (((~element(A, m)) | (~equalish(f(A), A))) | equalish(A, m)))), rewrite((((~element(A, m)) | (~equalish(f(A), A))) | equalish(A, m)) <=> (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))), ((((~equalish(f(A), A)) | (~element(A, m))) | equalish(A, m)) <=> (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 (![A: $i] : (((~equalish(f(A), A)) | (~element(A, m))) | equalish(A, m)) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.39 tff(76,axiom,(![A: $i] : (((~equalish(f(A), A)) | (~element(A, m))) | equalish(A, m))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_6')).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.21/0.39 tff(79,plain,(
% 0.21/0.39 ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[78])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 (((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))) | (equalish(n, m) | (~element(n, m)) | (~equalish(f(n), n)))) <=> ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))) | equalish(n, m) | (~element(n, m)) | (~equalish(f(n), n)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))) | (equalish(n, m) | (~element(n, m)) | (~equalish(f(n), n)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), A)))) | equalish(n, m) | (~element(n, m)) | (~equalish(f(n), n))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.39 tff(84,plain,
% 0.21/0.39 ((~element(n, m)) | (~equalish(f(n), n))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[83, 80, 70])).
% 0.21/0.39 tff(85,plain,
% 0.21/0.39 (~equalish(f(n), n)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[84, 63])).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 (((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | ((~equalish(n, f(n))) | equalish(f(n), n))) <=> ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | (~equalish(n, f(n))) | equalish(f(n), n))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(87,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | ((~equalish(n, f(n))) | equalish(f(n), n))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(88,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(Y, X))) | (~equalish(n, f(n))) | equalish(f(n), n)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.39 tff(89,plain,
% 0.21/0.39 (~equalish(n, f(n))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[88, 11, 85])).
% 0.21/0.39 tff(90,plain,
% 0.21/0.39 (^[A: $i] : refl((equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m))) <=> (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(91,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m))) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.39 tff(92,plain,
% 0.21/0.39 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m))) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(93,plain,
% 0.21/0.39 (^[A: $i] : trans(monotonicity(rewrite(((~equalish(f(A), m)) | (~element(A, m))) <=> ((~element(A, m)) | (~equalish(f(A), m)))), ((((~equalish(f(A), m)) | (~element(A, m))) | equalish(A, m)) <=> (((~element(A, m)) | (~equalish(f(A), m))) | equalish(A, m)))), rewrite((((~element(A, m)) | (~equalish(f(A), m))) | equalish(A, m)) <=> (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))), ((((~equalish(f(A), m)) | (~element(A, m))) | equalish(A, m)) <=> (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (![A: $i] : (((~equalish(f(A), m)) | (~element(A, m))) | equalish(A, m)) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.40 tff(95,axiom,(![A: $i] : (((~equalish(f(A), m)) | (~element(A, m))) | equalish(A, m))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_5')).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.40 tff(98,plain,(
% 0.21/0.40 ![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[97])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.21/0.40 tff(100,plain,
% 0.21/0.40 (((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))) | (equalish(n, m) | (~element(n, m)) | (~equalish(f(n), m)))) <=> ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))) | equalish(n, m) | (~element(n, m)) | (~equalish(f(n), m)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))) | (equalish(n, m) | (~element(n, m)) | (~equalish(f(n), m)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | (~equalish(f(A), m)))) | equalish(n, m) | (~element(n, m)) | (~equalish(f(n), m))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 (~equalish(f(n), m)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[102, 99, 70, 63])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 (^[A: $i] : refl((element(A, f(A)) | equalish(A, m) | (~element(A, m))) <=> (element(A, f(A)) | equalish(A, m) | (~element(A, m))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m))) <=> ![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m))) <=> ![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 (^[A: $i] : trans(monotonicity(rewrite((element(A, f(A)) | (~element(A, m))) <=> (element(A, f(A)) | (~element(A, m)))), (((element(A, f(A)) | (~element(A, m))) | equalish(A, m)) <=> ((element(A, f(A)) | (~element(A, m))) | equalish(A, m)))), rewrite(((element(A, f(A)) | (~element(A, m))) | equalish(A, m)) <=> (element(A, f(A)) | equalish(A, m) | (~element(A, m)))), (((element(A, f(A)) | (~element(A, m))) | equalish(A, m)) <=> (element(A, f(A)) | equalish(A, m) | (~element(A, m)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 (![A: $i] : ((element(A, f(A)) | (~element(A, m))) | equalish(A, m)) <=> ![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.40 tff(109,axiom,(![A: $i] : ((element(A, f(A)) | (~element(A, m))) | equalish(A, m))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_7')).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 (![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.40 tff(111,plain,
