%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:51:38 AM UTC 2026
% Result : Unsatisfiable 272.86s 283.14s
% Output : Proof 272.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 130 ( 92 unt; 0 nHn; 113 RR)
% Number of literals : 202 ( 0 equ; 74 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divides_substitution1,axiom,
( divides(C,A)
| ~ divides(C,B)
| ~ equalish(B,A) ),
file('theBenchmark.p',divides_substitution1) ).
cnf(closure_of_product,axiom,
product(A,B,multiply(A,B)),
file('theBenchmark.p',closure_of_product) ).
cnf(product_associativity1,axiom,
( product(F,E,C)
| ~ product(A,D,F)
| ~ product(D,E,B)
| ~ product(A,B,C) ),
file('theBenchmark.p',product_associativity1) ).
cnf(product_left_cancellation,axiom,
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(divides_implies_product,axiom,
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
file('theBenchmark.p',divides_implies_product) ).
cnf(product_divisible_by_operand,axiom,
( divides(A,C)
| ~ product(A,B,C) ),
file('theBenchmark.p',product_divisible_by_operand) ).
cnf(primes_lemma1,axiom,
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
file('theBenchmark.p',primes_lemma1) ).
cnf(a_is_prime,hypothesis,
prime(a),
file('theBenchmark.p',a_is_prime) ).
cnf(prove_there_is_no_common_divisor,negated_conjecture,
( ~ divides(A,b)
| ~ divides(A,c) ),
file('theBenchmark.p',prove_there_is_no_common_divisor) ).
cnf(t1,plain,
( ~ divides(second_divided_by_1st(a,a),c)
| ~ divides(second_divided_by_1st(a,a),b) ),
inference(start,[status(thm),parent(0:0)],[prove_there_is_no_common_divisor]) ).
cnf(t2,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),b),b)
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b))
| divides(second_divided_by_1st(a,a),b) ),
inference(extension,[status(thm),parent(t1:1)],[divides_substitution1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t2:2)],[divides_substitution1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t4:2)],[divides_substitution1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t6:2)],[divides_substitution1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t8:2)],[divides_substitution1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t10:2)],[product_divisible_by_operand]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t12:2)],[closure_of_product]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ product(U_5554,multiply(second_divided_by_1st(a,a),b),multiply(U_5554,multiply(second_divided_by_1st(a,a),b)))
| ~ product(U_5554,multiply(second_divided_by_1st(a,a),b),multiply(U_5554,multiply(second_divided_by_1st(a,a),b)))
| equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t10:3)],[product_left_cancellation]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
product(U_5554,multiply(second_divided_by_1st(a,a),b),multiply(U_5554,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t16:2)],[closure_of_product]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
product(U_5554,multiply(second_divided_by_1st(a,a),b),multiply(U_5554,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t16:3)],[closure_of_product]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( ~ product(U_5562,multiply(second_divided_by_1st(a,a),b),multiply(U_5562,multiply(second_divided_by_1st(a,a),b)))
| ~ product(U_5562,multiply(second_divided_by_1st(a,a),b),multiply(U_5562,multiply(second_divided_by_1st(a,a),b)))
| equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t8:3)],[product_left_cancellation]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t8:3]) ).
cnf(t24,plain,
product(U_5562,multiply(second_divided_by_1st(a,a),b),multiply(U_5562,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t22:2)],[closure_of_product]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
product(U_5562,multiply(second_divided_by_1st(a,a),b),multiply(U_5562,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t22:3)],[closure_of_product]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
( ~ product(U_5570,multiply(second_divided_by_1st(a,a),b),multiply(U_5570,multiply(second_divided_by_1st(a,a),b)))
| ~ product(U_5570,multiply(second_divided_by_1st(a,a),b),multiply(U_5570,multiply(second_divided_by_1st(a,a),b)))
| equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t6:3)],[product_left_cancellation]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t6:3]) ).
cnf(t30,plain,
product(U_5570,multiply(second_divided_by_1st(a,a),b),multiply(U_5570,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t28:2)],[closure_of_product]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
product(U_5570,multiply(second_divided_by_1st(a,a),b),multiply(U_5570,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t28:3)],[closure_of_product]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
( ~ product(U_5578,multiply(second_divided_by_1st(a,a),b),multiply(U_5578,multiply(second_divided_by_1st(a,a),b)))
| ~ product(U_5578,multiply(second_divided_by_1st(a,a),b),multiply(U_5578,multiply(second_divided_by_1st(a,a),b)))
| equalish(multiply(second_divided_by_1st(a,a),b),multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t4:3)],[product_left_cancellation]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t4:3]) ).
