%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:27:34 PM UTC 2026
% Result : Unsatisfiable 5.63s 1.19s
% Output : CNFRefutation 5.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 8
% Syntax : Number of clauses : 92 ( 92 unt; 0 nHn; 51 RR)
% Number of literals : 92 ( 91 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
sF0 = double_divide(b,a),
introduced(definition) ).
cnf(t6,plain,
double_divide(b,a) = sF0,
inference(orient,[status(thm)],[t2]) ).
cnf(t4,axiom,
sF2 = double_divide(a,b),
introduced(definition) ).
cnf(t7,plain,
double_divide(a,b) = sF2,
inference(orient,[status(thm)],[t4]) ).
cnf(t1,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t15,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(u1,axiom,
identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d1,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t0,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(definition_unfolding,[status(thm)],[u1,d1]) ).
cnf(t8,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t18,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t15,t8]) ).
cnf(t28,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t18]) ).
cnf(t29,plain,
identity = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(cp,[status(thm)],[t28,t8]) ).
cnf(t35,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(orient,[status(thm)],[t29]) ).
cnf(t36,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t15,t35]) ).
cnf(t928,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t36,t28]) ).
cnf(t41,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t928]) ).
cnf(t930,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity) = X1,
inference(step,[status(thm)],[t28,t41]) ).
cnf(t43,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity) = X1,
inference(rw,[status(thm)],[t930]) ).
cnf(t46,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity) = X1,
inference(orient,[status(thm)],[t43]) ).
cnf(t49,plain,
double_divide(identity,double_divide(identity,double_divide(X1,identity))) = double_divide(double_divide(identity,double_divide(identity,X1)),identity),
inference(cp,[status(thm)],[t46,t46]) ).
cnf(t57,plain,
double_divide(double_divide(identity,double_divide(identity,X1)),identity) = double_divide(identity,double_divide(identity,double_divide(X1,identity))),
inference(orient,[status(thm)],[t49]) ).
cnf(t934,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(step,[status(thm)],[t46,t57]) ).
cnf(t58,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(rw,[status(thm)],[t934]) ).
cnf(t66,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(orient,[status(thm)],[t58]) ).
cnf(t16,plain,
X1 = double_divide(double_divide(a,double_divide(double_divide(X1,sF0),double_divide(b,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t15,t6]) ).
cnf(t38,plain,
double_divide(double_divide(a,double_divide(double_divide(X1,sF0),double_divide(b,identity))),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t16]) ).
cnf(t933,plain,
double_divide(double_divide(a,double_divide(double_divide(X1,sF0),double_divide(b,identity))),identity) = X1,
inference(step,[status(thm)],[t38,t41]) ).
cnf(t45,plain,
double_divide(double_divide(a,double_divide(double_divide(X1,sF0),double_divide(b,identity))),identity) = X1,
inference(rw,[status(thm)],[t933]) ).
cnf(t68,plain,
double_divide(double_divide(a,double_divide(double_divide(X1,sF0),double_divide(b,identity))),identity) = X1,
inference(orient,[status(thm)],[t45]) ).
cnf(t70,plain,
double_divide(a,double_divide(double_divide(X1,sF0),double_divide(b,identity))) = double_divide(identity,double_divide(identity,double_divide(X1,identity))),
inference(cp,[status(thm)],[t66,t68]) ).
cnf(t107,plain,
double_divide(a,double_divide(double_divide(X1,sF0),double_divide(b,identity))) = double_divide(identity,double_divide(identity,double_divide(X1,identity))),
inference(orient,[status(thm)],[t70]) ).
cnf(t929,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),identity) = X2,
inference(step,[status(thm)],[t15,t41]) ).
cnf(t42,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),identity) = X2,
inference(rw,[status(thm)],[t929]) ).
cnf(t71,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),identity) = X2,
inference(orient,[status(thm)],[t42]) ).
cnf(t3,axiom,
sF1 = double_divide(double_divide(b,a),identity),
introduced(definition) ).
