%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP592-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:27:37 PM UTC 2026
% Result : Unsatisfiable 5.37s 1.13s
% Output : CNFRefutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 3
% Syntax : Number of clauses : 74 ( 74 unt; 0 nHn; 3 RR)
% Number of literals : 74 ( 73 equ; 2 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t2,plain,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),X2) = X3,
inference(orient,[status(thm)],[t1]) ).
cnf(t0,axiom,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t703,plain,
double_divide(multiply(inverse(double_divide(X1,inverse(X3))),double_divide(X1,X2)),X2) = X3,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t704,plain,
double_divide(multiply(multiply(inverse(X3),X1),double_divide(X1,X2)),X2) = X3,
inference(step,[status(thm)],[t703,t5]) ).
cnf(t6,plain,
double_divide(multiply(multiply(inverse(X3),X1),double_divide(X1,X2)),X2) = X3,
inference(rw,[status(thm)],[t704]) ).
cnf(t7,plain,
double_divide(multiply(multiply(inverse(X1),X2),double_divide(X2,X3)),X3) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t10,plain,
X1 = double_divide(multiply(multiply(inverse(X1),multiply(multiply(inverse(X2),X3),double_divide(X3,Y3))),X2),Y3),
inference(cp,[status(thm)],[t7,t7]) ).
cnf(t31,plain,
double_divide(multiply(multiply(inverse(X1),multiply(multiply(inverse(X2),X3),double_divide(X3,Y3))),X2),Y3) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t9,plain,
multiply(X1,multiply(multiply(inverse(X2),X3),double_divide(X3,X1))) = inverse(X2),
inference(cp,[status(thm)],[t5,t7]) ).
cnf(t11,plain,
multiply(X1,multiply(multiply(inverse(X2),X3),double_divide(X3,X1))) = inverse(X2),
inference(orient,[status(thm)],[t9]) ).
cnf(t32,plain,
X1 = double_divide(multiply(inverse(X2),X2),inverse(X1)),
inference(cp,[status(thm)],[t31,t11]) ).
cnf(t45,plain,
double_divide(multiply(inverse(X1),X1),inverse(X2)) = X2,
inference(orient,[status(thm)],[t32]) ).
cnf(t47,plain,
double_divide(X1,X2) = double_divide(multiply(inverse(X3),X3),multiply(X2,X1)),
inference(cp,[status(thm)],[t45,t5]) ).
cnf(t83,plain,
double_divide(multiply(inverse(X1),X1),multiply(X2,X3)) = double_divide(X3,X2),
inference(orient,[status(thm)],[t47]) ).
cnf(t88,plain,
X1 = double_divide(multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),double_divide(X3,Y3)),multiply(Y3,X3)),
inference(cp,[status(thm)],[t7,t83]) ).
cnf(t48,plain,
multiply(inverse(X1),multiply(inverse(X2),X2)) = inverse(X1),
inference(cp,[status(thm)],[t5,t45]) ).
cnf(t54,plain,
multiply(inverse(X1),multiply(inverse(X2),X2)) = inverse(X1),
inference(orient,[status(thm)],[t48]) ).
cnf(t708,plain,
X1 = double_divide(multiply(inverse(X1),double_divide(X3,Y3)),multiply(Y3,X3)),
inference(step,[status(thm)],[t88,t54]) ).
cnf(t169,plain,
double_divide(multiply(inverse(X1),double_divide(X2,X3)),multiply(X3,X2)) = X1,
inference(orient,[status(thm)],[t708]) ).
cnf(t57,plain,
X1 = double_divide(inverse(multiply(inverse(X2),X2)),inverse(X1)),
inference(cp,[status(thm)],[t45,t54]) ).
cnf(t62,plain,
double_divide(inverse(multiply(inverse(X1),X1)),inverse(X2)) = X2,
inference(orient,[status(thm)],[t57]) ).
cnf(t172,plain,
X1 = double_divide(multiply(inverse(X1),X2),multiply(inverse(X2),inverse(multiply(inverse(X3),X3)))),
inference(cp,[status(thm)],[t169,t62]) ).
cnf(t58,plain,
inverse(X1) = multiply(inverse(X1),inverse(multiply(inverse(X2),X2))),
inference(cp,[status(thm)],[t54,t54]) ).
cnf(t72,plain,
multiply(inverse(X1),inverse(multiply(inverse(X2),X2))) = inverse(X1),
inference(orient,[status(thm)],[t58]) ).
cnf(t709,plain,
X1 = double_divide(multiply(inverse(X1),X2),inverse(X2)),
inference(step,[status(thm)],[t172,t72]) ).
cnf(t190,plain,
double_divide(multiply(inverse(X1),X2),inverse(X2)) = X1,
inference(orient,[status(thm)],[t709]) ).
