%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 194.55s 194.89s
% Output : Proof 194.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 331 ( 277 unt; 0 nHn; 329 RR)
% Number of literals : 505 ( 209 equ; 176 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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,
( 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(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_6,axiom,
( product(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ product(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( ~ divides(second_divided_by_1st(a,a),b)
| ~ divides(second_divided_by_1st(a,a),c) ),
inference(start,[status(thm),parent(0:0)],[prove_there_is_no_common_divisor]) ).
cnf(t2,plain,
( ~ product(second_divided_by_1st(a,a),c,c)
| divides(second_divided_by_1st(a,a),c) ),
inference(extension,[status(thm),parent(t1:1)],[product_divisible_by_operand]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( multiply(second_divided_by_1st(a,a),c) != c
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,c) ),
inference(extension,[status(thm),parent(t2:2)],[equality_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t8:3)],[equality_6]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t12:3)],[equality_6]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t16:2)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t16:3)],[equality_6]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t20:2)],[equality_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t20:3)],[equality_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t24:2)],[equality_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t24:3)],[closure_of_product]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
c = c,
inference(extension,[status(thm),parent(t24:4)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t24:4]) ).
cnf(t32,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t24:5)],[equality_1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t24:5]) ).
cnf(t34,plain,
c = c,
inference(extension,[status(thm),parent(t20:4)],[equality_1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t20:4]) ).
cnf(t36,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t20:5)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t20:5]) ).
cnf(t38,plain,
c = c,
inference(extension,[status(thm),parent(t16:4)],[equality_1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t16:4]) ).
cnf(t40,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t16:5)],[equality_1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t16:5]) ).
cnf(t42,plain,
c = c,
inference(extension,[status(thm),parent(t12:4)],[equality_1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t12:4]) ).
cnf(t44,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t12:5)],[equality_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t12:5]) ).
cnf(t46,plain,
c = c,
inference(extension,[status(thm),parent(t8:4)],[equality_1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t8:4]) ).
cnf(t48,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t8:5)],[equality_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t8:5]) ).
cnf(t50,plain,
c = c,
inference(extension,[status(thm),parent(t4:4)],[equality_1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t4:4]) ).
cnf(t52,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)))
| multiply(second_divided_by_1st(a,a),c) = c ),
inference(extension,[status(thm),parent(t4:5)],[product_left_cancellation]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t4:5]) ).
cnf(t54,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),c)) != multiply(a,multiply(second_divided_by_1st(a,a),c))
| multiply(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)))
| a != a
| 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(t52:2)],[equality_6]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
a = a,
inference(extension,[status(thm),parent(t54:2)],[equality_1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),c)) != multiply(a,multiply(second_divided_by_1st(a,a),c))
| multiply(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)))
| a != a
| 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(t54:3)],[equality_6]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
a = a,
inference(extension,[status(thm),parent(t58:2)],[equality_1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),c)) != multiply(a,multiply(second_divided_by_1st(a,a),c))
| multiply(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)))
| a != a
| 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(t58:3)],[equality_6]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t58:3]) ).
cnf(t64,plain,
a = a,
inference(extension,[status(thm),parent(t62:2)],[equality_1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),c)) != multiply(a,multiply(second_divided_by_1st(a,a),c))
| multiply(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)))
| a != a
| 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(t62:3)],[equality_6]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t62:3]) ).
cnf(t68,plain,
a = a,
inference(extension,[status(thm),parent(t66:2)],[equality_1]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,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(t66:3)],[closure_of_product]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t66:3]) ).
cnf(t72,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t66:4)],[equality_1]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t66:4]) ).
cnf(t74,plain,
multiply(a,multiply(second_divided_by_1st(a,a),c)) = multiply(a,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t66:5)],[equality_1]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t66:5]) ).
cnf(t76,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t62:4)],[equality_1]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t62:4]) ).
cnf(t78,plain,
multiply(a,multiply(second_divided_by_1st(a,a),c)) = multiply(a,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t62:5)],[equality_1]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t62:5]) ).