cnf(t926,plain,
sF1 = double_divide(sF0,identity),
inference(step,[status(thm)],[t3,t6]) ).
cnf(t9,plain,
double_divide(sF0,identity) = sF1,
inference(orient,[status(thm)],[t926]) ).
cnf(t74,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,sF1),double_divide(sF0,identity))),identity),
inference(cp,[status(thm)],[t71,t9]) ).
cnf(t945,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,sF1),sF1)),identity),
inference(step,[status(thm)],[t74,t9]) ).
cnf(t111,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,sF1),sF1)),identity) = X1,
inference(orient,[status(thm)],[t945]) ).
cnf(t47,plain,
sF0 = double_divide(double_divide(identity,double_divide(identity,sF1)),identity),
inference(cp,[status(thm)],[t46,t9]) ).
cnf(t51,plain,
double_divide(double_divide(identity,double_divide(identity,sF1)),identity) = sF0,
inference(orient,[status(thm)],[t47]) ).
cnf(t935,plain,
double_divide(identity,double_divide(identity,double_divide(sF1,identity))) = sF0,
inference(step,[status(thm)],[t51,t57]) ).
cnf(t59,plain,
double_divide(identity,double_divide(identity,double_divide(sF1,identity))) = sF0,
inference(rw,[status(thm)],[t935]) ).
cnf(t62,plain,
double_divide(identity,double_divide(identity,double_divide(sF1,identity))) = sF0,
inference(orient,[status(thm)],[t59]) ).
cnf(t84,plain,
identity = double_divide(double_divide(double_divide(sF1,identity),double_divide(sF0,double_divide(identity,identity))),identity),
inference(cp,[status(thm)],[t71,t62]) ).
cnf(t937,plain,
identity = double_divide(double_divide(double_divide(sF1,identity),double_divide(sF0,identity)),identity),
inference(step,[status(thm)],[t84,t41]) ).
cnf(t938,plain,
identity = double_divide(double_divide(double_divide(sF1,identity),sF1),identity),
inference(step,[status(thm)],[t937,t9]) ).
cnf(t95,plain,
double_divide(double_divide(double_divide(sF1,identity),sF1),identity) = identity,
inference(orient,[status(thm)],[t938]) ).
cnf(t96,plain,
double_divide(double_divide(sF1,identity),sF1) = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
inference(cp,[status(thm)],[t66,t95]) ).
cnf(t939,plain,
double_divide(double_divide(sF1,identity),sF1) = double_divide(identity,identity),
inference(step,[status(thm)],[t96,t8]) ).
cnf(t940,plain,
double_divide(double_divide(sF1,identity),sF1) = identity,
inference(step,[status(thm)],[t939,t41]) ).
cnf(t98,plain,
double_divide(double_divide(sF1,identity),sF1) = identity,
inference(orient,[status(thm)],[t940]) ).
cnf(t112,plain,
double_divide(sF1,identity) = double_divide(double_divide(identity,double_divide(identity,sF1)),identity),
inference(cp,[status(thm)],[t111,t98]) ).
cnf(t946,plain,
double_divide(sF1,identity) = double_divide(identity,double_divide(identity,double_divide(sF1,identity))),
inference(step,[status(thm)],[t112,t57]) ).
cnf(t947,plain,
double_divide(sF1,identity) = sF0,
inference(step,[status(thm)],[t946,t62]) ).
cnf(t117,plain,
double_divide(sF1,identity) = sF0,
inference(orient,[status(thm)],[t947]) ).
cnf(t120,plain,
identity = double_divide(sF1,sF0),
inference(cp,[status(thm)],[t8,t117]) ).
cnf(t136,plain,
double_divide(sF1,sF0) = identity,
inference(orient,[status(thm)],[t120]) ).
cnf(t138,plain,
double_divide(identity,double_divide(identity,double_divide(sF1,identity))) = double_divide(a,double_divide(identity,double_divide(b,identity))),
inference(cp,[status(thm)],[t107,t136]) ).
