%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG013-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 3.14s 0.88s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 33 RR)
% Number of literals : 58 ( 57 equ; 5 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
sFlat0 = additive_inverse(a),
introduced(definition) ).
cnf(t65,plain,
additive_inverse(a) = sFlat0,
inference(orient,[status(thm)],[t13]) ).
cnf(t14,axiom,
sFlat1 = multiply(additive_inverse(a),b),
introduced(definition) ).
cnf(t37,plain,
multiply(additive_inverse(a),b) = sFlat1,
inference(orient,[status(thm)],[t14]) ).
cnf(t473,plain,
multiply(sFlat0,b) = sFlat1,
inference(step,[status(thm)],[t37,t65]) ).
cnf(t68,plain,
multiply(sFlat0,b) = sFlat1,
inference(rw,[status(thm)],[t473]) ).
cnf(t78,plain,
multiply(sFlat0,b) = sFlat1,
inference(orient,[status(thm)],[t68]) ).
cnf(t15,axiom,
sFlat2 = multiply(a,b),
introduced(definition) ).
cnf(t43,plain,
multiply(a,b) = sFlat2,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat3 = additive_inverse(multiply(a,b)),
introduced(definition) ).
cnf(t472,plain,
sFlat3 = additive_inverse(sFlat2),
inference(step,[status(thm)],[t16,t43]) ).
cnf(t62,plain,
additive_inverse(sFlat2) = sFlat3,
inference(orient,[status(thm)],[t472]) ).
cnf(t8,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t52,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(t57,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t61,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t52,t57]) ).
cnf(t1,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t477,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t61,t18]) ).
cnf(t106,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t477]) ).
cnf(t7,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t49,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t108,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t106,t49]) ).
cnf(t130,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t108]) ).
cnf(t2,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t133,plain,
X1 = add(additive_inverse(X2),add(X1,X2)),
inference(cp,[status(thm)],[t130,t19]) ).
cnf(t151,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(orient,[status(thm)],[t133]) ).
cnf(t12,axiom,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t30,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t44,plain,
multiply(add(a,X1),b) = add(sFlat2,multiply(X1,b)),
inference(cp,[status(thm)],[t30,t43]) ).
cnf(t436,plain,
add(sFlat2,multiply(X1,b)) = multiply(add(a,X1),b),
inference(orient,[status(thm)],[t44]) ).
cnf(t437,plain,
multiply(add(a,sFlat0),b) = add(sFlat2,sFlat1),
inference(cp,[status(thm)],[t436,t78]) ).
cnf(t488,plain,
multiply(add(sFlat0,a),b) = add(sFlat2,sFlat1),
inference(step,[status(thm)],[t437,t49]) ).
cnf(t67,plain,
additive_identity = add(a,sFlat0),
inference(cp,[status(thm)],[t57,t65]) ).
cnf(t474,plain,
additive_identity = add(sFlat0,a),
inference(step,[status(thm)],[t67,t49]) ).
cnf(t76,plain,
add(sFlat0,a) = additive_identity,
inference(orient,[status(thm)],[t474]) ).
cnf(t489,plain,
multiply(additive_identity,b) = add(sFlat2,sFlat1),
inference(step,[status(thm)],[t488,t76]) ).
cnf(t4,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t36,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t490,plain,
additive_identity = add(sFlat2,sFlat1),
inference(step,[status(thm)],[t489,t36]) ).
cnf(t491,plain,
additive_identity = add(sFlat1,sFlat2),
inference(step,[status(thm)],[t490,t49]) ).
cnf(t449,plain,
add(sFlat1,sFlat2) = additive_identity,
inference(orient,[status(thm)],[t491]) ).
cnf(t451,plain,
sFlat1 = add(additive_inverse(sFlat2),additive_identity),
inference(cp,[status(thm)],[t151,t449]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t492,plain,
sFlat1 = additive_inverse(sFlat2),
inference(step,[status(thm)],[t451,t17]) ).
cnf(t493,plain,
sFlat1 = sFlat3,
inference(step,[status(thm)],[t492,t62]) ).
cnf(t457,plain,
sFlat3 = sFlat1,
inference(orient,[status(thm)],[t493]) ).
cnf(t494,plain,
additive_inverse(sFlat2) = sFlat1,
inference(step,[status(thm)],[t62,t457]) ).
cnf(t458,plain,
additive_inverse(sFlat2) = sFlat1,
inference(orient,[status(thm)],[t494]) ).
cnf(goal_0,negated_conjecture,
multiply(additive_inverse(a),b) != additive_inverse(multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(sFlat0,b) != additive_inverse(multiply(a,b)),
inference(rw,[status(thm)],[goal_0,t65]) ).
cnf(g0_1,plain,
sFlat1 != additive_inverse(multiply(a,b)),
inference(rw,[status(thm)],[g0_0,t78]) ).
cnf(g0_2,plain,
sFlat1 != additive_inverse(sFlat2),
inference(rw,[status(thm)],[g0_1,t43]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t458]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG013-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 07:45:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.14/0.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.14/0.88 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------