%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 4.91s 6.31s
% Output : CNFRefutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 6 RR)
% Number of literals : 54 ( 53 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t38,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t5,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t43,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t47,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t38,t43]) ).
cnf(t1,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t10485,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t47,t16]) ).
cnf(t85,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t10485]) ).
cnf(t7,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t35,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t87,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t85,t35]) ).
cnf(t89,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t87]) ).
cnf(t2,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t94,plain,
X1 = add(additive_inverse(X2),add(X1,X2)),
inference(cp,[status(thm)],[t89,t17]) ).
cnf(t106,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(orient,[status(thm)],[t94]) ).
cnf(t88,plain,
X1 = add(additive_inverse(X2),add(X2,X1)),
inference(cp,[status(thm)],[t85,t17]) ).
cnf(t97,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(orient,[status(thm)],[t88]) ).
cnf(t109,plain,
additive_inverse(X1) = add(additive_inverse(add(X1,X2)),X2),
inference(cp,[status(thm)],[t106,t97]) ).
cnf(t10487,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(step,[status(thm)],[t109,t35]) ).
cnf(t122,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t10487]) ).
cnf(t13,axiom,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t13]) ).
cnf(t128,plain,
additive_inverse(multiply(X1,X2)) = add(multiply(X3,X2),additive_inverse(multiply(add(X1,X3),X2))),
inference(cp,[status(thm)],[t122,t28]) ).
cnf(t12,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t127,plain,
additive_inverse(multiply(X1,X2)) = add(multiply(X1,X3),additive_inverse(multiply(X1,add(X2,X3)))),
inference(cp,[status(thm)],[t122,t23]) ).
cnf(t1753,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X3,X2)))) = additive_inverse(multiply(X1,X3)),
inference(orient,[status(thm)],[t127]) ).
cnf(t1774,plain,
additive_inverse(multiply(X1,X2)) = add(multiply(X1,additive_inverse(X2)),additive_inverse(multiply(X1,additive_identity))),
inference(cp,[status(thm)],[t1753,t43]) ).
cnf(t3,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t10502,plain,
additive_inverse(multiply(X1,X2)) = add(multiply(X1,additive_inverse(X2)),additive_inverse(additive_identity)),
inference(step,[status(thm)],[t1774,t26]) ).
cnf(t45,plain,
additive_identity = additive_inverse(additive_identity),
inference(cp,[status(thm)],[t43,t16]) ).
cnf(t76,plain,
additive_inverse(additive_identity) = additive_identity,
inference(orient,[status(thm)],[t45]) ).
cnf(t10503,plain,
additive_inverse(multiply(X1,X2)) = add(multiply(X1,additive_inverse(X2)),additive_identity),
inference(step,[status(thm)],[t10502,t76]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t15,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t10504,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(step,[status(thm)],[t10503,t15]) ).
cnf(t1821,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(orient,[status(thm)],[t10504]) ).
cnf(t10727,plain,
multiply(X1,additive_inverse(X2)) = add(multiply(X3,X2),additive_inverse(multiply(add(X1,X3),X2))),
inference(step,[status(thm)],[t128,t1821]) ).
cnf(t10728,plain,
multiply(X1,additive_inverse(X2)) = add(multiply(X3,X2),multiply(add(X1,X3),additive_inverse(X2))),
inference(step,[status(thm)],[t10727,t1821]) ).
cnf(t10236,plain,
add(multiply(X1,X2),multiply(add(X3,X1),additive_inverse(X2))) = multiply(X3,additive_inverse(X2)),
inference(orient,[status(thm)],[t10728]) ).
cnf(t10274,plain,
multiply(X1,additive_inverse(X2)) = add(multiply(additive_inverse(X1),X2),multiply(additive_identity,additive_inverse(X2))),
inference(cp,[status(thm)],[t10236,t43]) ).
cnf(t10729,plain,
multiply(X1,additive_inverse(X2)) = add(multiply(additive_identity,additive_inverse(X2)),multiply(additive_inverse(X1),X2)),
inference(step,[status(thm)],[t10274,t35]) ).
cnf(t4,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t34,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t10730,plain,
multiply(X1,additive_inverse(X2)) = add(additive_identity,multiply(additive_inverse(X1),X2)),
inference(step,[status(thm)],[t10729,t34]) ).
cnf(t10731,plain,
multiply(X1,additive_inverse(X2)) = multiply(additive_inverse(X1),X2),
inference(step,[status(thm)],[t10730,t16]) ).
cnf(t10396,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(orient,[status(thm)],[t10731]) ).
cnf(goal_0,negated_conjecture,
multiply(additive_inverse(a),additive_inverse(b)) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a,additive_inverse(additive_inverse(b))) != multiply(a,b),
inference(rw,[status(thm)],[goal_0,t10396]) ).
cnf(g0_1,plain,
multiply(a,b) != multiply(a,b),
inference(rw,[status(thm)],[g0_0,t17]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.39 % Computer : n010.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Thu Sep 24 07:46:02 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.91/6.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.91/6.31 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------