cnf(t80,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t58:4)],[equality_1]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t58:4]) ).
cnf(t82,plain,
multiply(a,multiply(second_divided_by_1st(a,a),c)) = multiply(a,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t58:5)],[equality_1]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t58:5]) ).
cnf(t84,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t54:4)],[equality_1]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t54:4]) ).
cnf(t86,plain,
multiply(a,multiply(second_divided_by_1st(a,a),c)) = multiply(a,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t54:5)],[equality_1]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t54:5]) ).
cnf(t88,plain,
( ~ product(a,second_divided_by_1st(a,a),a)
| ~ product(a,multiply(second_divided_by_1st(a,a),c),multiply(a,multiply(second_divided_by_1st(a,a),c)))
| ~ product(second_divided_by_1st(a,a),c,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(t52:3)],[product_associativity1]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t52:3]) ).
cnf(t90,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t88:2)],[equality_6]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t90:2)],[equality_1]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t90:2]) ).
cnf(t94,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t90:3)],[equality_6]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t90:3]) ).
cnf(t96,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t94:2)],[equality_1]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t94:2]) ).
cnf(t98,plain,
( multiply(second_divided_by_1st(a,a),c) != multiply(second_divided_by_1st(a,a),c)
| c != c
| ~ product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)) ),
inference(extension,[status(thm),parent(t94:3)],[equality_6]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t94:3]) ).
cnf(t100,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t98:2)],[equality_1]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t98:2]) ).
cnf(t102,plain,
product(second_divided_by_1st(a,a),c,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t98:3)],[closure_of_product]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t98:3]) ).
cnf(t104,plain,
c = c,
inference(extension,[status(thm),parent(t98:4)],[equality_1]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t98:4]) ).
cnf(t106,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t98:5)],[equality_1]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t98:5]) ).
cnf(t108,plain,
c = c,
inference(extension,[status(thm),parent(t94:4)],[equality_1]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t94:4]) ).
cnf(t110,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t94:5)],[equality_1]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t94:5]) ).
cnf(t112,plain,
c = c,
inference(extension,[status(thm),parent(t90:4)],[equality_1]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t90:4]) ).
cnf(t114,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t90:5)],[equality_1]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t90:5]) ).
cnf(t116,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),c)) != multiply(a,multiply(second_divided_by_1st(a,a),c))
| multiply(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)))
| a != a
| 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(t88:3)],[equality_6]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t88:3]) ).
cnf(t118,plain,
a = a,
inference(extension,[status(thm),parent(t116:2)],[equality_1]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t116:2]) ).
cnf(t120,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),c)) != multiply(a,multiply(second_divided_by_1st(a,a),c))
| multiply(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)))
| a != a
| 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(t116:3)],[equality_6]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t116:3]) ).
cnf(t122,plain,
a = a,
inference(extension,[status(thm),parent(t120:2)],[equality_1]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t120:2]) ).
cnf(t124,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),c)) != multiply(a,multiply(second_divided_by_1st(a,a),c))
| multiply(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)))
| a != a
| 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(t120:3)],[equality_6]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t120:3]) ).
cnf(t126,plain,
a = a,
inference(extension,[status(thm),parent(t124:2)],[equality_1]) ).
cnf(t127,plain,
$false,
inference(connection,[status(thm),parent(t126:1)],[t126:1,t124:2]) ).
cnf(t128,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(t124:3)],[closure_of_product]) ).
cnf(t129,plain,
$false,
inference(connection,[status(thm),parent(t128:1)],[t128:1,t124:3]) ).
cnf(t130,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t124:4)],[equality_1]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t124:4]) ).
cnf(t132,plain,
multiply(a,multiply(second_divided_by_1st(a,a),c)) = multiply(a,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t124:5)],[equality_1]) ).
cnf(t133,plain,
$false,
inference(connection,[status(thm),parent(t132:1)],[t132:1,t124:5]) ).
cnf(t134,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t120:4)],[equality_1]) ).
cnf(t135,plain,
$false,
inference(connection,[status(thm),parent(t134:1)],[t134:1,t120:4]) ).
