%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM015-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:18:41 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM015-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 23:58:20 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(divides_type, type, (
% 0.20/0.37 divides: ( $i * $i ) > $o)).
% 0.20/0.37 tff(a_type, type, (
% 0.20/0.37 a: $i)).
% 0.20/0.37 tff(factor_of_type, type, (
% 0.20/0.37 factor_of: $i > $i)).
% 0.20/0.37 tff(divisor_type, type, (
% 0.20/0.37 divisor: $i > $i)).
% 0.20/0.37 tff(less_type, type, (
% 0.20/0.37 less: ( $i * $i ) > $o)).
% 0.20/0.37 tff(prime_type, type, (
% 0.20/0.37 prime: $i > $o)).
% 0.20/0.37 tff(n1_type, type, (
% 0.20/0.37 n1: $i)).
% 0.20/0.37 tff(1,assumption,(~divides(a, a)), introduced(assumption)).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (^[X: $i] : refl(divides(X, X) <=> divides(X, X))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![X: $i] : divides(X, X) <=> ![X: $i] : divides(X, X)),
% 0.20/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![X: $i] : divides(X, X) <=> ![X: $i] : divides(X, X)),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,axiom,(![X: $i] : divides(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','divide_self')).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (![X: $i] : divides(X, X)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.37 tff(7,plain,(
% 0.20/0.37 ![X: $i] : divides(X, X)),
% 0.20/0.37 inference(skolemize,[status(sab)],[6])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![X: $i] : divides(X, X)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 ((~![X: $i] : divides(X, X)) | divides(a, a)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.37 tff(11,plain,(divides(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (^[X: $i] : refl(((~prime(X)) | (~divides(X, a))) <=> ((~prime(X)) | (~divides(X, a))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (![X: $i] : ((~prime(X)) | (~divides(X, a))) <=> ![X: $i] : ((~prime(X)) | (~divides(X, a)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (![X: $i] : ((~prime(X)) | (~divides(X, a))) <=> ![X: $i] : ((~prime(X)) | (~divides(X, a)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(15,axiom,(![X: $i] : ((~prime(X)) | (~divides(X, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_a_has_prime_divisor')).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![X: $i] : ((~prime(X)) | (~divides(X, a)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.37 tff(17,plain,(
% 0.20/0.37 ![X: $i] : ((~prime(X)) | (~divides(X, a)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[16])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![X: $i] : ((~prime(X)) | (~divides(X, a)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | ((~prime(a)) | (~divides(a, a)))) <=> ((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | (~prime(a)) | (~divides(a, a)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 ((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | ((~prime(a)) | (~divides(a, a)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 ((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | (~prime(a)) | (~divides(a, a))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (~prime(a)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (^[X: $i] : refl((prime(X) | less(divisor(X), X)) <=> (prime(X) | less(divisor(X), X)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(divisor(X), X)) <=> ![X: $i] : (prime(X) | less(divisor(X), X))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(divisor(X), X)) <=> ![X: $i] : (prime(X) | less(divisor(X), X))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(26,axiom,(![X: $i] : (prime(X) | less(divisor(X), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','divisor2')).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(divisor(X), X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.37 tff(28,plain,(
% 0.20/0.37 ![X: $i] : (prime(X) | less(divisor(X), X))),
% 0.20/0.37 inference(skolemize,[status(sab)],[27])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(divisor(X), X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (((~![X: $i] : (prime(X) | less(divisor(X), X))) | (prime(a) | less(divisor(a), a))) <=> ((~![X: $i] : (prime(X) | less(divisor(X), X))) | prime(a) | less(divisor(a), a))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 ((~![X: $i] : (prime(X) | less(divisor(X), X))) | (prime(a) | less(divisor(a), a))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 ((~![X: $i] : (prime(X) | less(divisor(X), X))) | prime(a) | less(divisor(a), a)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (less(divisor(a), a)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 (^[X: $i] : refl((prime(X) | less(n1, divisor(X))) <=> (prime(X) | less(n1, divisor(X))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(n1, divisor(X))) <=> ![X: $i] : (prime(X) | less(n1, divisor(X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(n1, divisor(X))) <=> ![X: $i] : (prime(X) | less(n1, divisor(X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(37,axiom,(![X: $i] : (prime(X) | less(n1, divisor(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','divisor1')).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(n1, divisor(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.37 tff(39,plain,(
% 0.20/0.37 ![X: $i] : (prime(X) | less(n1, divisor(X)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[38])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (![X: $i] : (prime(X) | less(n1, divisor(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 (((~![X: $i] : (prime(X) | less(n1, divisor(X)))) | (prime(a) | less(n1, divisor(a)))) <=> ((~![X: $i] : (prime(X) | less(n1, divisor(X)))) | prime(a) | less(n1, divisor(a)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 ((~![X: $i] : (prime(X) | less(n1, divisor(X)))) | (prime(a) | less(n1, divisor(a)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 ((~![X: $i] : (prime(X) | less(n1, divisor(X)))) | prime(a) | less(n1, divisor(a))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 (prime(a) | less(n1, divisor(a))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 (less(n1, divisor(a))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[44, 22])).
