%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV007-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:31:19 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV007-1 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:21:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(less_than_type, type, (
% 0.11/0.37 less_than: ( $i * $i ) > $o)).
% 0.11/0.37 tff(m_type, type, (
% 0.11/0.37 m: $i)).
% 0.11/0.37 tff(n_type, type, (
% 0.11/0.37 n: $i)).
% 0.11/0.37 tff(successor_type, type, (
% 0.11/0.37 successor: $i > $i)).
% 0.11/0.37 tff(i_type, type, (
% 0.11/0.37 i: $i)).
% 0.11/0.37 tff(a_type, type, (
% 0.11/0.37 a: $i > $i)).
% 0.11/0.37 tff(k_type, type, (
% 0.11/0.37 k: $i)).
% 0.11/0.37 tff(1,assumption,(less_than(successor(n), m)), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[X: $i] : refl(less_than(X, successor(X)) <=> less_than(X, successor(X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X: $i] : less_than(X, successor(X)) <=> ![X: $i] : less_than(X, successor(X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X: $i] : less_than(X, successor(X)) <=> ![X: $i] : less_than(X, successor(X))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,axiom,(![X: $i] : less_than(X, successor(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax','less_than_successor')).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![X: $i] : less_than(X, successor(X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.37 tff(7,plain,(
% 0.11/0.37 ![X: $i] : less_than(X, successor(X))),
% 0.11/0.37 inference(skolemize,[status(sab)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![X: $i] : less_than(X, successor(X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 ((~![X: $i] : less_than(X, successor(X))) | less_than(n, successor(n))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (less_than(n, successor(n))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~less_than(n, m)) <=> (~less_than(n, m))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(12,axiom,(~less_than(n, m)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~less_than(n, m)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((less_than(X, Z) | (~less_than(X, Y))) <=> ((~less_than(X, Y)) | less_than(X, Z))), (((less_than(X, Z) | (~less_than(X, Y))) | (~less_than(Y, Z))) <=> (((~less_than(X, Y)) | less_than(X, Z)) | (~less_than(Y, Z))))), rewrite((((~less_than(X, Y)) | less_than(X, Z)) | (~less_than(Y, Z))) <=> ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))), (((less_than(X, Z) | (~less_than(X, Y))) | (~less_than(Y, Z))) <=> ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![Z: $i, Y: $i, X: $i] : ((less_than(X, Z) | (~less_than(X, Y))) | (~less_than(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.37 tff(18,axiom,(![Z: $i, Y: $i, X: $i] : ((less_than(X, Z) | (~less_than(X, Y))) | (~less_than(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax','transitivity_of_less_than')).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.37 tff(21,plain,(
% 0.11/0.37 ![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.11/0.37 inference(skolemize,[status(sab)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | (less_than(n, m) | (~less_than(n, successor(n))) | (~less_than(successor(n), m)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | less_than(n, m) | (~less_than(n, successor(n))) | (~less_than(successor(n), m)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (((~less_than(successor(n), m)) | (~less_than(n, successor(n))) | less_than(n, m)) <=> (less_than(n, m) | (~less_than(n, successor(n))) | (~less_than(successor(n), m)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(successor(n), m)) | (~less_than(n, successor(n))) | less_than(n, m))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | (less_than(n, m) | (~less_than(n, successor(n))) | (~less_than(successor(n), m))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(successor(n), m)) | (~less_than(n, successor(n))) | less_than(n, m))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | less_than(n, m) | (~less_than(n, successor(n))) | (~less_than(successor(n), m)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[25, 23])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(successor(n), m)) | (~less_than(n, successor(n))) | less_than(n, m))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | less_than(n, m) | (~less_than(n, successor(n))) | (~less_than(successor(n), m))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 22, 13, 10, 1])).