cnf(t136,plain,
multiply(a,multiply(second_divided_by_1st(a,a),c)) = multiply(a,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t120:5)],[equality_1]) ).
cnf(t137,plain,
$false,
inference(connection,[status(thm),parent(t136:1)],[t136:1,t120:5]) ).
cnf(t138,plain,
multiply(second_divided_by_1st(a,a),c) = multiply(second_divided_by_1st(a,a),c),
inference(extension,[status(thm),parent(t116:4)],[equality_1]) ).
cnf(t139,plain,
$false,
inference(connection,[status(thm),parent(t138:1)],[t138:1,t116:4]) ).
cnf(t140,plain,
multiply(a,multiply(second_divided_by_1st(a,a),c)) = multiply(a,multiply(second_divided_by_1st(a,a),c)),
inference(extension,[status(thm),parent(t116:5)],[equality_1]) ).
cnf(t141,plain,
$false,
inference(connection,[status(thm),parent(t140:1)],[t140:1,t116:5]) ).
cnf(t142,plain,
( ~ divides(a,a)
| product(a,second_divided_by_1st(a,a),a) ),
inference(extension,[status(thm),parent(t88:4)],[divides_implies_product]) ).
cnf(t143,plain,
$false,
inference(connection,[status(thm),parent(t142:1)],[t142:1,t88:4]) ).
cnf(t144,plain,
( ~ prime(a)
| ~ product(a,a,multiply(a,a))
| ~ divides(a,multiply(a,a))
| divides(a,a) ),
inference(extension,[status(thm),parent(t142:2)],[primes_lemma1]) ).
cnf(t145,plain,
$false,
inference(connection,[status(thm),parent(t144:1)],[t144:1,t142:2]) ).
cnf(t146,plain,
( ~ product(a,a,multiply(a,a))
| divides(a,multiply(a,a)) ),
inference(extension,[status(thm),parent(t144:2)],[product_divisible_by_operand]) ).
cnf(t147,plain,
$false,
inference(connection,[status(thm),parent(t146:1)],[t146:1,t144:2]) ).
cnf(t148,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t146:2)],[closure_of_product]) ).
cnf(t149,plain,
$false,
inference(connection,[status(thm),parent(t148:1)],[t148:1,t146:2]) ).
cnf(t150,plain,
( multiply(a,a) != multiply(a,a)
| a != a
| ~ product(a,a,multiply(a,a))
| a != a
| product(a,a,multiply(a,a)) ),
inference(extension,[status(thm),parent(t144:3)],[equality_6]) ).
cnf(t151,plain,
$false,
inference(connection,[status(thm),parent(t150:1)],[t150:1,t144:3]) ).
cnf(t152,plain,
a = a,
inference(extension,[status(thm),parent(t150:2)],[equality_1]) ).
cnf(t153,plain,
$false,
inference(connection,[status(thm),parent(t152:1)],[t152:1,t150:2]) ).
cnf(t154,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t150:3)],[closure_of_product]) ).
cnf(t155,plain,
$false,
inference(connection,[status(thm),parent(t154:1)],[t154:1,t150:3]) ).
cnf(t156,plain,
a = a,
inference(extension,[status(thm),parent(t150:4)],[equality_1]) ).
cnf(t157,plain,
$false,
inference(connection,[status(thm),parent(t156:1)],[t156:1,t150:4]) ).
cnf(t158,plain,
multiply(a,a) = multiply(a,a),
inference(extension,[status(thm),parent(t150:5)],[equality_1]) ).
cnf(t159,plain,
$false,
inference(connection,[status(thm),parent(t158:1)],[t158:1,t150:5]) ).
cnf(t160,plain,
prime(a),
inference(extension,[status(thm),parent(t144:4)],[a_is_prime]) ).
cnf(t161,plain,
$false,
inference(connection,[status(thm),parent(t160:1)],[t160:1,t144:4]) ).
