%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG016-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:37:28 PM UTC 2026
% Result : Unsatisfiable 6.63s 1.26s
% Output : CNFRefutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 53 RR)
% Number of literals : 87 ( 86 equ; 9 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
sF0 = multiply(x,z),
introduced(definition) ).
cnf(t28,plain,
multiply(x,z) = sF0,
inference(orient,[status(thm)],[t13]) ).
cnf(t14,axiom,
sF1 = multiply(y,z),
introduced(definition) ).
cnf(t29,plain,
multiply(y,z) = sF1,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sF2 = additive_inverse(multiply(y,z)),
introduced(definition) ).
cnf(t664,plain,
sF2 = additive_inverse(sF1),
inference(step,[status(thm)],[t15,t29]) ).
cnf(t38,plain,
additive_inverse(sF1) = sF2,
inference(orient,[status(thm)],[t664]) ).
cnf(t16,axiom,
sF3 = add(multiply(x,z),additive_inverse(multiply(y,z))),
introduced(definition) ).
cnf(t677,plain,
sF3 = add(sF0,additive_inverse(multiply(y,z))),
inference(step,[status(thm)],[t16,t28]) ).
cnf(t678,plain,
sF3 = add(sF0,additive_inverse(sF1)),
inference(step,[status(thm)],[t677,t29]) ).
cnf(t679,plain,
sF3 = add(sF0,sF2),
inference(step,[status(thm)],[t678,t38]) ).
cnf(t175,plain,
add(sF0,sF2) = sF3,
inference(orient,[status(thm)],[t679]) ).
cnf(t17,axiom,
sF4 = additive_inverse(y),
introduced(definition) ).
cnf(t20,plain,
additive_inverse(y) = sF4,
inference(orient,[status(thm)],[t17]) ).
cnf(t12,axiom,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t119,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t121,plain,
multiply(add(X1,x),z) = add(multiply(X1,z),sF0),
inference(cp,[status(thm)],[t119,t28]) ).
cnf(t7,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t57,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t683,plain,
multiply(add(X1,x),z) = add(sF0,multiply(X1,z)),
inference(step,[status(thm)],[t121,t57]) ).
cnf(t120,plain,
multiply(add(x,X1),z) = add(sF0,multiply(X1,z)),
inference(cp,[status(thm)],[t119,t28]) ).
cnf(t202,plain,
add(sF0,multiply(X1,z)) = multiply(add(x,X1),z),
inference(orient,[status(thm)],[t120]) ).
cnf(t684,plain,
multiply(add(X1,x),z) = multiply(add(x,X1),z),
inference(step,[status(thm)],[t683,t202]) ).
cnf(t210,plain,
multiply(add(X1,x),z) = multiply(add(x,X1),z),
inference(orient,[status(thm)],[t684]) ).
cnf(t18,axiom,
sF5 = add(x,additive_inverse(y)),
introduced(definition) ).
cnf(t665,plain,
sF5 = add(x,sF4),
inference(step,[status(thm)],[t18,t20]) ).
cnf(t45,plain,
add(x,sF4) = sF5,
inference(orient,[status(thm)],[t665]) ).
cnf(t666,plain,
add(sF4,x) = sF5,
inference(step,[status(thm)],[t45,t57]) ).
cnf(t61,plain,
add(sF4,x) = sF5,
inference(rw,[status(thm)],[t666]) ).
cnf(t67,plain,
add(sF4,x) = sF5,
inference(orient,[status(thm)],[t61]) ).
cnf(t19,axiom,
sF6 = multiply(add(x,additive_inverse(y)),z),
introduced(definition) ).
cnf(t680,plain,
sF6 = multiply(add(x,sF4),z),
inference(step,[status(thm)],[t19,t20]) ).
cnf(t681,plain,
sF6 = multiply(add(sF4,x),z),
inference(step,[status(thm)],[t680,t57]) ).
cnf(t682,plain,
sF6 = multiply(sF5,z),
inference(step,[status(thm)],[t681,t67]) ).
cnf(t196,plain,
multiply(sF5,z) = sF6,
inference(orient,[status(thm)],[t682]) ).
cnf(t8,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t46,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t200,plain,
multiply(add(sF5,X1),z) = add(sF6,multiply(X1,z)),
inference(cp,[status(thm)],[t119,t196]) ).
cnf(t407,plain,
add(sF6,multiply(X1,z)) = multiply(add(sF5,X1),z),
inference(orient,[status(thm)],[t200]) ).
cnf(t409,plain,
multiply(add(sF5,y),z) = add(sF6,sF1),
inference(cp,[status(thm)],[t407,t29]) ).
cnf(t5,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t30,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t2,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t24,plain,
y = additive_inverse(sF4),
inference(cp,[status(thm)],[t23,t20]) ).
cnf(t25,plain,
additive_inverse(sF4) = y,
inference(orient,[status(thm)],[t24]) ).
cnf(t33,plain,
additive_identity = add(sF4,y),
inference(cp,[status(thm)],[t30,t25]) ).
cnf(t37,plain,
add(sF4,y) = additive_identity,
inference(orient,[status(thm)],[t33]) ).