% 0.11/0.37 tff(30,plain,(~less_than(successor(n), m)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (less_than(i, m) <=> less_than(i, m)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(32,axiom,(less_than(i, m)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (less_than(i, m)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : refl(((~less_than(X, Y)) | (~less_than(Y, X))) <=> ((~less_than(X, Y)) | (~less_than(Y, X))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(37,axiom,(![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax','anti_symmetry_of_less_than')).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.37 tff(39,plain,(
% 0.11/0.37 ![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[38])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | ((~less_than(m, i)) | (~less_than(i, m)))) <=> ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | (~less_than(m, i)) | (~less_than(i, m)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | ((~less_than(m, i)) | (~less_than(i, m)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | (~less_than(m, i)) | (~less_than(i, m))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (~less_than(m, i)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (^[X: $i] : refl((less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n)))) <=> (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n)))) <=> ![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[45])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n)))) <=> ![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (^[X: $i] : trans(monotonicity(rewrite((less_than(X, i) | (~less_than(X, successor(n)))) <=> (less_than(X, i) | (~less_than(X, successor(n))))), (((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(k)))) <=> ((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(k)))))), rewrite(((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(k)))) <=> (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))), (((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(k)))) <=> (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (![X: $i] : ((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(k)))) <=> ![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[48])).
% 0.11/0.37 tff(50,axiom,(![X: $i] : ((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(k))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_11')).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.11/0.37 tff(53,plain,(
% 0.11/0.37 ![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[52])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 (![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (less_than(a(m), a(k)) <=> less_than(a(m), a(k))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(56,axiom,(less_than(a(m), a(k))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (less_than(a(m), a(k))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (((~![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))) | (less_than(m, i) | (~less_than(a(m), a(k))) | (~less_than(m, successor(n))))) <=> ((~![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))) | less_than(m, i) | (~less_than(a(m), a(k))) | (~less_than(m, successor(n))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 ((~![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))) | (less_than(m, i) | (~less_than(a(m), a(k))) | (~less_than(m, successor(n))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 ((~![X: $i] : (less_than(X, i) | (~less_than(a(X), a(k))) | (~less_than(X, successor(n))))) | less_than(m, i) | (~less_than(a(m), a(k))) | (~less_than(m, successor(n)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 (~less_than(m, successor(n))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[60, 57, 54, 44])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : refl(((X = Y) | less_than(Y, X) | less_than(X, Y)) <=> ((X = Y) | less_than(Y, X) | less_than(X, Y)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : rewrite(((less_than(X, Y) | less_than(Y, X)) | (X = Y)) <=> ((X = Y) | less_than(Y, X) | less_than(X, Y)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((less_than(X, Y) | less_than(Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.11/0.38 tff(67,axiom,(![Y: $i, X: $i] : ((less_than(X, Y) | less_than(Y, X)) | (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax','all_related')).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.11/0.38 tff(70,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))),
% 0.11/0.38 inference(skolemize,[status(sab)],[69])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | (less_than(m, successor(n)) | (m = successor(n)) | less_than(successor(n), m))) <=> ((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | less_than(m, successor(n)) | (m = successor(n)) | less_than(successor(n), m))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (((m = successor(n)) | less_than(successor(n), m) | less_than(m, successor(n))) <=> (less_than(m, successor(n)) | (m = successor(n)) | less_than(successor(n), m))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | ((m = successor(n)) | less_than(successor(n), m) | less_than(m, successor(n)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | (less_than(m, successor(n)) | (m = successor(n)) | less_than(successor(n), m)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[73])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | ((m = successor(n)) | less_than(successor(n), m) | less_than(m, successor(n)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | less_than(m, successor(n)) | (m = successor(n)) | less_than(successor(n), m))),
% 0.11/0.38 inference(transitivity,[status(thm)],[74, 72])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | ((m = successor(n)) | less_than(successor(n), m) | less_than(m, successor(n)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((X = Y) | less_than(Y, X) | less_than(X, Y))) | less_than(m, successor(n)) | (m = successor(n)) | less_than(successor(n), m)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 ((m = successor(n)) | less_than(successor(n), m)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[77, 71, 61])).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (m = successor(n)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[78, 30])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (less_than(n, m) <=> less_than(n, successor(n))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[79])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (less_than(n, successor(n)) <=> less_than(n, m)),
% 0.11/0.38 inference(symmetry,[status(thm)],[80])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 (less_than(n, m)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[10, 81])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[13, 82])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------