cnf(t162,plain,
( ~ product(second_divided_by_1st(a,a),b,b)
| divides(second_divided_by_1st(a,a),b) ),
inference(extension,[status(thm),parent(t1:2)],[product_divisible_by_operand]) ).
cnf(t163,plain,
$false,
inference(connection,[status(thm),parent(t162:1)],[t162:1,t1:2]) ).
cnf(t164,plain,
( multiply(second_divided_by_1st(a,a),b) != b
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,b) ),
inference(extension,[status(thm),parent(t162:2)],[equality_6]) ).
cnf(t165,plain,
$false,
inference(connection,[status(thm),parent(t164:1)],[t164:1,t162:2]) ).
cnf(t166,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t164:2)],[equality_1]) ).
cnf(t167,plain,
$false,
inference(connection,[status(thm),parent(t166:1)],[t166:1,t164:2]) ).
cnf(t168,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t164:3)],[equality_6]) ).
cnf(t169,plain,
$false,
inference(connection,[status(thm),parent(t168:1)],[t168:1,t164:3]) ).
cnf(t170,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t168:2)],[equality_1]) ).
cnf(t171,plain,
$false,
inference(connection,[status(thm),parent(t170:1)],[t170:1,t168:2]) ).
cnf(t172,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t168:3)],[equality_6]) ).
cnf(t173,plain,
$false,
inference(connection,[status(thm),parent(t172:1)],[t172:1,t168:3]) ).
cnf(t174,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t172:2)],[equality_1]) ).
cnf(t175,plain,
$false,
inference(connection,[status(thm),parent(t174:1)],[t174:1,t172:2]) ).
cnf(t176,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t172:3)],[equality_6]) ).
cnf(t177,plain,
$false,
inference(connection,[status(thm),parent(t176:1)],[t176:1,t172:3]) ).
cnf(t178,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t176:2)],[equality_1]) ).
cnf(t179,plain,
$false,
inference(connection,[status(thm),parent(t178:1)],[t178:1,t176:2]) ).
cnf(t180,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t176:3)],[equality_6]) ).
cnf(t181,plain,
$false,
inference(connection,[status(thm),parent(t180:1)],[t180:1,t176:3]) ).
cnf(t182,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t180:2)],[equality_1]) ).
cnf(t183,plain,
$false,
inference(connection,[status(thm),parent(t182:1)],[t182:1,t180:2]) ).
cnf(t184,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t180:3)],[equality_6]) ).
cnf(t185,plain,
$false,
inference(connection,[status(thm),parent(t184:1)],[t184:1,t180:3]) ).
cnf(t186,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t184:2)],[equality_1]) ).
cnf(t187,plain,
$false,
inference(connection,[status(thm),parent(t186:1)],[t186:1,t184:2]) ).
cnf(t188,plain,
product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t184:3)],[closure_of_product]) ).
cnf(t189,plain,
$false,
inference(connection,[status(thm),parent(t188:1)],[t188:1,t184:3]) ).
cnf(t190,plain,
b = b,
inference(extension,[status(thm),parent(t184:4)],[equality_1]) ).
cnf(t191,plain,
$false,
inference(connection,[status(thm),parent(t190:1)],[t190:1,t184:4]) ).
cnf(t192,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t184:5)],[equality_1]) ).
cnf(t193,plain,
$false,
inference(connection,[status(thm),parent(t192:1)],[t192:1,t184:5]) ).
cnf(t194,plain,
b = b,
inference(extension,[status(thm),parent(t180:4)],[equality_1]) ).
cnf(t195,plain,
$false,
inference(connection,[status(thm),parent(t194:1)],[t194:1,t180:4]) ).
cnf(t196,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t180:5)],[equality_1]) ).
cnf(t197,plain,
$false,
inference(connection,[status(thm),parent(t196:1)],[t196:1,t180:5]) ).
cnf(t198,plain,
b = b,
inference(extension,[status(thm),parent(t176:4)],[equality_1]) ).
cnf(t199,plain,
$false,
inference(connection,[status(thm),parent(t198:1)],[t198:1,t176:4]) ).
cnf(t200,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t176:5)],[equality_1]) ).