cnf(t36,plain,
product(U_5578,multiply(second_divided_by_1st(a,a),b),multiply(U_5578,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t34:2)],[closure_of_product]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
product(U_5578,multiply(second_divided_by_1st(a,a),b),multiply(U_5578,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t34:3)],[closure_of_product]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
( ~ product(a,b,multiply(a,multiply(second_divided_by_1st(a,a),b)))
| ~ product(a,multiply(second_divided_by_1st(a,a),b),multiply(a,multiply(second_divided_by_1st(a,a),b)))
| equalish(multiply(second_divided_by_1st(a,a),b),b) ),
inference(extension,[status(thm),parent(t2:3)],[product_left_cancellation]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t2:3]) ).
cnf(t42,plain,
product(a,multiply(second_divided_by_1st(a,a),b),multiply(a,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t40:2)],[closure_of_product]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( ~ product(a,second_divided_by_1st(a,a),a)
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| ~ product(a,multiply(second_divided_by_1st(a,a),b),multiply(a,multiply(second_divided_by_1st(a,a),b)))
| product(a,b,multiply(a,multiply(second_divided_by_1st(a,a),b))) ),
inference(extension,[status(thm),parent(t40:3)],[product_associativity1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
product(a,multiply(second_divided_by_1st(a,a),b),multiply(a,multiply(second_divided_by_1st(a,a),b))),
inference(extension,[status(thm),parent(t44:2)],[closure_of_product]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t44:3)],[closure_of_product]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
( ~ divides(a,a)
| product(a,second_divided_by_1st(a,a),a) ),
inference(extension,[status(thm),parent(t44:4)],[divides_implies_product]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t44:4]) ).
cnf(t52,plain,
( ~ divides(a,multiply(a,a))
| ~ prime(a)
| ~ product(a,a,multiply(a,a))
| divides(a,a) ),
inference(extension,[status(thm),parent(t50:2)],[primes_lemma1]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t52:2)],[closure_of_product]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
prime(a),
inference(extension,[status(thm),parent(t52:3)],[a_is_prime]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
( ~ product(a,a,multiply(a,a))
| divides(a,multiply(a,a)) ),
inference(extension,[status(thm),parent(t52:4)],[product_divisible_by_operand]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t52:4]) ).
cnf(t60,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t58:2)],[closure_of_product]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),c),c)
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c))
| divides(second_divided_by_1st(a,a),c) ),
inference(extension,[status(thm),parent(t1:2)],[divides_substitution1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t1:2]) ).
cnf(t64,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t62:2)],[divides_substitution1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t64:2)],[divides_substitution1]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t66:2)],[divides_substitution1]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
( ~ equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c))
| ~ divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t68:2)],[divides_substitution1]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
( ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| divides(second_divided_by_1st(a,a),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t70:2)],[product_divisible_by_operand]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t72:2)],[closure_of_product]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
( ~ product(U_5634,multiply(second_divided_by_1st(a,a),c),multiply(U_5634,multiply(second_divided_by_1st(a,a),c)))
| ~ product(U_5634,multiply(second_divided_by_1st(a,a),c),multiply(U_5634,multiply(second_divided_by_1st(a,a),c)))
| equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t70:3)],[product_left_cancellation]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t70:3]) ).
cnf(t78,plain,
product(U_5634,multiply(second_divided_by_1st(a,a),c),multiply(U_5634,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t76:2)],[closure_of_product]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
product(U_5634,multiply(second_divided_by_1st(a,a),c),multiply(U_5634,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t76:3)],[closure_of_product]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t76:3]) ).
cnf(t82,plain,
( ~ product(U_5642,multiply(second_divided_by_1st(a,a),c),multiply(U_5642,multiply(second_divided_by_1st(a,a),c)))
| ~ product(U_5642,multiply(second_divided_by_1st(a,a),c),multiply(U_5642,multiply(second_divided_by_1st(a,a),c)))
| equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t68:3)],[product_left_cancellation]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t68:3]) ).
cnf(t84,plain,
product(U_5642,multiply(second_divided_by_1st(a,a),c),multiply(U_5642,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t82:2)],[closure_of_product]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t82:2]) ).
