%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Thu Sep 24 01:44:13 PM UTC 2026
% Result : Unsatisfiable 1.45s 0.63s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of clauses : 107 ( 43 unt; 6 nHn; 62 RR)
% Number of literals : 228 ( 4 equ; 121 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 200 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(gcd_divides2,axiom,
( ~ gcd(X2,X3,X1)
| divides(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_divides2) ).
cnf(transitivity_of_divides,axiom,
( ~ divides(X3,X2)
| ~ divides(X1,X3)
| divides(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_divides) ).
cnf(c_is_gcd_of_a_and_b,negated_conjecture,
gcd(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_gcd_of_a_and_b) ).
cnf(divides_quotient_multiply3,axiom,
( ~ divides(X1,multiply(X2,X3))
| ~ divides(X2,X1)
| divides(quotient(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply3) ).
cnf(operand_divides_product,axiom,
divides(X1,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operand_divides_product) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(gcd_divides1,axiom,
( ~ gcd(X3,X2,X1)
| divides(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_divides1) ).
cnf(divides_quotient_multiply1,axiom,
( ~ divides(quotient(X1,X2),X3)
| ~ divides(X2,X1)
| divides(X1,multiply(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply1) ).
cnf(prove_lcm,negated_conjecture,
~ lcm(a,b,quotient(multiply(a,b),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lcm) ).
cnf(lcm2,axiom,
( ~ divides(X2,X3)
| ~ divides(X1,X3)
| divides(X2,k(X2,X1,X3))
| lcm(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm2) ).
cnf(lcm1,axiom,
( ~ divides(X2,X3)
| ~ divides(X1,X3)
| divides(X1,k(X2,X1,X3))
| lcm(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm1) ).
cnf(divides_and_multiply,axiom,
( ~ divides(X2,X3)
| divides(multiply(X1,X2),multiply(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_and_multiply) ).
cnf(one_divides_everything,axiom,
divides(quotient(X1,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_divides_everything) ).
cnf(commutativity_of_k,axiom,
k(X1,X2,X3) = k(X2,X1,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_k) ).
cnf(reflexivity_of_divides,axiom,
divides(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_divides) ).
cnf(commutativity_of_gcd,axiom,
( ~ gcd(X1,X2,X3)
| gcd(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_gcd) ).
cnf(property_of_gcd,axiom,
( ~ gcd(X2,X3,X4)
| gcd(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_gcd) ).
cnf(divides_quotient_multiply2,axiom,
( ~ divides(multiply(X1,X3),X2)
| ~ divides(X3,X2)
| divides(X1,quotient(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply2) ).
cnf(lcm3,axiom,
( ~ divides(X3,k(X2,X1,X3))
| ~ divides(X2,X3)
| ~ divides(X1,X3)
| lcm(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm3) ).
cnf(gcd1,axiom,
( ~ gcd(X3,X4,X2)
| ~ divides(X1,X4)
| ~ divides(X1,X3)
| divides(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd1) ).
cnf(c_0_20,plain,
( ~ gcd(X2,X3,X1)
| divides(X1,X2) ),
inference(fof_simplification,[status(thm)],[gcd_divides2]) ).
cnf(c_0_21,plain,
( ~ divides(X3,X2)
| ~ divides(X1,X3)
| divides(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_divides]) ).
cnf(c_0_22,plain,
( ~ gcd(X2,X3,X1)
| divides(X1,X2) ),
c_0_20 ).
cnf(c_0_23,negated_conjecture,
gcd(a,b,c),
c_is_gcd_of_a_and_b ).
cnf(c_0_24,plain,
( ~ divides(X1,multiply(X2,X3))
| ~ divides(X2,X1)
| divides(quotient(X1,X2),X3) ),
inference(fof_simplification,[status(thm)],[divides_quotient_multiply3]) ).
cnf(c_0_25,axiom,
divides(X1,multiply(X1,X2)),
operand_divides_product ).
cnf(c_0_26,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_27,plain,
( ~ divides(X3,X2)
| ~ divides(X1,X3)
| divides(X1,X2) ),
c_0_21 ).
cnf(c_0_28,negated_conjecture,
divides(c,a),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( ~ divides(X1,multiply(X2,X3))
| ~ divides(X2,X1)
| divides(quotient(X1,X2),X3) ),
c_0_24 ).