cnf(t201,plain,
$false,
inference(connection,[status(thm),parent(t200:1)],[t200:1,t176:5]) ).
cnf(t202,plain,
b = b,
inference(extension,[status(thm),parent(t172:4)],[equality_1]) ).
cnf(t203,plain,
$false,
inference(connection,[status(thm),parent(t202:1)],[t202:1,t172:4]) ).
cnf(t204,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t172:5)],[equality_1]) ).
cnf(t205,plain,
$false,
inference(connection,[status(thm),parent(t204:1)],[t204:1,t172:5]) ).
cnf(t206,plain,
b = b,
inference(extension,[status(thm),parent(t168:4)],[equality_1]) ).
cnf(t207,plain,
$false,
inference(connection,[status(thm),parent(t206:1)],[t206:1,t168:4]) ).
cnf(t208,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t168:5)],[equality_1]) ).
cnf(t209,plain,
$false,
inference(connection,[status(thm),parent(t208:1)],[t208:1,t168:5]) ).
cnf(t210,plain,
b = b,
inference(extension,[status(thm),parent(t164:4)],[equality_1]) ).
cnf(t211,plain,
$false,
inference(connection,[status(thm),parent(t210:1)],[t210:1,t164:4]) ).
cnf(t212,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)))
| multiply(second_divided_by_1st(a,a),b) = b ),
inference(extension,[status(thm),parent(t164:5)],[product_left_cancellation]) ).
cnf(t213,plain,
$false,
inference(connection,[status(thm),parent(t212:1)],[t212:1,t164:5]) ).
cnf(t214,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),b)) != multiply(a,multiply(second_divided_by_1st(a,a),b))
| multiply(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)))
| a != a
| 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(t212:2)],[equality_6]) ).
cnf(t215,plain,
$false,
inference(connection,[status(thm),parent(t214:1)],[t214:1,t212:2]) ).
cnf(t216,plain,
a = a,
inference(extension,[status(thm),parent(t214:2)],[equality_1]) ).
cnf(t217,plain,
$false,
inference(connection,[status(thm),parent(t216:1)],[t216:1,t214:2]) ).
cnf(t218,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),b)) != multiply(a,multiply(second_divided_by_1st(a,a),b))
| multiply(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)))
| a != a
| 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(t214:3)],[equality_6]) ).
cnf(t219,plain,
$false,
inference(connection,[status(thm),parent(t218:1)],[t218:1,t214:3]) ).
cnf(t220,plain,
a = a,
inference(extension,[status(thm),parent(t218:2)],[equality_1]) ).
cnf(t221,plain,
$false,
inference(connection,[status(thm),parent(t220:1)],[t220:1,t218:2]) ).
cnf(t222,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),b)) != multiply(a,multiply(second_divided_by_1st(a,a),b))
| multiply(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)))
| a != a
| 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(t218:3)],[equality_6]) ).
cnf(t223,plain,
$false,
inference(connection,[status(thm),parent(t222:1)],[t222:1,t218:3]) ).
cnf(t224,plain,
a = a,
inference(extension,[status(thm),parent(t222:2)],[equality_1]) ).
cnf(t225,plain,
$false,
inference(connection,[status(thm),parent(t224:1)],[t224:1,t222:2]) ).
cnf(t226,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),b)) != multiply(a,multiply(second_divided_by_1st(a,a),b))
| multiply(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)))
| a != a
| 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(t222:3)],[equality_6]) ).
cnf(t227,plain,
$false,
inference(connection,[status(thm),parent(t226:1)],[t226:1,t222:3]) ).
cnf(t228,plain,
a = a,
inference(extension,[status(thm),parent(t226:2)],[equality_1]) ).
cnf(t229,plain,
$false,
inference(connection,[status(thm),parent(t228:1)],[t228:1,t226:2]) ).
cnf(t230,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(t226:3)],[closure_of_product]) ).
cnf(t231,plain,
$false,
inference(connection,[status(thm),parent(t230:1)],[t230:1,t226:3]) ).
