TSTP Solution File: NUM016-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Sun Sep 18 13:02:39 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 06:32:13 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(less_type, type, (
% 0.13/0.40 less: ( $i * $i ) > $o)).
% 0.13/0.40 tff(factorial_plus_one_type, type, (
% 0.13/0.40 factorial_plus_one: $i > $i)).
% 0.13/0.40 tff(a_type, type, (
% 0.13/0.40 a: $i)).
% 0.13/0.40 tff(prime_type, type, (
% 0.13/0.40 prime: $i > $o)).
% 0.13/0.40 tff(prime_divisor_type, type, (
% 0.13/0.40 prime_divisor: $i > $i)).
% 0.13/0.40 tff(divides_type, type, (
% 0.13/0.40 divides: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X: $i] : refl(less(X, factorial_plus_one(X)) <=> less(X, factorial_plus_one(X)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X: $i] : less(X, factorial_plus_one(X)) <=> ![X: $i] : less(X, factorial_plus_one(X))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X: $i] : less(X, factorial_plus_one(X)) <=> ![X: $i] : less(X, factorial_plus_one(X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![X: $i] : less(X, factorial_plus_one(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_prime_is_less_than_the_next_one')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![X: $i] : less(X, factorial_plus_one(X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![X: $i] : less(X, factorial_plus_one(X))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i] : less(X, factorial_plus_one(X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![X: $i] : less(X, factorial_plus_one(X))) | less(a, factorial_plus_one(a))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (less(a, factorial_plus_one(a))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,assumption,(~prime(factorial_plus_one(a))), introduced(assumption)).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (^[X: $i] : refl((prime(X) | less(prime_divisor(X), X)) <=> (prime(X) | less(prime_divisor(X), X)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | less(prime_divisor(X), X)) <=> ![X: $i] : (prime(X) | less(prime_divisor(X), X))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | less(prime_divisor(X), X)) <=> ![X: $i] : (prime(X) | less(prime_divisor(X), X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,axiom,(![X: $i] : (prime(X) | less(prime_divisor(X), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','smaller_prime_divisors')).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | less(prime_divisor(X), X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.40 tff(16,plain,(
% 0.13/0.40 ![X: $i] : (prime(X) | less(prime_divisor(X), X))),
% 0.13/0.40 inference(skolemize,[status(sab)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | less(prime_divisor(X), X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (((~![X: $i] : (prime(X) | less(prime_divisor(X), X))) | (prime(factorial_plus_one(a)) | less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a)))) <=> ((~![X: $i] : (prime(X) | less(prime_divisor(X), X))) | prime(factorial_plus_one(a)) | less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 ((~![X: $i] : (prime(X) | less(prime_divisor(X), X))) | (prime(factorial_plus_one(a)) | less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~![X: $i] : (prime(X) | less(prime_divisor(X), X))) | prime(factorial_plus_one(a)) | less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (^[Y: $i, X: $i] : refl(((~less(X, Y)) | (~less(Y, X))) <=> ((~less(X, Y)) | (~less(Y, X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X))) <=> ![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X))) <=> ![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(25,axiom,(![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','numbers_are_different')).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.40 tff(27,plain,(
% 0.13/0.40 ![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[26])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | ((~less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a)))) | (~less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))))) <=> ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | (~less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a)))) | (~less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | ((~less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a)))) | (~less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | (~less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a)))) | (~less(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (~less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[31, 28, 21])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (^[X: $i] : refl((prime(X) | prime(prime_divisor(X))) <=> (prime(X) | prime(prime_divisor(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | prime(prime_divisor(X))) <=> ![X: $i] : (prime(X) | prime(prime_divisor(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | prime(prime_divisor(X))) <=> ![X: $i] : (prime(X) | prime(prime_divisor(X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(36,axiom,(![X: $i] : (prime(X) | prime(prime_divisor(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prime_divsiors')).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | prime(prime_divisor(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.40 tff(38,plain,(
% 0.13/0.40 ![X: $i] : (prime(X) | prime(prime_divisor(X)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | prime(prime_divisor(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (((~![X: $i] : (prime(X) | prime(prime_divisor(X)))) | (prime(factorial_plus_one(a)) | prime(prime_divisor(factorial_plus_one(a))))) <=> ((~![X: $i] : (prime(X) | prime(prime_divisor(X)))) | prime(factorial_plus_one(a)) | prime(prime_divisor(factorial_plus_one(a))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~![X: $i] : (prime(X) | prime(prime_divisor(X)))) | (prime(factorial_plus_one(a)) | prime(prime_divisor(factorial_plus_one(a))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 ((~![X: $i] : (prime(X) | prime(prime_divisor(X)))) | prime(factorial_plus_one(a)) | prime(prime_divisor(factorial_plus_one(a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (prime(prime_divisor(factorial_plus_one(a)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[42, 39, 10])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (^[X: $i] : refl((prime(X) | divides(prime_divisor(X), X)) <=> (prime(X) | divides(prime_divisor(X), X)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | divides(prime_divisor(X), X)) <=> ![X: $i] : (prime(X) | divides(prime_divisor(X), X))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | divides(prime_divisor(X), X)) <=> ![X: $i] : (prime(X) | divides(prime_divisor(X), X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(47,axiom,(![X: $i] : (prime(X) | divides(prime_divisor(X), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','division_by_prime_divisor')).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | divides(prime_divisor(X), X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.13/0.40 tff(49,plain,(
% 0.13/0.40 ![X: $i] : (prime(X) | divides(prime_divisor(X), X))),
