%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV006-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV006-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 09:21:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(less_than_type, type, (
% 0.12/0.37 less_than: ( $i * $i ) > $o)).
% 0.12/0.37 tff(i_type, type, (
% 0.12/0.37 i: $i)).
% 0.12/0.37 tff(successor_type, type, (
% 0.12/0.37 successor: $i > $i)).
% 0.12/0.37 tff(n_type, type, (
% 0.12/0.37 n: $i)).
% 0.12/0.37 tff(a_type, type, (
% 0.12/0.37 a: $i > $i)).
% 0.12/0.37 tff(m_type, type, (
% 0.12/0.37 m: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i] : refl(less_than(X, successor(X)) <=> less_than(X, successor(X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i] : less_than(X, successor(X)) <=> ![X: $i] : less_than(X, successor(X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i] : less_than(X, successor(X)) <=> ![X: $i] : less_than(X, successor(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![X: $i] : less_than(X, successor(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax','less_than_successor')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![X: $i] : less_than(X, successor(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![X: $i] : less_than(X, successor(X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i] : less_than(X, successor(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![X: $i] : less_than(X, successor(X))) | less_than(n, successor(n))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (less_than(n, successor(n))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,assumption,(~less_than(i, successor(n))), introduced(assumption)).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (less_than(i, n) <=> less_than(i, n)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(12,axiom,(less_than(i, n)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (less_than(i, n)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![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))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![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))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![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))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.37 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')).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.37 tff(21,plain,(
% 0.12/0.37 ![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.12/0.37 inference(skolemize,[status(sab)],[20])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(i, n)) | less_than(i, successor(n)) | (~less_than(n, successor(n))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | (~less_than(i, n)) | less_than(i, successor(n)) | (~less_than(n, successor(n))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (((~less_than(n, successor(n))) | (~less_than(i, n)) | less_than(i, successor(n))) <=> ((~less_than(i, n)) | less_than(i, successor(n)) | (~less_than(n, successor(n))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(n, successor(n))) | (~less_than(i, n)) | less_than(i, successor(n)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(i, n)) | less_than(i, successor(n)) | (~less_than(n, successor(n)))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(n, successor(n))) | (~less_than(i, n)) | less_than(i, successor(n)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | (~less_than(i, n)) | less_than(i, successor(n)) | (~less_than(n, successor(n))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[25, 23])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | ((~less_than(n, successor(n))) | (~less_than(i, n)) | less_than(i, successor(n)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ((~![Z: $i, Y: $i, X: $i] : ((~less_than(Y, Z)) | (~less_than(X, Y)) | less_than(X, Z))) | (~less_than(i, n)) | less_than(i, successor(n)) | (~less_than(n, successor(n)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[28, 22, 13, 10, 9])).
% 0.12/0.37 tff(30,plain,(less_than(i, successor(n))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (^[X: $i] : refl(((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i)) <=> ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i)) <=> ![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i)) <=> ![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (^[X: $i] : trans(monotonicity(rewrite((less_than(X, i) | (~less_than(X, successor(n)))) <=> ((~less_than(X, successor(n))) | less_than(X, i))), (((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(m)))) <=> (((~less_than(X, successor(n))) | less_than(X, i)) | (~less_than(a(X), a(m)))))), rewrite((((~less_than(X, successor(n))) | less_than(X, i)) | (~less_than(a(X), a(m)))) <=> ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))), (((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(m)))) <=> ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (![X: $i] : ((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(m)))) <=> ![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.37 tff(36,axiom,(![X: $i] : ((less_than(X, i) | (~less_than(X, successor(n)))) | (~less_than(a(X), a(m))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.38 tff(39,plain,(
% 0.12/0.38 ![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))),
% 0.12/0.38 inference(skolemize,[status(sab)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (less_than(a(i), a(m)) <=> less_than(a(i), a(m))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,axiom,(less_than(a(i), a(m))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (less_than(a(i), a(m))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))) | ((~less_than(a(i), a(m))) | (~less_than(i, successor(n))) | less_than(i, i))) <=> ((~![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))) | (~less_than(a(i), a(m))) | (~less_than(i, successor(n))) | less_than(i, i))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))) | ((~less_than(a(i), a(m))) | (~less_than(i, successor(n))) | less_than(i, i))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((~![X: $i] : ((~less_than(a(X), a(m))) | (~less_than(X, successor(n))) | less_than(X, i))) | (~less_than(a(i), a(m))) | (~less_than(i, successor(n))) | less_than(i, i)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~less_than(i, successor(n))) | less_than(i, i)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[46, 43, 40])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (less_than(i, i)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[47, 30])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : refl(((~less_than(X, Y)) | (~less_than(Y, X))) <=> ((~less_than(X, Y)) | (~less_than(Y, X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X))) <=> ![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(52,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')).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.38 tff(54,plain,(
% 0.12/0.38 ![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[53])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | (~less_than(i, i))) <=> ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | (~less_than(i, i)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (((~less_than(i, i)) | (~less_than(i, i))) <=> (~less_than(i, i))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | ((~less_than(i, i)) | (~less_than(i, i)))) <=> ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | (~less_than(i, i)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[57])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | ((~less_than(i, i)) | (~less_than(i, i)))) <=> ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | (~less_than(i, i)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[58, 56])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | ((~less_than(i, i)) | (~less_than(i, i)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~less_than(X, Y)) | (~less_than(Y, X)))) | (~less_than(i, i))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[61, 55, 48])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------