cnf(t232,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t226:4)],[equality_1]) ).
cnf(t233,plain,
$false,
inference(connection,[status(thm),parent(t232:1)],[t232:1,t226:4]) ).
cnf(t234,plain,
multiply(a,multiply(second_divided_by_1st(a,a),b)) = multiply(a,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t226:5)],[equality_1]) ).
cnf(t235,plain,
$false,
inference(connection,[status(thm),parent(t234:1)],[t234:1,t226:5]) ).
cnf(t236,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t222:4)],[equality_1]) ).
cnf(t237,plain,
$false,
inference(connection,[status(thm),parent(t236:1)],[t236:1,t222:4]) ).
cnf(t238,plain,
multiply(a,multiply(second_divided_by_1st(a,a),b)) = multiply(a,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t222:5)],[equality_1]) ).
cnf(t239,plain,
$false,
inference(connection,[status(thm),parent(t238:1)],[t238:1,t222:5]) ).
cnf(t240,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t218:4)],[equality_1]) ).
cnf(t241,plain,
$false,
inference(connection,[status(thm),parent(t240:1)],[t240:1,t218:4]) ).
cnf(t242,plain,
multiply(a,multiply(second_divided_by_1st(a,a),b)) = multiply(a,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t218:5)],[equality_1]) ).
cnf(t243,plain,
$false,
inference(connection,[status(thm),parent(t242:1)],[t242:1,t218:5]) ).
cnf(t244,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t214:4)],[equality_1]) ).
cnf(t245,plain,
$false,
inference(connection,[status(thm),parent(t244:1)],[t244:1,t214:4]) ).
cnf(t246,plain,
multiply(a,multiply(second_divided_by_1st(a,a),b)) = multiply(a,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t214:5)],[equality_1]) ).
cnf(t247,plain,
$false,
inference(connection,[status(thm),parent(t246:1)],[t246:1,t214:5]) ).
cnf(t248,plain,
( ~ product(a,second_divided_by_1st(a,a),a)
| ~ product(a,multiply(second_divided_by_1st(a,a),b),multiply(a,multiply(second_divided_by_1st(a,a),b)))
| ~ product(second_divided_by_1st(a,a),b,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(t212:3)],[product_associativity1]) ).
cnf(t249,plain,
$false,
inference(connection,[status(thm),parent(t248:1)],[t248:1,t212:3]) ).
cnf(t250,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t248:2)],[equality_6]) ).
cnf(t251,plain,
$false,
inference(connection,[status(thm),parent(t250:1)],[t250:1,t248:2]) ).
cnf(t252,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t250:2)],[equality_1]) ).
cnf(t253,plain,
$false,
inference(connection,[status(thm),parent(t252:1)],[t252:1,t250:2]) ).
cnf(t254,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t250:3)],[equality_6]) ).
cnf(t255,plain,
$false,
inference(connection,[status(thm),parent(t254:1)],[t254:1,t250:3]) ).
cnf(t256,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t254:2)],[equality_1]) ).
cnf(t257,plain,
$false,
inference(connection,[status(thm),parent(t256:1)],[t256:1,t254:2]) ).
cnf(t258,plain,
( multiply(second_divided_by_1st(a,a),b) != multiply(second_divided_by_1st(a,a),b)
| b != b
| ~ product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b))
| second_divided_by_1st(a,a) != second_divided_by_1st(a,a)
| product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)) ),
inference(extension,[status(thm),parent(t254:3)],[equality_6]) ).
cnf(t259,plain,
$false,
inference(connection,[status(thm),parent(t258:1)],[t258:1,t254:3]) ).
cnf(t260,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(a,a),
inference(extension,[status(thm),parent(t258:2)],[equality_1]) ).
cnf(t261,plain,
$false,
inference(connection,[status(thm),parent(t260:1)],[t260:1,t258:2]) ).
cnf(t262,plain,
product(second_divided_by_1st(a,a),b,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t258:3)],[closure_of_product]) ).
cnf(t263,plain,
$false,
inference(connection,[status(thm),parent(t262:1)],[t262:1,t258:3]) ).
