%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:23:13 PM UTC 2026
% Result : Unsatisfiable 60.32s 15.49s
% Output : CNFRefutation 60.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 98 ( 26 unt; 0 def)
% Number of atoms : 243 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 282 ( 137 ~; 145 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 188 ( 0 sgn 188 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : divides(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_divides) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ divides(X2,X1)
| ~ divides(X0,X2)
| divides(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_divides) ).
fof(f3,axiom,
! [X0,X1] : divides(X0,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operand_divides_product) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ divides(X1,X2)
| divides(multiply(X0,X1),multiply(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_and_multiply) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ divides(quotient(X0,X1),X2)
| ~ divides(X1,X0)
| divides(X0,multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply1) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ divides(multiply(X0,X2),X1)
| ~ divides(X2,X1)
| divides(X0,quotient(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply2) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ divides(X0,multiply(X1,X2))
| ~ divides(X1,X0)
| divides(quotient(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply3) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ gcd(X2,X1,X0)
| divides(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_divides1) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ gcd(X1,X2,X0)
| divides(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_divides2) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ gcd(X2,X3,X1)
| ~ divides(X0,X3)
| ~ divides(X0,X2)
| divides(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd1) ).
fof(f13,axiom,
! [X2,X0,X1] :
( divides(h(X1,X0,X2),X1)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| gcd(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd3) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ divides(h(X1,X0,X2),X2)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| gcd(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd4) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ gcd(X1,X2,X3)
| gcd(multiply(X0,X1),multiply(X0,X2),multiply(X0,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_gcd) ).
fof(f16,axiom,
! [X2,X0,X1] :
( divides(X0,k(X1,X0,X2))
| ~ divides(X1,X2)
| ~ divides(X0,X2)
| lcm(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm1) ).
fof(f17,axiom,
! [X2,X0,X1] :
( divides(X1,k(X1,X0,X2))
| ~ divides(X1,X2)
| ~ divides(X0,X2)
| lcm(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm2) ).
fof(f18,axiom,
! [X2,X0,X1] :
( ~ divides(X2,k(X1,X0,X2))
| ~ divides(X1,X2)
| ~ divides(X0,X2)
| lcm(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm3) ).
fof(f23,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f25,axiom,
! [X2,X0,X1] :
( gcd(X1,X0,X2)
| ~ gcd(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_gcd) ).
fof(f26,negated_conjecture,
gcd(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_gcd_of_a_and_b) ).
fof(f27,negated_conjecture,
~ lcm(a,b,quotient(multiply(a,b),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lcm) ).
tcf(c_74,negated_conjecture,
gcd(a,b,c),
inference(cnf_transformation,[],[f26]) ).
tcf(c_75,negated_conjecture,
~ lcm(a,b,quotient(multiply(a,b),c)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( gcd(X1,X0,X2)
| ~ gcd(X0,X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( gcd(multiply(X3,X0),multiply(X3,X1),multiply(X3,X2))
| ~ gcd(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( divides(X3,X2)
| ~ divides(X3,X1)
| ~ divides(X3,X0)
| ~ gcd(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(X2,X0)
| ~ gcd(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(X2,X1)
| ~ gcd(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(multiply(X2,X0),multiply(X2,X1))
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : divides(X0,multiply(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(quotient(X0,X1),X2)
| ~ divides(X1,X0)
| ~ divides(X0,multiply(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(X0,quotient(X2,X1))
| ~ divides(X1,X2)
| ~ divides(multiply(X0,X1),X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(X0,multiply(X1,X2))
| ~ divides(X1,X0)
| ~ divides(quotient(X0,X1),X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( lcm(X2,X1,X0)
| ~ divides(X2,X0)
| ~ divides(X1,X0)
| ~ divides(X0,k(X1,X2,X0)) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( lcm(X0,X2,X1)
| divides(X2,k(X2,X0,X1))
| ~ divides(X2,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( lcm(X0,X2,X1)
| divides(X0,k(X2,X0,X1))
| ~ divides(X2,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_92,plain,
! [X0: $i] : divides(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( gcd(X1,X0,X2)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| ~ divides(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( gcd(X1,X2,X0)
| divides(h(X2,X1,X0),X2)
| ~ divides(X0,X2)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_99,plain,
divides(a,a),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_342,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( divides(X0,X2)
| ~ divides(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_693,plain,
divides(c,a),
inference(superposition,[status(thm)],[c_74,c_79]) ).
tcf(c_698,plain,
divides(c,b),
inference(superposition,[status(thm)],[c_74,c_80]) ).
tcf(c_699,plain,
! [X0: $i,X1: $i] : divides(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_94,c_82]) ).