cnf(t86,plain,
product(U_5642,multiply(second_divided_by_1st(a,a),c),multiply(U_5642,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t82:3)],[closure_of_product]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t82:3]) ).
cnf(t88,plain,
( ~ product(U_5650,multiply(second_divided_by_1st(a,a),c),multiply(U_5650,multiply(second_divided_by_1st(a,a),c)))
| ~ product(U_5650,multiply(second_divided_by_1st(a,a),c),multiply(U_5650,multiply(second_divided_by_1st(a,a),c)))
| equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t66:3)],[product_left_cancellation]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t66:3]) ).
cnf(t90,plain,
product(U_5650,multiply(second_divided_by_1st(a,a),c),multiply(U_5650,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t88:2)],[closure_of_product]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,plain,
product(U_5650,multiply(second_divided_by_1st(a,a),c),multiply(U_5650,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t88:3)],[closure_of_product]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t88:3]) ).
cnf(t94,plain,
( ~ product(U_5658,multiply(second_divided_by_1st(a,a),c),multiply(U_5658,multiply(second_divided_by_1st(a,a),c)))
| ~ product(U_5658,multiply(second_divided_by_1st(a,a),c),multiply(U_5658,multiply(second_divided_by_1st(a,a),c)))
| equalish(multiply(second_divided_by_1st(a,a),c),multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t64:3)],[product_left_cancellation]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t64:3]) ).
cnf(t96,plain,
product(U_5658,multiply(second_divided_by_1st(a,a),c),multiply(U_5658,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t94:2)],[closure_of_product]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t94:2]) ).
cnf(t98,plain,
product(U_5658,multiply(second_divided_by_1st(a,a),c),multiply(U_5658,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t94:3)],[closure_of_product]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t94:3]) ).
cnf(t100,plain,
( ~ product(a,c,multiply(a,multiply(second_divided_by_1st(a,a),c)))
| ~ product(a,multiply(second_divided_by_1st(a,a),c),multiply(a,multiply(second_divided_by_1st(a,a),c)))
| equalish(multiply(second_divided_by_1st(a,a),c),c) ),
inference(extension,[status(thm),parent(t62:3)],[product_left_cancellation]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t62:3]) ).
cnf(t102,plain,
product(a,multiply(second_divided_by_1st(a,a),c),multiply(a,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t100:2)],[closure_of_product]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t100:2]) ).
cnf(t104,plain,
( ~ product(a,second_divided_by_1st(a,a),a)
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| ~ product(a,multiply(second_divided_by_1st(a,a),c),multiply(a,multiply(second_divided_by_1st(a,a),c)))
| product(a,c,multiply(a,multiply(second_divided_by_1st(a,a),c))) ),
inference(extension,[status(thm),parent(t100:3)],[product_associativity1]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t100:3]) ).
cnf(t106,plain,
product(a,multiply(second_divided_by_1st(a,a),c),multiply(a,multiply(second_divided_by_1st(a,a),c))),
inference(extension,[status(thm),parent(t104:2)],[closure_of_product]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t104:2]) ).
cnf(t108,plain,
product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t104:3)],[closure_of_product]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t104:3]) ).
cnf(t110,plain,
( ~ divides(a,a)
| product(a,second_divided_by_1st(a,a),a) ),
inference(extension,[status(thm),parent(t104:4)],[divides_implies_product]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t104:4]) ).
cnf(t112,plain,
( ~ divides(a,multiply(a,a))
| ~ prime(a)
| ~ product(a,a,multiply(a,a))
| divides(a,a) ),
inference(extension,[status(thm),parent(t110:2)],[primes_lemma1]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t110:2]) ).
cnf(t114,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t112:2)],[closure_of_product]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t112:2]) ).
cnf(t116,plain,
prime(a),
inference(extension,[status(thm),parent(t112:3)],[a_is_prime]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t112:3]) ).
cnf(t118,plain,
( ~ product(a,a,multiply(a,a))
| divides(a,multiply(a,a)) ),
inference(extension,[status(thm),parent(t112:4)],[product_divisible_by_operand]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t112:4]) ).
cnf(t120,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t118:2)],[closure_of_product]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t118:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n020.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Sat Sep 19 17:36:28 UTC 2026
% 0.10/10.37 % CPUTime :
% 272.86/283.14 % SZS status Unsatisfiable for theBenchmark
% 272.86/283.14 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------