cnf(c_0_30,plain,
divides(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( ~ gcd(X3,X2,X1)
| divides(X1,X2) ),
inference(fof_simplification,[status(thm)],[gcd_divides1]) ).
cnf(c_0_32,plain,
( ~ divides(quotient(X1,X2),X3)
| ~ divides(X2,X1)
| divides(X1,multiply(X2,X3)) ),
inference(fof_simplification,[status(thm)],[divides_quotient_multiply1]) ).
cnf(c_0_33,negated_conjecture,
( ~ divides(X1,c)
| divides(X1,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ divides(X2,X1)
| divides(quotient(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ gcd(X3,X2,X1)
| divides(X1,X2) ),
c_0_31 ).
cnf(c_0_36,plain,
( ~ divides(quotient(X1,X2),X3)
| ~ divides(X2,X1)
| divides(X1,multiply(X2,X3)) ),
c_0_32 ).
cnf(c_0_37,negated_conjecture,
( ~ divides(X1,c)
| divides(quotient(c,X1),a) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
divides(c,b),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_39,negated_conjecture,
~ lcm(a,b,quotient(multiply(a,b),c)),
inference(fof_simplification,[status(thm)],[prove_lcm]) ).
cnf(c_0_40,plain,
( ~ divides(X2,X3)
| ~ divides(X1,X3)
| divides(X2,k(X2,X1,X3))
| lcm(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[lcm2]) ).
cnf(c_0_41,plain,
( ~ divides(X2,X3)
| ~ divides(X1,X3)
| divides(X1,k(X2,X1,X3))
| lcm(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[lcm1]) ).
cnf(c_0_42,plain,
( ~ divides(X2,X3)
| divides(multiply(X1,X2),multiply(X1,X3)) ),
inference(fof_simplification,[status(thm)],[divides_and_multiply]) ).
cnf(c_0_43,negated_conjecture,
( ~ divides(X1,c)
| divides(c,multiply(X1,a)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,axiom,
divides(quotient(X1,X1),X2),
one_divides_everything ).
cnf(c_0_45,negated_conjecture,
( ~ divides(X1,c)
| divides(X1,b) ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
~ lcm(a,b,quotient(multiply(a,b),c)),
c_0_39 ).
cnf(c_0_47,plain,
( ~ divides(X2,X3)
| ~ divides(X1,X3)
| divides(X2,k(X2,X1,X3))
| lcm(X1,X2,X3) ),
c_0_40 ).
cnf(c_0_48,axiom,
k(X1,X2,X3) = k(X2,X1,X3),
commutativity_of_k ).
cnf(c_0_49,plain,
( ~ divides(X2,X3)
| ~ divides(X1,X3)
| divides(X1,k(X2,X1,X3))
| lcm(X1,X2,X3) ),
c_0_41 ).
cnf(c_0_50,axiom,
divides(X1,X1),
reflexivity_of_divides ).
cnf(c_0_51,plain,
( ~ divides(X2,X3)
| divides(multiply(X1,X2),multiply(X1,X3)) ),
c_0_42 ).
cnf(c_0_52,negated_conjecture,
divides(c,multiply(quotient(X1,X1),a)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
( ~ divides(X1,c)
| divides(quotient(c,X1),b) ),
inference(spm,[status(thm)],[c_0_45,c_0_34]) ).
cnf(c_0_54,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(b,k(a,b,quotient(multiply(a,b),c))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(a,k(a,b,quotient(multiply(a,b),c))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_49]),c_0_48]) ).
cnf(c_0_56,plain,
divides(quotient(multiply(X1,X2),X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_50]),c_0_25])]) ).
cnf(c_0_57,plain,
( ~ divides(X4,X3)
| ~ divides(X1,multiply(X2,X4))
| divides(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
divides(c,multiply(a,quotient(X1,X1))),
inference(spm,[status(thm)],[c_0_52,c_0_26]) ).
cnf(c_0_59,negated_conjecture,
( ~ divides(X1,c)
| divides(c,multiply(X1,b)) ),
inference(spm,[status(thm)],[c_0_36,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( ~ divides(X1,b)
| ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(X1,k(a,b,quotient(multiply(a,b),c))) ),
inference(spm,[status(thm)],[c_0_27,c_0_54]) ).
cnf(c_0_61,plain,
( ~ gcd(X1,X2,X3)
| gcd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_gcd]) ).