cnf(t264,plain,
b = b,
inference(extension,[status(thm),parent(t258:4)],[equality_1]) ).
cnf(t265,plain,
$false,
inference(connection,[status(thm),parent(t264:1)],[t264:1,t258:4]) ).
cnf(t266,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t258:5)],[equality_1]) ).
cnf(t267,plain,
$false,
inference(connection,[status(thm),parent(t266:1)],[t266:1,t258:5]) ).
cnf(t268,plain,
b = b,
inference(extension,[status(thm),parent(t254:4)],[equality_1]) ).
cnf(t269,plain,
$false,
inference(connection,[status(thm),parent(t268:1)],[t268:1,t254:4]) ).
cnf(t270,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t254:5)],[equality_1]) ).
cnf(t271,plain,
$false,
inference(connection,[status(thm),parent(t270:1)],[t270:1,t254:5]) ).
cnf(t272,plain,
b = b,
inference(extension,[status(thm),parent(t250:4)],[equality_1]) ).
cnf(t273,plain,
$false,
inference(connection,[status(thm),parent(t272:1)],[t272:1,t250:4]) ).
cnf(t274,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t250:5)],[equality_1]) ).
cnf(t275,plain,
$false,
inference(connection,[status(thm),parent(t274:1)],[t274:1,t250:5]) ).
cnf(t276,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),b)) != multiply(a,multiply(second_divided_by_1st(a,a),b))
| multiply(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)))
| a != a
| 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(t248:3)],[equality_6]) ).
cnf(t277,plain,
$false,
inference(connection,[status(thm),parent(t276:1)],[t276:1,t248:3]) ).
cnf(t278,plain,
a = a,
inference(extension,[status(thm),parent(t276:2)],[equality_1]) ).
cnf(t279,plain,
$false,
inference(connection,[status(thm),parent(t278:1)],[t278:1,t276:2]) ).
cnf(t280,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),b)) != multiply(a,multiply(second_divided_by_1st(a,a),b))
| multiply(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)))
| a != a
| 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(t276:3)],[equality_6]) ).
cnf(t281,plain,
$false,
inference(connection,[status(thm),parent(t280:1)],[t280:1,t276:3]) ).
cnf(t282,plain,
a = a,
inference(extension,[status(thm),parent(t280:2)],[equality_1]) ).
cnf(t283,plain,
$false,
inference(connection,[status(thm),parent(t282:1)],[t282:1,t280:2]) ).
cnf(t284,plain,
( multiply(a,multiply(second_divided_by_1st(a,a),b)) != multiply(a,multiply(second_divided_by_1st(a,a),b))
| multiply(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)))
| a != a
| 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(t280:3)],[equality_6]) ).
cnf(t285,plain,
$false,
inference(connection,[status(thm),parent(t284:1)],[t284:1,t280:3]) ).
cnf(t286,plain,
a = a,
inference(extension,[status(thm),parent(t284:2)],[equality_1]) ).
cnf(t287,plain,
$false,
inference(connection,[status(thm),parent(t286:1)],[t286:1,t284:2]) ).
cnf(t288,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(t284:3)],[closure_of_product]) ).
cnf(t289,plain,
$false,
inference(connection,[status(thm),parent(t288:1)],[t288:1,t284:3]) ).
cnf(t290,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t284:4)],[equality_1]) ).
cnf(t291,plain,
$false,
inference(connection,[status(thm),parent(t290:1)],[t290:1,t284:4]) ).
cnf(t292,plain,
multiply(a,multiply(second_divided_by_1st(a,a),b)) = multiply(a,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t284:5)],[equality_1]) ).
cnf(t293,plain,
$false,
inference(connection,[status(thm),parent(t292:1)],[t292:1,t284:5]) ).
cnf(t294,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t280:4)],[equality_1]) ).
cnf(t295,plain,
$false,
inference(connection,[status(thm),parent(t294:1)],[t294:1,t280:4]) ).