% 0.21/0.40 (![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.21/0.40 tff(112,plain,(
% 0.21/0.40 ![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[111])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 (![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.21/0.40 tff(114,plain,
% 0.21/0.40 (((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | (equalish(n, m) | (~element(n, m)) | element(n, f(n)))) <=> ((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | equalish(n, m) | (~element(n, m)) | element(n, f(n)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 ((element(n, f(n)) | equalish(n, m) | (~element(n, m))) <=> (equalish(n, m) | (~element(n, m)) | element(n, f(n)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | (element(n, f(n)) | equalish(n, m) | (~element(n, m)))) <=> ((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | (equalish(n, m) | (~element(n, m)) | element(n, f(n))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[115])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 (((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | (element(n, f(n)) | equalish(n, m) | (~element(n, m)))) <=> ((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | equalish(n, m) | (~element(n, m)) | element(n, f(n)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[116, 114])).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 ((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | (element(n, f(n)) | equalish(n, m) | (~element(n, m)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 ((~![A: $i] : (element(A, f(A)) | equalish(A, m) | (~element(A, m)))) | equalish(n, m) | (~element(n, m)) | element(n, f(n))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 ((~element(n, m)) | element(n, f(n))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[119, 113, 70])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 (element(n, f(n))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[120, 63])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 (^[A: $i] : refl((equalish(A, m) | (~element(A, m)) | element(f(A), A)) <=> (equalish(A, m) | (~element(A, m)) | element(f(A), A)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A)) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A)) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 (^[A: $i] : trans(monotonicity(rewrite((element(f(A), A) | (~element(A, m))) <=> ((~element(A, m)) | element(f(A), A))), (((element(f(A), A) | (~element(A, m))) | equalish(A, m)) <=> (((~element(A, m)) | element(f(A), A)) | equalish(A, m)))), rewrite((((~element(A, m)) | element(f(A), A)) | equalish(A, m)) <=> (equalish(A, m) | (~element(A, m)) | element(f(A), A))), (((element(f(A), A) | (~element(A, m))) | equalish(A, m)) <=> (equalish(A, m) | (~element(A, m)) | element(f(A), A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (![A: $i] : ((element(f(A), A) | (~element(A, m))) | equalish(A, m)) <=> ![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.40 tff(127,axiom,(![A: $i] : ((element(f(A), A) | (~element(A, m))) | equalish(A, m))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_8')).
% 0.21/0.40 tff(128,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.40 tff(129,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.21/0.40 tff(130,plain,(
% 0.21/0.40 ![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))),
% 0.21/0.40 inference(skolemize,[status(sab)],[129])).
% 0.21/0.40 tff(131,plain,
% 0.21/0.40 (![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.21/0.40 tff(132,plain,
% 0.21/0.40 (((~![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))) | (equalish(n, m) | (~element(n, m)) | element(f(n), n))) <=> ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))) | equalish(n, m) | (~element(n, m)) | element(f(n), n))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(133,plain,
% 0.21/0.40 ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))) | (equalish(n, m) | (~element(n, m)) | element(f(n), n))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(134,plain,
% 0.21/0.40 ((~![A: $i] : (equalish(A, m) | (~element(A, m)) | element(f(A), A))) | equalish(n, m) | (~element(n, m)) | element(f(n), n)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.40 tff(135,plain,
% 0.21/0.40 ((~element(n, m)) | element(f(n), n)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[134, 131, 70])).