% 0.20/0.37 tff(46,plain,
% 0.20/0.37 (^[X: $i] : refl(((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X)) <=> ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(47,plain,
% 0.20/0.37 (![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X)) <=> ![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.37 tff(48,plain,
% 0.20/0.37 (![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X)) <=> ![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(49,plain,
% 0.20/0.37 (^[X: $i] : rewrite((((~less(n1, X)) | (~less(X, a))) | divides(factor_of(X), X)) <=> ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(50,plain,
% 0.20/0.37 (![X: $i] : (((~less(n1, X)) | (~less(X, a))) | divides(factor_of(X), X)) <=> ![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.37 tff(51,axiom,(![X: $i] : (((~less(n1, X)) | (~less(X, a))) | divides(factor_of(X), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','factor2')).
% 0.20/0.37 tff(52,plain,
% 0.20/0.37 (![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.37 tff(53,plain,
% 0.20/0.37 (![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.37 tff(54,plain,(
% 0.20/0.37 ![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))),
% 0.20/0.37 inference(skolemize,[status(sab)],[53])).
% 0.20/0.37 tff(55,plain,
% 0.20/0.37 (![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.20/0.37 tff(56,plain,
% 0.20/0.37 (((~![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))) | ((~less(divisor(a), a)) | (~less(n1, divisor(a))) | divides(factor_of(divisor(a)), divisor(a)))) <=> ((~![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))) | (~less(divisor(a), a)) | (~less(n1, divisor(a))) | divides(factor_of(divisor(a)), divisor(a)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 ((~![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))) | ((~less(divisor(a), a)) | (~less(n1, divisor(a))) | divides(factor_of(divisor(a)), divisor(a)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 ((~![X: $i] : ((~less(X, a)) | (~less(n1, X)) | divides(factor_of(X), X))) | (~less(divisor(a), a)) | (~less(n1, divisor(a))) | divides(factor_of(divisor(a)), divisor(a))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (divides(factor_of(divisor(a)), divisor(a))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[58, 55, 45, 33])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (^[X: $i] : refl((prime(X) | divides(divisor(X), X)) <=> (prime(X) | divides(divisor(X), X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (![X: $i] : (prime(X) | divides(divisor(X), X)) <=> ![X: $i] : (prime(X) | divides(divisor(X), X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (![X: $i] : (prime(X) | divides(divisor(X), X)) <=> ![X: $i] : (prime(X) | divides(divisor(X), X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(63,axiom,(![X: $i] : (prime(X) | divides(divisor(X), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prime')).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (![X: $i] : (prime(X) | divides(divisor(X), X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.38 tff(65,plain,(
% 0.20/0.38 ![X: $i] : (prime(X) | divides(divisor(X), X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[64])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (![X: $i] : (prime(X) | divides(divisor(X), X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (((~![X: $i] : (prime(X) | divides(divisor(X), X))) | (prime(a) | divides(divisor(a), a))) <=> ((~![X: $i] : (prime(X) | divides(divisor(X), X))) | prime(a) | divides(divisor(a), a))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 ((~![X: $i] : (prime(X) | divides(divisor(X), X))) | (prime(a) | divides(divisor(a), a))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 ((~![X: $i] : (prime(X) | divides(divisor(X), X))) | prime(a) | divides(divisor(a), a)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 (divides(divisor(a), a)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[69, 66, 22])).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 (![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 (^[Z: $i, Y: $i, X: $i] : rewrite((((~divides(X, Y)) | (~divides(Y, Z))) | divides(X, Z)) <=> (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 (![Z: $i, Y: $i, X: $i] : (((~divides(X, Y)) | (~divides(Y, Z))) | divides(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.38 tff(75,axiom,(![Z: $i, Y: $i, X: $i] : (((~divides(X, Y)) | (~divides(Y, Z))) | divides(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitive_divide')).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 (![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.38 tff(77,plain,
% 0.20/0.38 (![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.38 tff(78,plain,(
% 0.20/0.38 ![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[77])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 (![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 (((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | ((~divides(divisor(a), a)) | divides(factor_of(divisor(a)), a) | (~divides(factor_of(divisor(a)), divisor(a))))) <=> ((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | (~divides(divisor(a), a)) | divides(factor_of(divisor(a)), a) | (~divides(factor_of(divisor(a)), divisor(a))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(81,plain,
