%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP571-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:27:33 PM UTC 2026
% Result : Unsatisfiable 5.10s 1.30s
% Output : CNFRefutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 5
% Syntax : Number of clauses : 100 ( 100 unt; 0 nHn; 10 RR)
% Number of literals : 100 ( 99 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 179 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t0,axiom,
double_divide(X1,identity) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
double_divide(X1,identity) = inverse(X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t714,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3))),double_divide(identity,identity)) = X2,
inference(step,[status(thm)],[t4,t7]) ).
cnf(t715,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3))),inverse(identity)) = X2,
inference(step,[status(thm)],[t714,t7]) ).
cnf(t8,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3))),inverse(identity)) = X2,
inference(rw,[status(thm)],[t715]) ).
cnf(t69,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3))),inverse(identity)) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t70,plain,
X1 = double_divide(double_divide(X2,double_divide(double_divide(X1,inverse(X2)),inverse(identity))),inverse(identity)),
inference(cp,[status(thm)],[t69,t7]) ).
cnf(t127,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,inverse(X1)),inverse(identity))),inverse(identity)) = X2,
inference(orient,[status(thm)],[t70]) ).
cnf(t1,axiom,
double_divide(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
double_divide(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t1]) ).
cnf(t71,plain,
X1 = double_divide(double_divide(X2,double_divide(double_divide(X1,identity),inverse(inverse(X2)))),inverse(identity)),
inference(cp,[status(thm)],[t69,t9]) ).
cnf(t717,plain,
X1 = double_divide(double_divide(X2,double_divide(inverse(X1),inverse(inverse(X2)))),inverse(identity)),
inference(step,[status(thm)],[t71,t7]) ).
cnf(t2,axiom,
double_divide(double_divide(X1,X2),identity) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t716,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(step,[status(thm)],[t2,t7]) ).
cnf(t10,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t716]) ).
cnf(t11,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t10,t7]) ).
cnf(t14,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t718,plain,
X1 = double_divide(double_divide(X2,double_divide(inverse(X1),multiply(identity,X2))),inverse(identity)),
inference(step,[status(thm)],[t717,t14]) ).
cnf(t85,plain,
double_divide(double_divide(X1,double_divide(inverse(X2),multiply(identity,X1))),inverse(identity)) = X2,
inference(orient,[status(thm)],[t718]) ).
cnf(t16,plain,
identity = double_divide(inverse(X1),multiply(identity,X1)),
inference(cp,[status(thm)],[t9,t14]) ).
cnf(t24,plain,
double_divide(inverse(X1),multiply(identity,X1)) = identity,
inference(orient,[status(thm)],[t16]) ).
cnf(t86,plain,
X1 = double_divide(double_divide(X1,identity),inverse(identity)),
inference(cp,[status(thm)],[t85,t24]) ).
cnf(t719,plain,
X1 = double_divide(inverse(X1),inverse(identity)),
inference(step,[status(thm)],[t86,t7]) ).
cnf(t96,plain,
double_divide(inverse(X1),inverse(identity)) = X1,
inference(orient,[status(thm)],[t719]) ).
cnf(t131,plain,
inverse(X1) = double_divide(double_divide(identity,double_divide(X1,inverse(identity))),inverse(identity)),
inference(cp,[status(thm)],[t127,t96]) ).
cnf(t141,plain,
double_divide(double_divide(identity,double_divide(X1,inverse(identity))),inverse(identity)) = inverse(X1),
inference(orient,[status(thm)],[t131]) ).
cnf(t144,plain,
inverse(identity) = double_divide(double_divide(identity,identity),inverse(identity)),
inference(cp,[status(thm)],[t141,t9]) ).
cnf(t721,plain,
inverse(identity) = double_divide(inverse(identity),inverse(identity)),
inference(step,[status(thm)],[t144,t7]) ).
cnf(t722,plain,
inverse(identity) = identity,
inference(step,[status(thm)],[t721,t96]) ).
cnf(t157,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t722]) ).
cnf(t752,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3))),identity) = X2,
inference(step,[status(thm)],[t69,t157]) ).