% 0.21/0.40 tff(136,plain,
% 0.21/0.40 (element(f(n), n)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[135, 63])).
% 0.21/0.40 tff(137,plain,
% 0.21/0.40 (^[B: $i, A: $i] : refl((equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A))) <=> (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(138,plain,
% 0.21/0.40 (![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A))) <=> ![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.40 tff(139,plain,
% 0.21/0.40 (![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A))) <=> ![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(140,plain,
% 0.21/0.40 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) <=> (equalish(A, B) | (~element(A, B)) | (~element(B, A)))), (((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) <=> ((equalish(A, B) | (~element(A, B)) | (~element(B, A))) | equalish(A, m)))), rewrite(((equalish(A, B) | (~element(A, B)) | (~element(B, A))) | equalish(A, m)) <=> (equalish(A, B) | (~element(A, B)) | equalish(A, m) | (~element(B, A)))), (((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) <=> (equalish(A, B) | (~element(A, B)) | equalish(A, m) | (~element(B, A))))), ((((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) | element(B, m)) <=> ((equalish(A, B) | (~element(A, B)) | equalish(A, m) | (~element(B, A))) | element(B, m)))), rewrite(((equalish(A, B) | (~element(A, B)) | equalish(A, m) | (~element(B, A))) | element(B, m)) <=> (equalish(A, B) | (~element(A, B)) | equalish(A, m) | element(B, m) | (~element(B, A)))), ((((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) | element(B, m)) <=> (equalish(A, B) | (~element(A, B)) | equalish(A, m) | element(B, m) | (~element(B, A))))), (((((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) | element(B, m)) | equalish(B, m)) <=> ((equalish(A, B) | (~element(A, B)) | equalish(A, m) | element(B, m) | (~element(B, A))) | equalish(B, m)))), rewrite(((equalish(A, B) | (~element(A, B)) | equalish(A, m) | element(B, m) | (~element(B, A))) | equalish(B, m)) <=> (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))), (((((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) | element(B, m)) | equalish(B, m)) <=> (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(141,plain,
% 0.21/0.40 (![B: $i, A: $i] : ((((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) | element(B, m)) | equalish(B, m)) <=> ![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[140])).
% 0.21/0.40 tff(142,axiom,(![B: $i, A: $i] : ((((((~element(A, B)) | (~element(B, A))) | equalish(A, B)) | equalish(A, m)) | element(B, m)) | equalish(B, m))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_9')).
% 0.21/0.40 tff(143,plain,
% 0.21/0.40 (![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 (![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.21/0.41 tff(145,plain,(
% 0.21/0.41 ![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[144])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 (![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | (equalish(n, m) | (~element(f(n), n)) | (~element(n, f(n))) | equalish(f(n), m) | equalish(n, f(n)) | element(f(n), m))) <=> ((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | equalish(n, m) | (~element(f(n), n)) | (~element(n, f(n))) | equalish(f(n), m) | equalish(n, f(n)) | element(f(n), m))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(148,plain,
% 0.21/0.41 ((equalish(n, f(n)) | (~element(n, f(n))) | equalish(n, m) | equalish(f(n), m) | element(f(n), m) | (~element(f(n), n))) <=> (equalish(n, m) | (~element(f(n), n)) | (~element(n, f(n))) | equalish(f(n), m) | equalish(n, f(n)) | element(f(n), m))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | (equalish(n, f(n)) | (~element(n, f(n))) | equalish(n, m) | equalish(f(n), m) | element(f(n), m) | (~element(f(n), n)))) <=> ((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | (equalish(n, m) | (~element(f(n), n)) | (~element(n, f(n))) | equalish(f(n), m) | equalish(n, f(n)) | element(f(n), m)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[148])).
% 0.21/0.41 tff(150,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | (equalish(n, f(n)) | (~element(n, f(n))) | equalish(n, m) | equalish(f(n), m) | element(f(n), m) | (~element(f(n), n)))) <=> ((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | equalish(n, m) | (~element(f(n), n)) | (~element(n, f(n))) | equalish(f(n), m) | equalish(n, f(n)) | element(f(n), m))),
% 0.21/0.41 inference(transitivity,[status(thm)],[149, 147])).