cnf(t51,plain,
add(sF4,add(y,X1)) = add(additive_identity,X1),
inference(cp,[status(thm)],[t46,t37]) ).
cnf(t1,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t667,plain,
add(sF4,add(y,X1)) = X1,
inference(step,[status(thm)],[t51,t22]) ).
cnf(t75,plain,
add(sF4,add(y,X1)) = X1,
inference(orient,[status(thm)],[t667]) ).
cnf(t77,plain,
X1 = add(sF4,add(X1,y)),
inference(cp,[status(thm)],[t75,t57]) ).
cnf(t111,plain,
add(sF4,add(X1,y)) = X1,
inference(orient,[status(thm)],[t77]) ).
cnf(t69,plain,
add(sF4,add(x,X1)) = add(sF5,X1),
inference(cp,[status(thm)],[t46,t67]) ).
cnf(t90,plain,
add(sF4,add(x,X1)) = add(sF5,X1),
inference(orient,[status(thm)],[t69]) ).
cnf(t114,plain,
x = add(sF5,y),
inference(cp,[status(thm)],[t111,t90]) ).
cnf(t116,plain,
add(sF5,y) = x,
inference(orient,[status(thm)],[t114]) ).
cnf(t699,plain,
multiply(x,z) = add(sF6,sF1),
inference(step,[status(thm)],[t409,t116]) ).
cnf(t700,plain,
sF0 = add(sF6,sF1),
inference(step,[status(thm)],[t699,t28]) ).
cnf(t701,plain,
sF0 = add(sF1,sF6),
inference(step,[status(thm)],[t700,t57]) ).
cnf(t418,plain,
add(sF1,sF6) = sF0,
inference(orient,[status(thm)],[t701]) ).
cnf(t420,plain,
add(sF1,add(sF6,X1)) = add(sF0,X1),
inference(cp,[status(thm)],[t46,t418]) ).
cnf(t634,plain,
add(sF1,add(sF6,X1)) = add(sF0,X1),
inference(orient,[status(thm)],[t420]) ).
cnf(t40,plain,
additive_identity = add(sF1,sF2),
inference(cp,[status(thm)],[t30,t38]) ).
cnf(t43,plain,
add(sF1,sF2) = additive_identity,
inference(orient,[status(thm)],[t40]) ).
cnf(t52,plain,
add(sF1,add(sF2,X1)) = add(additive_identity,X1),
inference(cp,[status(thm)],[t46,t43]) ).
cnf(t668,plain,
add(sF1,add(sF2,X1)) = X1,
inference(step,[status(thm)],[t52,t22]) ).
cnf(t87,plain,
add(sF1,add(sF2,X1)) = X1,
inference(orient,[status(thm)],[t668]) ).
cnf(t89,plain,
X1 = add(sF1,add(X1,sF2)),
inference(cp,[status(thm)],[t87,t57]) ).
cnf(t165,plain,
add(sF1,add(X1,sF2)) = X1,
inference(orient,[status(thm)],[t89]) ).
cnf(t638,plain,
add(sF0,sF2) = sF6,
inference(cp,[status(thm)],[t634,t165]) ).
cnf(t714,plain,
sF3 = sF6,
inference(step,[status(thm)],[t638,t175]) ).
cnf(t649,plain,
sF6 = sF3,
inference(orient,[status(thm)],[t714]) ).
cnf(t715,plain,
multiply(sF5,z) = sF3,
inference(step,[status(thm)],[t196,t649]) ).
cnf(t650,plain,
multiply(sF5,z) = sF3,
inference(orient,[status(thm)],[t715]) ).
cnf(goal_0,negated_conjecture,
add(multiply(x,z),additive_inverse(multiply(y,z))) != multiply(add(x,additive_inverse(y)),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
add(sF0,additive_inverse(multiply(y,z))) != multiply(add(x,additive_inverse(y)),z),
inference(rw,[status(thm)],[goal_0,t28]) ).
cnf(g0_1,plain,
add(sF0,additive_inverse(sF1)) != multiply(add(x,additive_inverse(y)),z),
inference(rw,[status(thm)],[g0_0,t29]) ).
cnf(g0_2,plain,
add(sF0,sF2) != multiply(add(x,additive_inverse(y)),z),
inference(rw,[status(thm)],[g0_1,t38]) ).
cnf(g0_3,plain,
sF3 != multiply(add(x,additive_inverse(y)),z),
inference(rw,[status(thm)],[g0_2,t175]) ).
cnf(g0_4,plain,
sF3 != multiply(add(x,sF4),z),
inference(rw,[status(thm)],[g0_3,t20]) ).
cnf(g0_5,plain,
sF3 != multiply(add(sF4,x),z),
inference(rw,[status(thm)],[g0_4,t210]) ).
cnf(g0_6,plain,
sF3 != multiply(sF5,z),
inference(rw,[status(thm)],[g0_5,t67]) ).
cnf(g0_7,plain,
sF3 != sF3,
inference(rw,[status(thm)],[g0_6,t650]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG016-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Thu Sep 24 07:49:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.63/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.63/1.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------