cnf(t753,plain,
inverse(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3)))) = X2,
inference(step,[status(thm)],[t752,t7]) ).
cnf(t754,plain,
multiply(double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3)),X1) = X2,
inference(step,[status(thm)],[t753,t10]) ).
cnf(t187,plain,
multiply(double_divide(double_divide(X2,double_divide(X1,X3)),inverse(X3)),X1) = X2,
inference(rw,[status(thm)],[t754]) ).
cnf(t755,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,inverse(X1)),identity)),inverse(identity)) = X2,
inference(step,[status(thm)],[t127,t157]) ).
cnf(t756,plain,
double_divide(double_divide(X1,inverse(double_divide(X2,inverse(X1)))),inverse(identity)) = X2,
inference(step,[status(thm)],[t755,t7]) ).
cnf(t757,plain,
double_divide(double_divide(X1,multiply(inverse(X1),X2)),inverse(identity)) = X2,
inference(step,[status(thm)],[t756,t10]) ).
cnf(t758,plain,
double_divide(double_divide(X1,multiply(inverse(X1),X2)),identity) = X2,
inference(step,[status(thm)],[t757,t157]) ).
cnf(t759,plain,
inverse(double_divide(X1,multiply(inverse(X1),X2))) = X2,
inference(step,[status(thm)],[t758,t7]) ).
cnf(t760,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(step,[status(thm)],[t759,t10]) ).
cnf(t188,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(rw,[status(thm)],[t760]) ).
cnf(t218,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(orient,[status(thm)],[t188]) ).
cnf(t739,plain,
double_divide(inverse(X1),identity) = X1,
inference(step,[status(thm)],[t96,t157]) ).
cnf(t740,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t739,t7]) ).
cnf(t741,plain,
multiply(identity,X1) = X1,
inference(step,[status(thm)],[t740,t14]) ).
cnf(t183,plain,
multiply(identity,X1) = X1,
inference(rw,[status(thm)],[t741]) ).
cnf(t190,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t183]) ).
cnf(t761,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t14,t190]) ).
cnf(t191,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t761]) ).
cnf(t221,plain,
X1 = multiply(multiply(X2,X1),inverse(X2)),
inference(cp,[status(thm)],[t218,t191]) ).
cnf(t225,plain,
multiply(multiply(X1,X2),inverse(X1)) = X2,
inference(orient,[status(thm)],[t221]) ).
cnf(t229,plain,
inverse(X1) = multiply(X2,inverse(multiply(X1,X2))),
inference(cp,[status(thm)],[t225,t225]) ).
cnf(t98,plain,
double_divide(X1,X2) = double_divide(multiply(X2,X1),inverse(identity)),
inference(cp,[status(thm)],[t96,t10]) ).
cnf(t115,plain,
double_divide(multiply(X1,X2),inverse(identity)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t98]) ).
cnf(t736,plain,
double_divide(multiply(X1,X2),identity) = double_divide(X2,X1),
inference(step,[status(thm)],[t115,t157]) ).
cnf(t737,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(step,[status(thm)],[t736,t7]) ).
cnf(t181,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(rw,[status(thm)],[t737]) ).
cnf(t213,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t181]) ).
cnf(t775,plain,
inverse(X1) = multiply(X2,double_divide(X2,X1)),
inference(step,[status(thm)],[t229,t213]) ).
cnf(t233,plain,
multiply(X1,double_divide(X1,X2)) = inverse(X2),
inference(orient,[status(thm)],[t775]) ).
cnf(t238,plain,
double_divide(inverse(X1),X2) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t218,t233]) ).
cnf(t246,plain,
double_divide(inverse(X1),X2) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t238]) ).
cnf(t255,plain,
multiply(X1,inverse(X2)) = inverse(multiply(inverse(X1),X2)),
inference(cp,[status(thm)],[t10,t246]) ).
cnf(t777,plain,
multiply(X1,inverse(X2)) = double_divide(X2,inverse(X1)),
inference(step,[status(thm)],[t255,t213]) ).
cnf(t256,plain,
double_divide(X1,inverse(X2)) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t777]) ).