% 0.21/0.41 tff(151,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | (equalish(n, f(n)) | (~element(n, f(n))) | equalish(n, m) | equalish(f(n), m) | element(f(n), m) | (~element(f(n), n)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(152,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : (equalish(A, B) | (~element(A, B)) | equalish(A, m) | equalish(B, m) | element(B, m) | (~element(B, A)))) | equalish(n, m) | (~element(f(n), n)) | (~element(n, f(n))) | equalish(f(n), m) | equalish(n, f(n)) | element(f(n), m)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.41 tff(153,plain,
% 0.21/0.41 (equalish(n, f(n)) | element(f(n), m)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[152, 146, 70, 136, 121, 103])).
% 0.21/0.41 tff(154,plain,
% 0.21/0.41 (element(f(n), m)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[153, 89])).
% 0.21/0.41 tff(155,plain,
% 0.21/0.41 (((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(m, k)) | (~element(f(n), m)) | element(f(n), k))) <=> ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | (~equalish(m, k)) | (~element(f(n), m)) | element(f(n), k))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(156,plain,
% 0.21/0.41 (((~equalish(m, k)) | element(f(n), k) | (~element(f(n), m))) <=> ((~equalish(m, k)) | (~element(f(n), m)) | element(f(n), k))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(157,plain,
% 0.21/0.41 (((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(m, k)) | element(f(n), k) | (~element(f(n), m)))) <=> ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(m, k)) | (~element(f(n), m)) | element(f(n), k)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[156])).
% 0.21/0.41 tff(158,plain,
% 0.21/0.41 (((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(m, k)) | element(f(n), k) | (~element(f(n), m)))) <=> ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | (~equalish(m, k)) | (~element(f(n), m)) | element(f(n), k))),
% 0.21/0.41 inference(transitivity,[status(thm)],[157, 155])).
% 0.21/0.41 tff(159,plain,
% 0.21/0.41 ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | ((~equalish(m, k)) | element(f(n), k) | (~element(f(n), m)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(160,plain,
% 0.21/0.41 ((~![B: $i, A: $i, C: $i] : ((~equalish(A, B)) | element(C, B) | (~element(C, A)))) | (~equalish(m, k)) | (~element(f(n), m)) | element(f(n), k)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.21/0.41 tff(161,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[160, 55, 4, 154, 1])).
% 0.21/0.41 tff(162,plain,(element(f(n), k)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(163,plain,
% 0.21/0.41 (^[A: $i] : refl((equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k))) <=> (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(164,plain,
% 0.21/0.41 (![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k))) <=> ![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[163])).
% 0.21/0.41 tff(165,plain,
% 0.21/0.41 (![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k))) <=> ![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(166,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(rewrite((((~element(A, k)) | equalish(A, n)) | equalish(A, m)) <=> (equalish(A, n) | equalish(A, m) | (~element(A, k)))), (((((~element(A, k)) | equalish(A, n)) | equalish(A, m)) | equalish(A, k)) <=> ((equalish(A, n) | equalish(A, m) | (~element(A, k))) | equalish(A, k)))), rewrite(((equalish(A, n) | equalish(A, m) | (~element(A, k))) | equalish(A, k)) <=> (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))), (((((~element(A, k)) | equalish(A, n)) | equalish(A, m)) | equalish(A, k)) <=> (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(167,plain,
% 0.21/0.41 (![A: $i] : ((((~element(A, k)) | equalish(A, n)) | equalish(A, m)) | equalish(A, k)) <=> ![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[166])).
% 0.21/0.41 tff(168,axiom,(![A: $i] : ((((~element(A, k)) | equalish(A, n)) | equalish(A, m)) | equalish(A, k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_17')).
% 0.21/0.41 tff(169,plain,
% 0.21/0.41 (![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.41 tff(170,plain,
% 0.21/0.41 (![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.21/0.41 tff(171,plain,(
% 0.21/0.41 ![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[170])).