tcf(c_705,plain,
gcd(b,a,c),
inference(superposition,[status(thm)],[c_74,c_76]) ).
tcf(c_738,plain,
! [X0: $i] :
( divides(c,X0)
| ~ divides(b,X0) ),
inference(superposition,[status(thm)],[c_698,c_91]) ).
tcf(c_765,plain,
! [X0: $i] : divides(c,multiply(X0,b)),
inference(superposition,[status(thm)],[c_699,c_738]) ).
tcf(c_766,plain,
divides(c,multiply(a,b)),
inference(instantiation,[status(thm)],[c_765]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(X0,quotient(multiply(X0,X2),X1))
| ~ divides(X1,multiply(X0,X2))
| ~ divides(multiply(X0,X1),multiply(X0,X2)) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( divides(X0,quotient(multiply(X2,X3),X1))
| ~ divides(X1,multiply(X2,X3))
| ~ divides(multiply(X0,X1),multiply(X2,X3)) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_920,plain,
( lcm(a,b,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(quotient(multiply(a,b),c),k(b,a,quotient(multiply(a,b),c))) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_940,plain,
( lcm(a,b,quotient(multiply(a,b),c))
| divides(b,k(b,a,quotient(multiply(a,b),c)))
| ~ divides(b,quotient(multiply(a,b),c))
| ~ divides(a,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_941,plain,
( lcm(a,b,quotient(multiply(a,b),c))
| divides(a,k(b,a,quotient(multiply(a,b),c)))
| ~ divides(b,quotient(multiply(a,b),c))
| ~ divides(a,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( divides(multiply(X0,X1),X3)
| ~ divides(X2,X4)
| ( X3 != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_345]) ).
tcf(c_1054,plain,
b = b,
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i] : divides(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_94,c_82]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( divides(multiply(X0,X1),X2)
| ~ divides(multiply(X0,X1),X3)
| ( X2 != X3 )
| ( multiply(X0,X1) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_969]) ).
tcf(c_1299,plain,
( divides(a,quotient(multiply(a,b),c))
| ~ divides(c,multiply(a,b))
| ~ divides(multiply(a,c),multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_1344,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(multiply(X2,X0),multiply(X1,X2))
| ~ divides(X0,X1) ),
inference(superposition,[status(thm)],[c_94,c_81]) ).
tcf(c_1561,plain,
( divides(multiply(a,c),multiply(a,b))
| ~ divides(c,b) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_1778,plain,
! [X0: $i] :
( divides(X0,quotient(multiply(a,b),c))
| ~ divides(c,multiply(a,b))
| ~ divides(multiply(X0,c),multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_917]) ).
tcf(c_2053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( gcd(multiply(X0,X3),multiply(X3,X1),multiply(X3,X2))
| ~ gcd(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_94,c_77]) ).
tcf(c_2062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( divides(multiply(X3,X2),multiply(X3,X0))
| ~ gcd(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_77,c_79]) ).
tcf(c_2321,plain,
! [X0: $i,X1: $i] :
( divides(quotient(multiply(X0,X1),X0),X1)
| ~ divides(X0,multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_83]) ).
tcf(c_2330,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(quotient(X0,X2),X1)
| ~ divides(X2,X0)
| ~ divides(X0,multiply(X1,X2)) ),
inference(superposition,[status(thm)],[c_94,c_83]) ).
tcf(c_2344,plain,
! [X0: $i,X1: $i] : divides(quotient(multiply(X0,X1),X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_2321,c_82]) ).
tcf(c_2411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( divides(multiply(X0,X1),X2)
| ~ divides(multiply(X0,X1),multiply(X0,X3))
| ( X2 != multiply(X0,X3) )
| ( multiply(X0,X1) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_1247]) ).
tcf(c_3067,plain,
! [X0: $i,X1: $i] : divides(quotient(multiply(X0,X1),X1),X0),
inference(superposition,[status(thm)],[c_94,c_2344]) ).
tcf(c_3639,plain,
( divides(b,quotient(multiply(a,b),c))
| ~ divides(c,multiply(a,b))
| ~ divides(multiply(b,c),multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_1778]) ).
tcf(c_3777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( divides(X0,multiply(X2,X4))
| ~ gcd(X1,X3,X4)
| ~ divides(X0,multiply(X2,X3))
| ~ divides(X0,multiply(X1,X2)) ),
inference(superposition,[status(thm)],[c_2053,c_78]) ).
tcf(c_3984,plain,
c = c,
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_5182,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(multiply(X0,X1),multiply(X2,X0))
| ~ divides(multiply(X0,X1),multiply(X0,X2))
| ( multiply(X2,X0) != multiply(X0,X2) )
| ( multiply(X0,X1) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_2411]) ).