cnf(t950,plain,
double_divide(identity,double_divide(identity,sF0)) = double_divide(a,double_divide(identity,double_divide(b,identity))),
inference(step,[status(thm)],[t138,t117]) ).
cnf(t948,plain,
double_divide(identity,double_divide(identity,sF0)) = sF0,
inference(step,[status(thm)],[t62,t117]) ).
cnf(t118,plain,
double_divide(identity,double_divide(identity,sF0)) = sF0,
inference(rw,[status(thm)],[t948]) ).
cnf(t139,plain,
double_divide(identity,double_divide(identity,sF0)) = sF0,
inference(orient,[status(thm)],[t118]) ).
cnf(t951,plain,
sF0 = double_divide(a,double_divide(identity,double_divide(b,identity))),
inference(step,[status(thm)],[t950,t139]) ).
cnf(t156,plain,
double_divide(a,double_divide(identity,double_divide(b,identity))) = sF0,
inference(orient,[status(thm)],[t951]) ).
cnf(t67,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),identity))) = double_divide(double_divide(identity,X1),identity),
inference(cp,[status(thm)],[t57,t66]) ).
cnf(t223,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),identity))) = double_divide(double_divide(identity,X1),identity),
inference(orient,[status(thm)],[t67]) ).
cnf(t80,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(identity,identity))),identity),
inference(cp,[status(thm)],[t71,t41]) ).
cnf(t999,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),identity),
inference(step,[status(thm)],[t80,t41]) ).
cnf(t443,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),identity) = X1,
inference(orient,[status(thm)],[t999]) ).
cnf(t1000,plain,
double_divide(identity,double_divide(identity,X1)) = double_divide(double_divide(identity,X1),identity),
inference(step,[status(thm)],[t223,t443]) ).
cnf(t444,plain,
double_divide(identity,double_divide(identity,X1)) = double_divide(double_divide(identity,X1),identity),
inference(rw,[status(thm)],[t1000]) ).
cnf(t465,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(identity,double_divide(identity,X1)),
inference(orient,[status(thm)],[t444]) ).
cnf(t469,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity)))) = double_divide(X1,identity),
inference(cp,[status(thm)],[t465,t66]) ).
cnf(t1014,plain,
double_divide(identity,X1) = double_divide(X1,identity),
inference(step,[status(thm)],[t469,t66]) ).
cnf(t510,plain,
double_divide(identity,X1) = double_divide(X1,identity),
inference(orient,[status(thm)],[t1014]) ).
cnf(t1018,plain,
double_divide(a,double_divide(identity,double_divide(identity,b))) = sF0,
inference(step,[status(thm)],[t156,t510]) ).
cnf(t514,plain,
double_divide(a,double_divide(identity,double_divide(identity,b))) = sF0,
inference(rw,[status(thm)],[t1018]) ).
cnf(t563,plain,
double_divide(a,double_divide(identity,double_divide(identity,b))) = sF0,
inference(orient,[status(thm)],[t514]) ).
cnf(t899,plain,
double_divide(a,b) = sF0,
inference(rw,[status(thm)],[t563]) ).
cnf(t1102,plain,
sF2 = sF0,
inference(step,[status(thm)],[t899,t7]) ).
cnf(t917,plain,
sF2 = sF0,
inference(orient,[status(thm)],[t1102]) ).
cnf(t1103,plain,
double_divide(a,b) = sF0,
inference(step,[status(thm)],[t7,t917]) ).
cnf(t918,plain,
double_divide(a,b) = sF0,
inference(orient,[status(thm)],[t1103]) ).
cnf(u0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
double_divide(sF0,identity) != double_divide(double_divide(a,b),identity),
inference(rw,[status(thm)],[goal_0,t6]) ).
cnf(g0_1,plain,
double_divide(sF0,identity) != double_divide(sF0,identity),
inference(rw,[status(thm)],[g0_0,t918]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 15:09:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.63/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.63/1.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------