% 0.21/0.41 tff(172,plain,
% 0.21/0.41 (![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.21/0.41 tff(173,plain,
% 0.21/0.41 (((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | (equalish(f(n), n) | equalish(f(n), k) | equalish(f(n), m) | (~element(f(n), k)))) <=> ((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | equalish(f(n), n) | equalish(f(n), k) | equalish(f(n), m) | (~element(f(n), k)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(174,plain,
% 0.21/0.41 ((equalish(f(n), k) | equalish(f(n), n) | equalish(f(n), m) | (~element(f(n), k))) <=> (equalish(f(n), n) | equalish(f(n), k) | equalish(f(n), m) | (~element(f(n), k)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(175,plain,
% 0.21/0.41 (((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | (equalish(f(n), k) | equalish(f(n), n) | equalish(f(n), m) | (~element(f(n), k)))) <=> ((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | (equalish(f(n), n) | equalish(f(n), k) | equalish(f(n), m) | (~element(f(n), k))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[174])).
% 0.21/0.41 tff(176,plain,
% 0.21/0.41 (((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | (equalish(f(n), k) | equalish(f(n), n) | equalish(f(n), m) | (~element(f(n), k)))) <=> ((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | equalish(f(n), n) | equalish(f(n), k) | equalish(f(n), m) | (~element(f(n), k)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[175, 173])).
% 0.21/0.41 tff(177,plain,
% 0.21/0.41 ((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | (equalish(f(n), k) | equalish(f(n), n) | equalish(f(n), m) | (~element(f(n), k)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(178,plain,
% 0.21/0.41 ((~![A: $i] : (equalish(A, k) | equalish(A, n) | equalish(A, m) | (~element(A, k)))) | equalish(f(n), n) | equalish(f(n), k) | equalish(f(n), m) | (~element(f(n), k))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.41 tff(179,plain,
% 0.21/0.41 (equalish(f(n), k) | (~element(f(n), k))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[178, 172, 85, 103])).
% 0.21/0.41 tff(180,plain,
% 0.21/0.41 (equalish(f(n), k)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[179, 162])).
% 0.21/0.41 tff(181,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(182,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(183,plain,
% 0.21/0.41 (^[Z: $i, Y: $i, X: $i] : rewrite((((~equalish(X, Y)) | (~equalish(Y, Z))) | equalish(X, Z)) <=> ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(184,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : (((~equalish(X, Y)) | (~equalish(Y, Z))) | equalish(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[183])).
% 0.21/0.41 tff(185,axiom,(![Z: $i, Y: $i, X: $i] : (((~equalish(X, Y)) | (~equalish(Y, Z))) | equalish(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivityish')).
% 0.21/0.41 tff(186,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.21/0.41 tff(187,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.21/0.41 tff(188,plain,(
% 0.21/0.41 ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[187])).
% 0.21/0.41 tff(189,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.21/0.41 tff(190,plain,
% 0.21/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | ((~equalish(k, m)) | equalish(f(n), m) | (~equalish(f(n), k)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | (~equalish(k, m)) | equalish(f(n), m) | (~equalish(f(n), k)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(191,plain,
% 0.21/0.41 (((~equalish(f(n), k)) | equalish(f(n), m) | (~equalish(k, m))) <=> ((~equalish(k, m)) | equalish(f(n), m) | (~equalish(f(n), k)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(192,plain,
% 0.21/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | ((~equalish(f(n), k)) | equalish(f(n), m) | (~equalish(k, m)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | ((~equalish(k, m)) | equalish(f(n), m) | (~equalish(f(n), k))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.42 tff(193,plain,
% 0.21/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | ((~equalish(f(n), k)) | equalish(f(n), m) | (~equalish(k, m)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | (~equalish(k, m)) | equalish(f(n), m) | (~equalish(f(n), k)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.42 tff(194,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | ((~equalish(f(n), k)) | equalish(f(n), m) | (~equalish(k, m)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(195,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | (~equalish(k, m)) | equalish(f(n), m) | (~equalish(f(n), k))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.42 tff(196,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[195, 189, 15, 103, 180])).
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------