% 0.13/0.40 inference(skolemize,[status(sab)],[48])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (![X: $i] : (prime(X) | divides(prime_divisor(X), X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (((~![X: $i] : (prime(X) | divides(prime_divisor(X), X))) | (prime(factorial_plus_one(a)) | divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a)))) <=> ((~![X: $i] : (prime(X) | divides(prime_divisor(X), X))) | prime(factorial_plus_one(a)) | divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ((~![X: $i] : (prime(X) | divides(prime_divisor(X), X))) | (prime(factorial_plus_one(a)) | divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ((~![X: $i] : (prime(X) | divides(prime_divisor(X), X))) | prime(factorial_plus_one(a)) | divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[53, 50, 10])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (^[Y: $i, X: $i] : refl(((~divides(X, factorial_plus_one(Y))) | less(Y, X)) <=> ((~divides(X, factorial_plus_one(Y))) | less(Y, X)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X)) <=> ![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X)) <=> ![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(58,axiom,(![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','divisor_is_smaller')).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.13/0.40 tff(60,plain,(
% 0.13/0.40 ![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))),
% 0.13/0.40 inference(skolemize,[status(sab)],[59])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (((~![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))) | ((~divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))) | less(a, prime_divisor(factorial_plus_one(a))))) <=> ((~![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))) | (~divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))) | less(a, prime_divisor(factorial_plus_one(a))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))) | ((~divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))) | less(a, prime_divisor(factorial_plus_one(a))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : ((~divides(X, factorial_plus_one(Y))) | less(Y, X))) | (~divides(prime_divisor(factorial_plus_one(a)), factorial_plus_one(a))) | less(a, prime_divisor(factorial_plus_one(a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (less(a, prime_divisor(factorial_plus_one(a)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 61, 54])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (^[X: $i] : refl((less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X))) <=> (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X))) <=> ![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X))) <=> ![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (^[X: $i] : rewrite((((~prime(X)) | (~less(a, X))) | less(factorial_plus_one(a), X)) <=> (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (![X: $i] : (((~prime(X)) | (~less(a, X))) | less(factorial_plus_one(a), X)) <=> ![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.13/0.40 tff(71,axiom,(![X: $i] : (((~prime(X)) | (~less(a, X))) | less(factorial_plus_one(a), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_there_is_another_prime')).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.13/0.40 tff(74,plain,(
% 0.13/0.40 ![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[73])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 (((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | (less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a))) | (~less(a, prime_divisor(factorial_plus_one(a)))) | (~prime(prime_divisor(factorial_plus_one(a)))))) <=> ((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a))) | (~less(a, prime_divisor(factorial_plus_one(a)))) | (~prime(prime_divisor(factorial_plus_one(a)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 ((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | (less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a))) | (~less(a, prime_divisor(factorial_plus_one(a)))) | (~prime(prime_divisor(factorial_plus_one(a)))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 ((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | less(factorial_plus_one(a), prime_divisor(factorial_plus_one(a))) | (~less(a, prime_divisor(factorial_plus_one(a)))) | (~prime(prime_divisor(factorial_plus_one(a))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[78, 75, 65, 43, 32])).
% 0.13/0.40 tff(80,plain,(prime(factorial_plus_one(a))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | (less(factorial_plus_one(a), factorial_plus_one(a)) | (~less(a, factorial_plus_one(a))) | (~prime(factorial_plus_one(a))))) <=> ((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | less(factorial_plus_one(a), factorial_plus_one(a)) | (~less(a, factorial_plus_one(a))) | (~prime(factorial_plus_one(a))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 ((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | (less(factorial_plus_one(a), factorial_plus_one(a)) | (~less(a, factorial_plus_one(a))) | (~prime(factorial_plus_one(a))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 ((~![X: $i] : (less(factorial_plus_one(a), X) | (~less(a, X)) | (~prime(X)))) | less(factorial_plus_one(a), factorial_plus_one(a)) | (~less(a, factorial_plus_one(a))) | (~prime(factorial_plus_one(a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (less(factorial_plus_one(a), factorial_plus_one(a)) | (~less(a, factorial_plus_one(a)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[83, 75, 80])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (less(factorial_plus_one(a), factorial_plus_one(a))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[84, 9])).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 (((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | (~less(factorial_plus_one(a), factorial_plus_one(a)))) <=> ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | (~less(factorial_plus_one(a), factorial_plus_one(a))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(87,plain,
% 0.13/0.41 (((~less(factorial_plus_one(a), factorial_plus_one(a))) | (~less(factorial_plus_one(a), factorial_plus_one(a)))) <=> (~less(factorial_plus_one(a), factorial_plus_one(a)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(88,plain,
% 0.13/0.41 (((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | ((~less(factorial_plus_one(a), factorial_plus_one(a))) | (~less(factorial_plus_one(a), factorial_plus_one(a))))) <=> ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | (~less(factorial_plus_one(a), factorial_plus_one(a))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[87])).
% 0.13/0.41 tff(89,plain,
% 0.13/0.41 (((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | ((~less(factorial_plus_one(a), factorial_plus_one(a))) | (~less(factorial_plus_one(a), factorial_plus_one(a))))) <=> ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | (~less(factorial_plus_one(a), factorial_plus_one(a))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[88, 86])).
% 0.13/0.41 tff(90,plain,
% 0.13/0.41 ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | ((~less(factorial_plus_one(a), factorial_plus_one(a))) | (~less(factorial_plus_one(a), factorial_plus_one(a))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(91,plain,
% 0.13/0.41 ((~![Y: $i, X: $i] : ((~less(X, Y)) | (~less(Y, X)))) | (~less(factorial_plus_one(a), factorial_plus_one(a)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.13/0.41 tff(92,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[91, 28, 85])).
% 0.13/0.41 % SZS output end Proof
%------------------------------------------------------------------------------