% 0.20/0.38 ((divides(factor_of(divisor(a)), a) | (~divides(divisor(a), a)) | (~divides(factor_of(divisor(a)), divisor(a)))) <=> ((~divides(divisor(a), a)) | divides(factor_of(divisor(a)), a) | (~divides(factor_of(divisor(a)), divisor(a))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | (divides(factor_of(divisor(a)), a) | (~divides(divisor(a), a)) | (~divides(factor_of(divisor(a)), divisor(a))))) <=> ((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | ((~divides(divisor(a), a)) | divides(factor_of(divisor(a)), a) | (~divides(factor_of(divisor(a)), divisor(a)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | (divides(factor_of(divisor(a)), a) | (~divides(divisor(a), a)) | (~divides(factor_of(divisor(a)), divisor(a))))) <=> ((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | (~divides(divisor(a), a)) | divides(factor_of(divisor(a)), a) | (~divides(factor_of(divisor(a)), divisor(a))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.38 tff(84,plain,
% 0.20/0.38 ((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | (divides(factor_of(divisor(a)), a) | (~divides(divisor(a), a)) | (~divides(factor_of(divisor(a)), divisor(a))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 ((~![Z: $i, Y: $i, X: $i] : (divides(X, Z) | (~divides(Y, Z)) | (~divides(X, Y)))) | (~divides(divisor(a), a)) | divides(factor_of(divisor(a)), a) | (~divides(factor_of(divisor(a)), divisor(a)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.38 tff(86,plain,
% 0.20/0.38 (divides(factor_of(divisor(a)), a)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[85, 79, 70, 59])).
% 0.20/0.38 tff(87,plain,
% 0.20/0.38 (^[X: $i] : refl((prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X))) <=> (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(88,plain,
% 0.20/0.38 (![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X))) <=> ![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.38 tff(89,plain,
% 0.20/0.38 (![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X))) <=> ![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(90,plain,
% 0.20/0.38 (^[X: $i] : rewrite((((~less(n1, X)) | (~less(X, a))) | prime(factor_of(X))) <=> (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(91,plain,
% 0.20/0.38 (![X: $i] : (((~less(n1, X)) | (~less(X, a))) | prime(factor_of(X))) <=> ![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.38 tff(92,axiom,(![X: $i] : (((~less(n1, X)) | (~less(X, a))) | prime(factor_of(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','factor1')).
% 0.20/0.38 tff(93,plain,
% 0.20/0.38 (![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.38 tff(94,plain,
% 0.20/0.38 (![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.38 tff(95,plain,(
% 0.20/0.38 ![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[94])).
% 0.20/0.38 tff(96,plain,
% 0.20/0.38 (![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.38 tff(97,plain,
% 0.20/0.38 (((~![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))) | (prime(factor_of(divisor(a))) | (~less(divisor(a), a)) | (~less(n1, divisor(a))))) <=> ((~![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))) | prime(factor_of(divisor(a))) | (~less(divisor(a), a)) | (~less(n1, divisor(a))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(98,plain,
% 0.20/0.38 ((~![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))) | (prime(factor_of(divisor(a))) | (~less(divisor(a), a)) | (~less(n1, divisor(a))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(99,plain,
% 0.20/0.38 ((~![X: $i] : (prime(factor_of(X)) | (~less(X, a)) | (~less(n1, X)))) | prime(factor_of(divisor(a))) | (~less(divisor(a), a)) | (~less(n1, divisor(a)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.38 tff(100,plain,
% 0.20/0.38 (prime(factor_of(divisor(a)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[99, 96, 45, 33])).
% 0.20/0.38 tff(101,plain,
% 0.20/0.38 (((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | ((~prime(factor_of(divisor(a)))) | (~divides(factor_of(divisor(a)), a)))) <=> ((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | (~prime(factor_of(divisor(a)))) | (~divides(factor_of(divisor(a)), a)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(102,plain,
% 0.20/0.38 ((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | ((~prime(factor_of(divisor(a)))) | (~divides(factor_of(divisor(a)), a)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(103,plain,
% 0.20/0.38 ((~![X: $i] : ((~prime(X)) | (~divides(X, a)))) | (~prime(factor_of(divisor(a)))) | (~divides(factor_of(divisor(a)), a))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.38 tff(104,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[103, 18, 100, 86])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------