cnf(c_0_62,plain,
( ~ gcd(X2,X3,X4)
| gcd(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4)) ),
inference(fof_simplification,[status(thm)],[property_of_gcd]) ).
cnf(c_0_63,negated_conjecture,
( ~ divides(X1,a)
| ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(X1,k(a,b,quotient(multiply(a,b),c))) ),
inference(spm,[status(thm)],[c_0_27,c_0_55]) ).
cnf(c_0_64,plain,
( ~ divides(multiply(X1,X3),X2)
| ~ divides(X3,X2)
| divides(X1,quotient(X2,X3)) ),
inference(fof_simplification,[status(thm)],[divides_quotient_multiply2]) ).
cnf(c_0_65,negated_conjecture,
divides(quotient(multiply(X1,c),X1),a),
inference(spm,[status(thm)],[c_0_33,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
divides(c,multiply(a,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_44])]) ).
cnf(c_0_67,negated_conjecture,
divides(c,multiply(quotient(X1,X1),b)),
inference(spm,[status(thm)],[c_0_59,c_0_44]) ).
cnf(c_0_68,negated_conjecture,
( ~ divides(X1,X2)
| ~ divides(X2,b)
| ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(X1,k(a,b,quotient(multiply(a,b),c))) ),
inference(spm,[status(thm)],[c_0_27,c_0_60]) ).
cnf(c_0_69,plain,
( ~ gcd(X1,X2,X3)
| gcd(X2,X1,X3) ),
c_0_61 ).
cnf(c_0_70,plain,
( ~ gcd(X2,X3,X4)
| gcd(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4)) ),
c_0_62 ).
cnf(c_0_71,negated_conjecture,
( ~ divides(X2,X1)
| ~ divides(quotient(X1,X2),a)
| ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(X1,multiply(X2,k(a,b,quotient(multiply(a,b),c)))) ),
inference(spm,[status(thm)],[c_0_36,c_0_63]) ).
cnf(c_0_72,plain,
divides(quotient(multiply(X1,X2),X2),X1),
inference(spm,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_73,plain,
( ~ divides(multiply(X1,X3),X2)
| ~ divides(X3,X2)
| divides(X1,quotient(X2,X3)) ),
c_0_64 ).
cnf(c_0_74,negated_conjecture,
divides(multiply(X1,c),multiply(X1,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_65]),c_0_25])]) ).
cnf(c_0_75,negated_conjecture,
divides(c,multiply(X1,a)),
inference(spm,[status(thm)],[c_0_66,c_0_26]) ).
cnf(c_0_76,negated_conjecture,
divides(c,multiply(b,quotient(X1,X1))),
inference(spm,[status(thm)],[c_0_67,c_0_26]) ).
cnf(c_0_77,negated_conjecture,
( ~ divides(X1,quotient(multiply(X2,b),X2))
| ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(X1,k(a,b,quotient(multiply(a,b),c))) ),
inference(spm,[status(thm)],[c_0_68,c_0_56]) ).
cnf(c_0_78,plain,
( ~ gcd(X3,X2,X4)
| gcd(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_79,negated_conjecture,
gcd(b,a,c),
inference(spm,[status(thm)],[c_0_69,c_0_23]) ).
cnf(c_0_80,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(multiply(a,X1),multiply(X1,k(a,b,quotient(multiply(a,b),c)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_30])]) ).
cnf(c_0_81,negated_conjecture,
divides(X1,quotient(multiply(X1,a),c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_82,negated_conjecture,
divides(quotient(multiply(X1,c),X1),b),
inference(spm,[status(thm)],[c_0_45,c_0_56]) ).
cnf(c_0_83,negated_conjecture,
divides(c,multiply(b,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_76]),c_0_44])]) ).
cnf(c_0_84,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(quotient(multiply(X1,b),X1),k(a,b,quotient(multiply(a,b),c))) ),
inference(spm,[status(thm)],[c_0_77,c_0_50]) ).
cnf(c_0_85,plain,
( ~ divides(X3,k(X2,X1,X3))
| ~ divides(X2,X3)
| ~ divides(X1,X3)
| lcm(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[lcm3]) ).
cnf(c_0_86,plain,
( ~ gcd(X3,X4,X2)
| ~ divides(X1,X4)
| ~ divides(X1,X3)
| divides(X1,X2) ),
inference(fof_simplification,[status(thm)],[gcd1]) ).