cnf(t780,plain,
multiply(multiply(X3,inverse(double_divide(X2,double_divide(X1,X3)))),X1) = X2,
inference(step,[status(thm)],[t187,t256]) ).
cnf(t781,plain,
multiply(multiply(X3,multiply(double_divide(X1,X3),X2)),X1) = X2,
inference(step,[status(thm)],[t780,t10]) ).
cnf(t296,plain,
multiply(multiply(X1,multiply(double_divide(X2,X1),X3)),X2) = X3,
inference(orient,[status(thm)],[t781]) ).
cnf(t235,plain,
double_divide(double_divide(X1,X2),X1) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t213,t233]) ).
cnf(t776,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(step,[status(thm)],[t235,t191]) ).
cnf(t239,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t776]) ).
cnf(t257,plain,
multiply(X1,inverse(double_divide(inverse(X1),X2))) = X2,
inference(cp,[status(thm)],[t256,t239]) ).
cnf(t778,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(step,[status(thm)],[t257,t10]) ).
cnf(t274,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(orient,[status(thm)],[t778]) ).
cnf(t298,plain,
inverse(X1) = multiply(double_divide(X2,X1),X2),
inference(cp,[status(thm)],[t296,t274]) ).
cnf(t320,plain,
multiply(double_divide(X1,X2),X1) = inverse(X2),
inference(orient,[status(thm)],[t298]) ).
cnf(t240,plain,
X1 = double_divide(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t239,t239]) ).
cnf(t242,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t240]) ).
cnf(t323,plain,
inverse(double_divide(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t320,t242]) ).
cnf(t784,plain,
multiply(X2,X1) = multiply(X1,X2),
inference(step,[status(thm)],[t323,t10]) ).
cnf(t371,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t784]) ).
cnf(t386,plain,
multiply(multiply(X1,multiply(double_divide(X2,X1),X3)),X2) = X3,
inference(rw,[status(thm)],[t296]) ).
cnf(t790,plain,
multiply(X2,multiply(X1,multiply(double_divide(X2,X1),X3))) = X3,
inference(step,[status(thm)],[t386,t371]) ).
cnf(t648,plain,
multiply(X1,multiply(X2,multiply(double_divide(X1,X2),X3))) = X3,
inference(orient,[status(thm)],[t790]) ).
cnf(t326,plain,
inverse(X1) = multiply(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t320,t239]) ).
cnf(t361,plain,
multiply(X1,double_divide(X2,X1)) = inverse(X2),
inference(orient,[status(thm)],[t326]) ).
cnf(t365,plain,
inverse(inverse(X1)) = multiply(X2,multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t361,t246]) ).
cnf(t785,plain,
X1 = multiply(X2,multiply(inverse(X2),X1)),
inference(step,[status(thm)],[t365,t191]) ).
cnf(t396,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t785]) ).
cnf(t654,plain,
multiply(inverse(double_divide(X1,X2)),X3) = multiply(X1,multiply(X2,X3)),
inference(cp,[status(thm)],[t648,t396]) ).
cnf(t791,plain,
multiply(multiply(X2,X1),X3) = multiply(X1,multiply(X2,X3)),
inference(step,[status(thm)],[t654,t10]) ).
cnf(t682,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(orient,[status(thm)],[t791]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(multiply(a3,b3),c3) != multiply(multiply(b3,a3),c3),
inference(rw,[status(thm)],[goal_0,t371]) ).
cnf(g0_1,plain,
multiply(multiply(a3,b3),c3) != multiply(c3,multiply(b3,a3)),
inference(rw,[status(thm)],[g0_0,t371]) ).
cnf(g0_2,plain,
multiply(multiply(b3,c3),a3) != multiply(c3,multiply(b3,a3)),
inference(rw,[status(thm)],[g0_1,t371]) ).
cnf(g0_3,plain,
multiply(c3,multiply(b3,a3)) != multiply(c3,multiply(b3,a3)),
inference(rw,[status(thm)],[g0_2,t682]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP571-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n006.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 : Wed Sep 23 15:06:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.10/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.10/1.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------