cnf(t296,plain,
multiply(a,multiply(second_divided_by_1st(a,a),b)) = multiply(a,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t280:5)],[equality_1]) ).
cnf(t297,plain,
$false,
inference(connection,[status(thm),parent(t296:1)],[t296:1,t280:5]) ).
cnf(t298,plain,
multiply(second_divided_by_1st(a,a),b) = multiply(second_divided_by_1st(a,a),b),
inference(extension,[status(thm),parent(t276:4)],[equality_1]) ).
cnf(t299,plain,
$false,
inference(connection,[status(thm),parent(t298:1)],[t298:1,t276:4]) ).
cnf(t300,plain,
multiply(a,multiply(second_divided_by_1st(a,a),b)) = multiply(a,multiply(second_divided_by_1st(a,a),b)),
inference(extension,[status(thm),parent(t276:5)],[equality_1]) ).
cnf(t301,plain,
$false,
inference(connection,[status(thm),parent(t300:1)],[t300:1,t276:5]) ).
cnf(t302,plain,
( ~ divides(a,a)
| product(a,second_divided_by_1st(a,a),a) ),
inference(extension,[status(thm),parent(t248:4)],[divides_implies_product]) ).
cnf(t303,plain,
$false,
inference(connection,[status(thm),parent(t302:1)],[t302:1,t248:4]) ).
cnf(t304,plain,
( ~ prime(a)
| ~ product(a,a,multiply(a,a))
| ~ divides(a,multiply(a,a))
| divides(a,a) ),
inference(extension,[status(thm),parent(t302:2)],[primes_lemma1]) ).
cnf(t305,plain,
$false,
inference(connection,[status(thm),parent(t304:1)],[t304:1,t302:2]) ).
cnf(t306,plain,
( ~ product(a,a,multiply(a,a))
| divides(a,multiply(a,a)) ),
inference(extension,[status(thm),parent(t304:2)],[product_divisible_by_operand]) ).
cnf(t307,plain,
$false,
inference(connection,[status(thm),parent(t306:1)],[t306:1,t304:2]) ).
cnf(t308,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t306:2)],[closure_of_product]) ).
cnf(t309,plain,
$false,
inference(connection,[status(thm),parent(t308:1)],[t308:1,t306:2]) ).
cnf(t310,plain,
( multiply(a,a) != multiply(a,a)
| a != a
| ~ product(a,a,multiply(a,a))
| a != a
| product(a,a,multiply(a,a)) ),
inference(extension,[status(thm),parent(t304:3)],[equality_6]) ).
cnf(t311,plain,
$false,
inference(connection,[status(thm),parent(t310:1)],[t310:1,t304:3]) ).
cnf(t312,plain,
a = a,
inference(extension,[status(thm),parent(t310:2)],[equality_1]) ).
cnf(t313,plain,
$false,
inference(connection,[status(thm),parent(t312:1)],[t312:1,t310:2]) ).
cnf(t314,plain,
product(a,a,multiply(a,a)),
inference(extension,[status(thm),parent(t310:3)],[closure_of_product]) ).
cnf(t315,plain,
$false,
inference(connection,[status(thm),parent(t314:1)],[t314:1,t310:3]) ).
cnf(t316,plain,
a = a,
inference(extension,[status(thm),parent(t310:4)],[equality_1]) ).
cnf(t317,plain,
$false,
inference(connection,[status(thm),parent(t316:1)],[t316:1,t310:4]) ).
cnf(t318,plain,
multiply(a,a) = multiply(a,a),
inference(extension,[status(thm),parent(t310:5)],[equality_1]) ).
cnf(t319,plain,
$false,
inference(connection,[status(thm),parent(t318:1)],[t318:1,t310:5]) ).
cnf(t320,plain,
prime(a),
inference(extension,[status(thm),parent(t304:4)],[a_is_prime]) ).
cnf(t321,plain,
$false,
inference(connection,[status(thm),parent(t320:1)],[t320:1,t304:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 17:35:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 194.55/194.89 % SZS status Unsatisfiable for theBenchmark
% 194.55/194.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------