cnf(c_0_87,negated_conjecture,
gcd(multiply(X1,a),multiply(X1,b),multiply(X1,c)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_88,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(multiply(a,X1),multiply(k(a,b,quotient(multiply(a,b),c)),X1)) ),
inference(spm,[status(thm)],[c_0_80,c_0_26]) ).
cnf(c_0_89,negated_conjecture,
divides(X1,quotient(multiply(a,X1),c)),
inference(spm,[status(thm)],[c_0_81,c_0_26]) ).
cnf(c_0_90,negated_conjecture,
divides(multiply(X1,c),multiply(X1,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_82]),c_0_25])]) ).
cnf(c_0_91,negated_conjecture,
divides(c,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_83,c_0_26]) ).
cnf(c_0_92,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(multiply(X1,b),multiply(X1,k(a,b,quotient(multiply(a,b),c)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_84]),c_0_25])]) ).
cnf(c_0_93,plain,
( ~ divides(X3,k(X2,X1,X3))
| ~ divides(X2,X3)
| ~ divides(X1,X3)
| lcm(X1,X2,X3) ),
c_0_85 ).
cnf(c_0_94,plain,
( ~ gcd(X3,X4,X2)
| ~ divides(X1,X4)
| ~ divides(X1,X3)
| divides(X1,X2) ),
c_0_86 ).
cnf(c_0_95,negated_conjecture,
gcd(multiply(X1,a),multiply(X1,b),multiply(c,X1)),
inference(spm,[status(thm)],[c_0_87,c_0_26]) ).
cnf(c_0_96,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| divides(multiply(a,X1),multiply(k(a,b,quotient(multiply(a,b),c)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]) ).
cnf(c_0_97,negated_conjecture,
divides(X1,quotient(multiply(X1,b),c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_90]),c_0_91])]) ).
cnf(c_0_98,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| divides(multiply(X1,b),multiply(X1,k(a,b,quotient(multiply(a,b),c)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_89])]) ).
cnf(c_0_99,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| ~ divides(quotient(multiply(a,b),c),k(a,b,quotient(multiply(a,b),c))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_93]),c_0_48]) ).
cnf(c_0_100,negated_conjecture,
( ~ divides(X1,multiply(X2,a))
| ~ divides(X1,multiply(X2,b))
| divides(X1,multiply(c,X2)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
divides(multiply(a,X1),multiply(k(a,b,quotient(multiply(a,b),c)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]) ).
cnf(c_0_102,negated_conjecture,
divides(multiply(X1,b),multiply(X1,k(a,b,quotient(multiply(a,b),c)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_97])]) ).
cnf(c_0_103,negated_conjecture,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(quotient(multiply(a,b),c),k(a,b,quotient(multiply(a,b),c))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_89])]) ).
cnf(c_0_104,negated_conjecture,
divides(multiply(a,b),multiply(c,k(a,b,quotient(multiply(a,b),c)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_26]),c_0_102])]) ).
cnf(c_0_105,negated_conjecture,
~ divides(quotient(multiply(a,b),c),k(a,b,quotient(multiply(a,b),c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_97])]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_104]),c_0_91])]),c_0_105]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.35 % Computer : n015.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8046.5625MB
% 0.12/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Sep 21 02:00:50 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.45/0.63 % Version: 3.5.1
% 1.45/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.45/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.45/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.45/0.63 % Starting new_bool_1 with 300s (1) cores
% 1.45/0.63 % Starting sh5l with 300s (1) cores
% 1.45/0.63 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 321091 completed with status 0
% 1.45/0.63 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.45/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.45/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.45/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.45/0.63 % No SInE strategy applied
% 1.45/0.63 % Search class: FGUSM-FFMF32-SFFFFFNN
% 1.45/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.45/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.45/0.63 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 226s (1) cores
% 1.45/0.63 % Starting new_bool_3 with 226s (1) cores
% 1.45/0.63 % Starting G-E--_215_C46_F1_AE_CS_SP_PS_S2S with 226s (1) cores
% 1.45/0.63 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 321098 completed with status 0
% 1.45/0.63 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 1.45/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.45/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.45/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.45/0.63 % No SInE strategy applied
% 1.45/0.63 % Search class: FGUSM-FFMF32-SFFFFFNN
% 1.45/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.45/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.45/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.45/0.63 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 226s (1) cores
% 1.45/0.63 % Preprocessing time : 0.001 s
% 1.45/0.63 % Presaturation interreduction done
% 1.45/0.63
% 1.45/0.63 % Proof found!