cnf(t197,plain,
multiply(inverse(X1),multiply(inverse(X2),X1)) = inverse(X2),
inference(cp,[status(thm)],[t5,t190]) ).
cnf(t205,plain,
multiply(inverse(X1),multiply(inverse(X2),X1)) = inverse(X2),
inference(orient,[status(thm)],[t197]) ).
cnf(t214,plain,
X1 = double_divide(inverse(X2),inverse(multiply(inverse(X2),X1))),
inference(cp,[status(thm)],[t190,t205]) ).
cnf(t335,plain,
double_divide(inverse(X1),inverse(multiply(inverse(X1),X2))) = X2,
inference(orient,[status(thm)],[t214]) ).
cnf(t336,plain,
X1 = multiply(inverse(multiply(inverse(X2),X2)),X1),
inference(cp,[status(thm)],[t335,t62]) ).
cnf(t355,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = X2,
inference(orient,[status(thm)],[t336]) ).
cnf(t191,plain,
X1 = double_divide(inverse(X1),inverse(multiply(inverse(X2),X2))),
inference(cp,[status(thm)],[t190,t54]) ).
cnf(t218,plain,
double_divide(inverse(X1),inverse(multiply(inverse(X2),X2))) = X1,
inference(orient,[status(thm)],[t191]) ).
cnf(t219,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(cp,[status(thm)],[t218,t62]) ).
cnf(t235,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t219]) ).
cnf(t243,plain,
double_divide(X1,inverse(X1)) = double_divide(multiply(inverse(X2),X2),multiply(inverse(X3),X3)),
inference(cp,[status(thm)],[t83,t235]) ).
cnf(t710,plain,
double_divide(X1,inverse(X1)) = double_divide(X3,inverse(X3)),
inference(step,[status(thm)],[t243,t83]) ).
cnf(t253,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(orient,[status(thm)],[t710]) ).
cnf(t258,plain,
double_divide(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(cp,[status(thm)],[t253,t45]) ).
cnf(t269,plain,
double_divide(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t258]) ).
cnf(t366,plain,
X1 = multiply(inverse(double_divide(X2,inverse(X2))),X1),
inference(cp,[status(thm)],[t355,t269]) ).
cnf(t712,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(step,[status(thm)],[t366,t5]) ).
cnf(t383,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t712]) ).
cnf(t397,plain,
X1 = double_divide(double_divide(X1,X2),X2),
inference(cp,[status(thm)],[t7,t383]) ).
cnf(t407,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t397]) ).
cnf(t411,plain,
multiply(inverse(X1),X2) = double_divide(X1,inverse(X2)),
inference(cp,[status(thm)],[t407,t190]) ).
cnf(t431,plain,
double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t411]) ).
cnf(t432,plain,
multiply(inverse(double_divide(X1,inverse(X2))),X2) = X1,
inference(cp,[status(thm)],[t431,t407]) ).
cnf(t726,plain,
multiply(multiply(inverse(X2),X1),X2) = X1,
inference(step,[status(thm)],[t432,t5]) ).
cnf(t566,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(orient,[status(thm)],[t726]) ).
cnf(t717,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),X2)) = X1,
inference(step,[status(thm)],[t218,t431]) ).
cnf(t718,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t717,t54]) ).
cnf(t449,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[t718]) ).
cnf(t453,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t449]) ).
cnf(t455,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(cp,[status(thm)],[t431,t453]) ).
cnf(t515,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(orient,[status(thm)],[t455]) ).
cnf(t567,plain,
inverse(X1) = multiply(double_divide(X2,X1),X2),
inference(cp,[status(thm)],[t566,t515]) ).
cnf(t581,plain,
multiply(double_divide(X1,X2),X1) = inverse(X2),
inference(orient,[status(thm)],[t567]) ).
cnf(t454,plain,
double_divide(X1,X2) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t453,t5]) ).
cnf(t476,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t454]) ).
cnf(t589,plain,
double_divide(X1,double_divide(X1,X2)) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t476,t581]) ).
cnf(t727,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(step,[status(thm)],[t589,t453]) ).
cnf(t592,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t727]) ).
cnf(t603,plain,
X1 = double_divide(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t407,t592]) ).
cnf(t629,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t603]) ).
cnf(t641,plain,
inverse(double_divide(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t581,t629]) ).
cnf(t728,plain,
multiply(X2,X1) = multiply(X1,X2),
inference(step,[status(thm)],[t641,t5]) ).
cnf(t687,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t728]) ).
cnf(goal_0,negated_conjecture,
multiply(b,a) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(b,a) != multiply(b,a),
inference(rw,[status(thm)],[goal_0,t687]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP592-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 15:14:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.37/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.37/1.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------