tcf(c_5225,plain,
! [X0: $i,X1: $i] :
( divides(multiply(X1,X0),multiply(X0,X1))
| ~ divides(X0,multiply(X1,X0)) ),
inference(superposition,[status(thm)],[c_3067,c_85]) ).
tcf(c_5230,plain,
! [X0: $i,X1: $i] : divides(multiply(X0,X1),multiply(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_5225,c_1194]) ).
tcf(c_6335,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(multiply(X1,X0),X2)
| ~ divides(multiply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_5230,c_91]) ).
tcf(c_13009,plain,
multiply(a,b) = multiply(b,a),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_21623,plain,
( divides(multiply(b,c),multiply(a,b))
| ~ divides(multiply(b,c),multiply(b,a))
| ( multiply(b,c) != multiply(b,c) )
| ( multiply(a,b) != multiply(b,a) ) ),
inference(instantiation,[status(thm)],[c_5182]) ).
tcf(c_28474,plain,
( divides(multiply(b,c),multiply(b,a))
| ~ divides(c,a) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_28867,plain,
( ( multiply(b,c) = multiply(b,c) )
| ( c != c )
| ( b != b ) ),
inference(instantiation,[status(thm)],[c_346]) ).
tcf(c_128722,plain,
! [X0: $i] :
( gcd(k(b,a,quotient(multiply(a,b),c)),X0,a)
| divides(h(X0,k(b,a,quotient(multiply(a,b),c)),a),X0)
| ~ divides(a,X0)
| ~ divides(a,k(b,a,quotient(multiply(a,b),c))) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_128723,plain,
( gcd(k(b,a,quotient(multiply(a,b),c)),a,a)
| divides(h(a,k(b,a,quotient(multiply(a,b),c)),a),a)
| ~ divides(a,a)
| ~ divides(a,k(b,a,quotient(multiply(a,b),c))) ),
inference(instantiation,[status(thm)],[c_128722]) ).
tcf(c_128725,plain,
! [X0: $i] :
( gcd(k(b,a,quotient(multiply(a,b),c)),X0,a)
| ~ divides(a,X0)
| ~ divides(a,k(b,a,quotient(multiply(a,b),c)))
| ~ divides(h(X0,k(b,a,quotient(multiply(a,b),c)),a),a) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_128728,plain,
( gcd(k(b,a,quotient(multiply(a,b),c)),a,a)
| ~ divides(a,a)
| ~ divides(a,k(b,a,quotient(multiply(a,b),c)))
| ~ divides(h(a,k(b,a,quotient(multiply(a,b),c)),a),a) ),
inference(instantiation,[status(thm)],[c_128725]) ).
tcf(c_158709,plain,
! [X0: $i,X1: $i] :
( divides(multiply(X1,b),multiply(X0,X1))
| ~ divides(b,X0) ),
inference(instantiation,[status(thm)],[c_1344]) ).
tcf(c_158849,plain,
! [X0: $i,X1: $i,X2: $i] :
( divides(multiply(X1,X0),multiply(X0,X2))
| ~ divides(multiply(X0,X1),multiply(X0,X2)) ),
inference(instantiation,[status(thm)],[c_6335]) ).
tcf(c_159704,plain,
( divides(quotient(multiply(a,b),c),k(b,a,quotient(multiply(a,b),c)))
| ~ divides(c,multiply(a,b))
| ~ divides(multiply(a,b),multiply(k(b,a,quotient(multiply(a,b),c)),c)) ),
inference(instantiation,[status(thm)],[c_2330]) ).
tcf(c_162587,plain,
! [X0: $i] :
( divides(multiply(X0,b),multiply(k(b,a,quotient(multiply(a,b),c)),X0))
| ~ divides(b,k(b,a,quotient(multiply(a,b),c))) ),
inference(instantiation,[status(thm)],[c_158709]) ).
tcf(c_162588,plain,
( divides(multiply(a,b),multiply(k(b,a,quotient(multiply(a,b),c)),a))
| ~ divides(b,k(b,a,quotient(multiply(a,b),c))) ),
inference(instantiation,[status(thm)],[c_162587]) ).
tcf(c_174715,plain,
! [X0: $i] :
( divides(multiply(X0,b),multiply(b,k(b,a,quotient(multiply(a,b),c))))
| ~ divides(multiply(b,X0),multiply(b,k(b,a,quotient(multiply(a,b),c)))) ),
inference(instantiation,[status(thm)],[c_158849]) ).
tcf(c_174717,plain,
( divides(multiply(a,b),multiply(b,k(b,a,quotient(multiply(a,b),c))))
| ~ divides(multiply(b,a),multiply(b,k(b,a,quotient(multiply(a,b),c)))) ),
inference(instantiation,[status(thm)],[c_174715]) ).