% 1.45/0.63 % SZS status Unsatisfiable
% 1.45/0.63 % SZS output start CNFRefutation
% See solution above
% 1.45/0.63 % Parsed axioms : 25
% 1.45/0.63 % Removed by relevancy pruning/SinE : 0
% 1.45/0.63 % Initial clauses : 25
% 1.45/0.63 % Removed in clause preprocessing : 0
% 1.45/0.63 % Initial clauses in saturation : 25
% 1.45/0.63 % Processed clauses : 1711
% 1.45/0.63 % ...of these trivial : 379
% 1.45/0.63 % ...subsumed : 679
% 1.45/0.63 % ...remaining for further processing : 653
% 1.45/0.63 % Other redundant clauses eliminated : 0
% 1.45/0.63 % Clauses deleted for lack of memory : 0
% 1.45/0.63 % Backward-subsumed : 8
% 1.45/0.63 % Backward-rewritten : 155
% 1.45/0.63 % Generated clauses : 11731
% 1.45/0.63 % ...of the previous two non-redundant : 9252
% 1.45/0.63 % ...aggressively subsumed : 0
% 1.45/0.63 % Contextual simplify-reflections : 2
% 1.45/0.63 % Paramodulations : 11731
% 1.45/0.63 % Factorizations : 0
% 1.45/0.63 % NegExts : 0
% 1.45/0.63 % Equation resolutions : 0
% 1.45/0.63 % Disequality decompositions : 0
% 1.45/0.63 % Total rewrite steps : 4393
% 1.45/0.63 % ...of those cached : 3828
% 1.45/0.63 % Propositional unsat checks : 0
% 1.45/0.63 % Propositional check models : 0
% 1.45/0.63 % Propositional check unsatisfiable : 0
% 1.45/0.63 % Propositional clauses : 0
% 1.45/0.63 % Propositional clauses after purity: 0
% 1.45/0.63 % Propositional unsat core size : 0
% 1.45/0.63 % Propositional preprocessing time : 0.000
% 1.45/0.63 % Propositional encoding time : 0.000
% 1.45/0.63 % Propositional solver time : 0.000
% 1.45/0.63 % Success case prop preproc time : 0.000
% 1.45/0.63 % Success case prop encoding time : 0.000
% 1.45/0.63 % Success case prop solver time : 0.000
% 1.45/0.63 % Current number of processed clauses : 465
% 1.45/0.63 % Positive orientable unit clauses : 209
% 1.45/0.63 % Positive unorientable unit clauses: 3
% 1.45/0.63 % Negative unit clauses : 7
% 1.45/0.63 % Non-unit-clauses : 246
% 1.45/0.63 % Current number of unprocessed clauses: 7421
% 1.45/0.63 % ...number of literals in the above : 18108
% 1.45/0.63 % Current number of archived formulas : 0
% 1.45/0.63 % Current number of archived clauses : 188
% 1.45/0.63 % Clause-clause subsumption calls (NU) : 43059
% 1.45/0.63 % Rec. Clause-clause subsumption calls : 38334
% 1.45/0.63 % Non-unit clause-clause subsumptions : 681
% 1.45/0.63 % Unit Clause-clause subsumption calls : 3347
% 1.45/0.63 % Rewrite failures with RHS unbound : 0
% 1.45/0.63 % BW rewrite match attempts : 687
% 1.45/0.63 % BW rewrite match successes : 29
% 1.45/0.63 % Condensation attempts : 0
% 1.45/0.63 % Condensation successes : 0
% 1.45/0.63 % Termbank termtop insertions : 210101
% 1.45/0.63 % Search garbage collected termcells : 62
% 1.45/0.63
% 1.45/0.63 % -------------------------------------------------
% 1.45/0.63 % User time : 0.197 s
% 1.45/0.63 % System time : 0.015 s
% 1.45/0.63 % Total time : 0.213 s
% 1.45/0.63 % Maximum resident set size: 3648 pages
% 1.45/0.63
% 1.45/0.63 % -------------------------------------------------
% 1.45/0.63 % User time : 0.849 s
% 1.45/0.63 % System time : 0.081 s
% 1.45/0.63 % Total time : 0.930 s
% 1.45/0.63 % Maximum resident set size: 4608 pages
% 1.45/0.63 % E exiting
%------------------------------------------------------------------------------