%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n013.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 08:54:59 AM UTC 2026
% Result : Unsatisfiable 275.78s 276.05s
% Output : Proof 275.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of clauses : 55 ( 42 unt; 0 nHn; 49 RR)
% Number of literals : 90 ( 0 equ; 37 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sum_substitution1,axiom,
( sum(Y,W,Z)
| ~ sum(X,W,Z)
| ~ equalish(X,Y) ),
file('theBenchmark.p',sum_substitution1) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('theBenchmark.p',closure_of_multiplication) ).
cnf(associativity_of_addition1,axiom,
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('theBenchmark.p',associativity_of_addition1) ).
cnf(associativity_of_multiplication2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('theBenchmark.p',associativity_of_multiplication2) ).
cnf(distributivity3,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('theBenchmark.p',distributivity3) ).
cnf(sum_left_cancellation,axiom,
( equalish(D,A)
| ~ sum(D,B,C)
| ~ sum(A,B,C) ),
file('theBenchmark.p',sum_left_cancellation) ).
cnf(sum_right_concellation,axiom,
( equalish(D,B)
| ~ sum(A,D,C)
| ~ sum(A,B,C) ),
file('theBenchmark.p',sum_right_concellation) ).
cnf(absorbtion1,axiom,
sum(A,add(A,B),B),
file('theBenchmark.p',absorbtion1) ).
cnf(absorbtion2,axiom,
sum(add(A,B),B,A),
file('theBenchmark.p',absorbtion2) ).
cnf(clause43,axiom,
product(A,multiply(A,B),multiply(A,B)),
file('theBenchmark.p',clause43) ).
cnf(clause44,axiom,
product(a,multiply(b,A),multiply(B,A)),
file('theBenchmark.p',clause44) ).
cnf(clause45,axiom,
product(a,b,multiply(c,b)),
file('theBenchmark.p',clause45) ).
cnf(clause71,axiom,
product(A,A,A),
file('theBenchmark.p',clause71) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equalish(c,d),
file('theBenchmark.p',prove_c_equals_d) ).
cnf(t1,plain,
~ equalish(c,d),
inference(start,[status(thm),parent(0:0)],[prove_c_equals_d]) ).
cnf(t2,plain,
( ~ sum(add(multiply(add(multiply(c,b),add(d,c)),add(d,c)),d),c,multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| ~ sum(add(multiply(add(multiply(c,b),add(d,c)),add(d,c)),d),d,multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| equalish(c,d) ),
inference(extension,[status(thm),parent(t1:1)],[sum_right_concellation]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
sum(add(multiply(add(multiply(c,b),add(d,c)),add(d,c)),d),d,multiply(add(multiply(c,b),add(d,c)),add(d,c))),
inference(extension,[status(thm),parent(t2:2)],[absorbtion2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ sum(multiply(add(multiply(c,b),add(d,c)),add(d,c)),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| ~ sum(d,add(d,c),c)
| ~ sum(add(multiply(add(multiply(c,b),add(d,c)),add(d,c)),d),d,multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| sum(add(multiply(add(multiply(c,b),add(d,c)),add(d,c)),d),c,multiply(add(multiply(c,b),add(d,c)),add(d,c))) ),
inference(extension,[status(thm),parent(t2:3)],[associativity_of_addition1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
sum(add(multiply(add(multiply(c,b),add(d,c)),add(d,c)),d),d,multiply(add(multiply(c,b),add(d,c)),add(d,c))),
inference(extension,[status(thm),parent(t6:2)],[absorbtion2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ equalish(add(c,add(d,c)),d)
| ~ sum(add(c,add(d,c)),add(d,c),c)
| sum(d,add(d,c),c) ),
inference(extension,[status(thm),parent(t6:3)],[sum_substitution1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
sum(add(c,add(d,c)),add(d,c),c),
inference(extension,[status(thm),parent(t10:2)],[absorbtion2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ sum(add(c,add(d,c)),add(d,c),c)
| ~ sum(d,add(d,c),c)
| equalish(add(c,add(d,c)),d) ),
inference(extension,[status(thm),parent(t10:3)],[sum_left_cancellation]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
sum(d,add(d,c),c),
inference(extension,[status(thm),parent(t14:2)],[absorbtion1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
sum(add(c,add(d,c)),add(d,c),c),
inference(extension,[status(thm),parent(t14:3)],[absorbtion2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
( ~ product(add(multiply(c,b),add(d,c)),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| ~ sum(add(multiply(c,b),add(d,c)),add(d,c),multiply(c,b))
| ~ product(multiply(c,b),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| ~ product(add(d,c),add(d,c),add(d,c))
| sum(multiply(add(multiply(c,b),add(d,c)),add(d,c)),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c))) ),
inference(extension,[status(thm),parent(t6:4)],[distributivity3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t6:4]) ).
cnf(t22,plain,
product(add(d,c),add(d,c),add(d,c)),
inference(extension,[status(thm),parent(t20:2)],[clause71]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( ~ product(a,multiply(b,add(d,c)),multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| ~ product(b,add(d,c),multiply(b,add(d,c)))
| ~ product(a,b,multiply(c,b))
| product(multiply(c,b),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c))) ),
inference(extension,[status(thm),parent(t20:3)],[associativity_of_multiplication2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
product(a,b,multiply(c,b)),
inference(extension,[status(thm),parent(t24:2)],[clause45]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
product(b,add(d,c),multiply(b,add(d,c))),
inference(extension,[status(thm),parent(t24:3)],[closure_of_multiplication]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
product(a,multiply(b,add(d,c)),multiply(add(multiply(c,b),add(d,c)),add(d,c))),
inference(extension,[status(thm),parent(t24:4)],[clause44]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t24:4]) ).
cnf(t32,plain,
sum(add(multiply(c,b),add(d,c)),add(d,c),multiply(c,b)),
inference(extension,[status(thm),parent(t20:4)],[absorbtion2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t20:4]) ).
cnf(t34,plain,
( ~ product(add(multiply(c,b),add(d,c)),multiply(add(multiply(c,b),add(d,c)),add(d,c)),multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| ~ product(add(multiply(c,b),add(d,c)),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c)))
| ~ product(add(multiply(c,b),add(d,c)),add(multiply(c,b),add(d,c)),add(multiply(c,b),add(d,c)))
| product(add(multiply(c,b),add(d,c)),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c))) ),
inference(extension,[status(thm),parent(t20:5)],[associativity_of_multiplication2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t20:5]) ).
cnf(t36,plain,
product(add(multiply(c,b),add(d,c)),add(multiply(c,b),add(d,c)),add(multiply(c,b),add(d,c))),
inference(extension,[status(thm),parent(t34:2)],[clause71]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
product(add(multiply(c,b),add(d,c)),add(d,c),multiply(add(multiply(c,b),add(d,c)),add(d,c))),
inference(extension,[status(thm),parent(t34:3)],[closure_of_multiplication]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
product(add(multiply(c,b),add(d,c)),multiply(add(multiply(c,b),add(d,c)),add(d,c)),multiply(add(multiply(c,b),add(d,c)),add(d,c))),
inference(extension,[status(thm),parent(t34:4)],[clause43]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t34:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_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
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 20:43:50 UTC 2026
% 0.14/0.36 % CPUTime :
% 275.78/276.05 % SZS status Unsatisfiable for theBenchmark
% 275.78/276.05 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------