tcf(c_174731,plain,
! [X0: $i,X1: $i] :
( divides(multiply(b,X1),multiply(b,k(b,a,quotient(multiply(a,b),c))))
| ~ gcd(k(b,a,quotient(multiply(a,b),c)),X0,X1) ),
inference(instantiation,[status(thm)],[c_2062]) ).
tcf(c_174733,plain,
( divides(multiply(b,a),multiply(b,k(b,a,quotient(multiply(a,b),c))))
| ~ gcd(k(b,a,quotient(multiply(a,b),c)),a,a) ),
inference(instantiation,[status(thm)],[c_174731]) ).
tcf(c_237878,plain,
! [X0: $i,X1: $i] :
( divides(multiply(a,b),multiply(k(b,a,quotient(multiply(a,b),c)),c))
| ~ gcd(X1,X0,c)
| ~ divides(multiply(a,b),multiply(X1,k(b,a,quotient(multiply(a,b),c))))
| ~ divides(multiply(a,b),multiply(k(b,a,quotient(multiply(a,b),c)),X0)) ),
inference(instantiation,[status(thm)],[c_3777]) ).
tcf(c_244416,plain,
( divides(multiply(a,b),multiply(k(b,a,quotient(multiply(a,b),c)),c))
| ~ gcd(b,a,c)
| ~ divides(multiply(a,b),multiply(b,k(b,a,quotient(multiply(a,b),c))))
| ~ divides(multiply(a,b),multiply(k(b,a,quotient(multiply(a,b),c)),a)) ),
inference(instantiation,[status(thm)],[c_237878]) ).
tcf(c_244417,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_244416,c_174733,c_174717,c_162588,c_159704,c_128728,c_128723,c_28867,c_28474,c_21623,c_13009,c_3984,c_3639,c_1561,c_1299,c_1054,c_941,c_940,c_920,c_766,c_705,c_698,c_693,c_75,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n007.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 02:36:09 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 60.32/15.49 % SZS status Started for theBenchmark.p
% 60.32/15.49 % SZS status Unsatisfiable for theBenchmark.p
% 60.32/15.49
% 60.32/15.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 60.32/15.49
% 60.32/15.49 % ------ iProver source info
% 60.32/15.49
% 60.32/15.49 % git: date: 2026-07-19 20:42:38 +0200
% 60.32/15.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 60.32/15.49 % git: non_committed_changes: false
% 60.32/15.49
% 60.32/15.49 % ------ Parsing...% successful
% 60.32/15.49
% 60.32/15.49
% 60.32/15.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 60.32/15.49
% 60.32/15.49 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 60.32/15.49
% 60.32/15.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 60.32/15.49
% 60.32/15.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 60.32/15.49 % ------ Proving...
% 60.32/15.49 % ------ Problem Properties
% 60.32/15.49
% 60.32/15.49 %
% 60.32/15.49 % clauses 25
% 60.32/15.49 % conjectures 2
% 60.32/15.49 % EPR 8
% 60.32/15.49 % Horn 21
% 60.32/15.49 % unary 8
% 60.32/15.49 % binary 6
% 60.32/15.49 % lits 60
% 60.32/15.49 % lits eq 3
% 60.32/15.49 % fd_pure 0
% 60.32/15.49 % fd_pseudo 0
% 60.32/15.49 % fd_cond 0
% 60.32/15.49 % fd_pseudo_cond 0
% 60.32/15.49 % AC symbols 0
% 60.32/15.49
% 60.32/15.49 % ------ Schedule dynamic 5 is on
% 60.32/15.49
% 60.32/15.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 60.32/15.49
% 60.32/15.49
% 60.32/15.49 % ------
% 60.32/15.49 % Current options:
% 60.32/15.49 % ------
% 60.32/15.49
% 60.32/15.49
% 60.32/15.49 %
% 60.32/15.49
% 60.32/15.49 % ------ Proving...
% 60.32/15.49 % Proof_search_loop: time out after: 5428 full_loop iterations
% 60.32/15.49
% 60.32/15.49 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 60.32/15.49
% 60.32/15.49
% 60.32/15.49 % ------
% 60.32/15.49 % Current options:
% 60.32/15.49 % ------
% 60.32/15.49
% 60.32/15.49
% 60.32/15.49 %
% 60.32/15.49
% 60.32/15.49 % ------ Proving...
% 60.32/15.49 %
% 60.32/15.49
% 60.32/15.49 % SZS status Unsatisfiable for theBenchmark.p
% 60.32/15.49
% 60.32/15.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 60.32/15.49
% 60.32/15.49
%------------------------------------------------------------------------------