%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP608-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 01:27:39 PM UTC 2026
% Result : Unsatisfiable 5.53s 1.18s
% Output : CNFRefutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 3
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 3 RR)
% Number of literals : 91 ( 90 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 : 259 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t1,axiom,
double_divide(inverse(double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3))))),X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t2,plain,
double_divide(inverse(double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3))))),X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t1742,plain,
double_divide(multiply(inverse(double_divide(inverse(X2),double_divide(X1,X3))),X1),X3) = X2,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t1743,plain,
double_divide(multiply(multiply(double_divide(X1,X3),inverse(X2)),X1),X3) = X2,
inference(step,[status(thm)],[t1742,t5]) ).
cnf(t6,plain,
double_divide(multiply(multiply(double_divide(X1,X3),inverse(X2)),X1),X3) = X2,
inference(rw,[status(thm)],[t1743]) ).
cnf(t7,plain,
double_divide(multiply(multiply(double_divide(X1,X2),inverse(X3)),X1),X2) = X3,
inference(orient,[status(thm)],[t6]) ).
cnf(t9,plain,
multiply(X1,multiply(multiply(double_divide(X2,X1),inverse(X3)),X2)) = inverse(X3),
inference(cp,[status(thm)],[t5,t7]) ).
cnf(t11,plain,
multiply(X1,multiply(multiply(double_divide(X2,X1),inverse(X3)),X2)) = inverse(X3),
inference(orient,[status(thm)],[t9]) ).
cnf(t13,plain,
inverse(double_divide(X1,X2)) = multiply(X3,multiply(multiply(double_divide(Y3,X3),multiply(X2,X1)),Y3)),
inference(cp,[status(thm)],[t11,t5]) ).
cnf(t1744,plain,
multiply(X2,X1) = multiply(X3,multiply(multiply(double_divide(Y3,X3),multiply(X2,X1)),Y3)),
inference(step,[status(thm)],[t13,t5]) ).
cnf(t21,plain,
multiply(X1,multiply(multiply(double_divide(X2,X1),multiply(X3,Y3)),X2)) = multiply(X3,Y3),
inference(orient,[status(thm)],[t1744]) ).
cnf(t22,plain,
multiply(multiply(double_divide(X1,double_divide(X2,X3)),inverse(Y3)),X1) = multiply(X3,multiply(inverse(Y3),X2)),
inference(cp,[status(thm)],[t21,t11]) ).
cnf(t39,plain,
multiply(multiply(double_divide(X1,double_divide(X2,X3)),inverse(Y3)),X1) = multiply(X3,multiply(inverse(Y3),X2)),
inference(orient,[status(thm)],[t22]) ).
cnf(t46,plain,
X1 = double_divide(multiply(X2,multiply(inverse(X1),X3)),double_divide(X3,X2)),
inference(cp,[status(thm)],[t7,t39]) ).
cnf(t48,plain,
double_divide(multiply(X1,multiply(inverse(X2),X3)),double_divide(X3,X1)) = X2,
inference(orient,[status(thm)],[t46]) ).
cnf(t47,plain,
inverse(X1) = multiply(double_divide(X2,X3),multiply(X3,multiply(inverse(X1),X2))),
inference(cp,[status(thm)],[t11,t39]) ).
cnf(t66,plain,
multiply(double_divide(X1,X2),multiply(X2,multiply(inverse(X3),X1))) = inverse(X3),
inference(orient,[status(thm)],[t47]) ).
cnf(t74,plain,
inverse(double_divide(X1,X2)) = multiply(double_divide(X3,Y3),multiply(Y3,multiply(multiply(X2,X1),X3))),
inference(cp,[status(thm)],[t66,t5]) ).
cnf(t1745,plain,
multiply(X2,X1) = multiply(double_divide(X3,Y3),multiply(Y3,multiply(multiply(X2,X1),X3))),
inference(step,[status(thm)],[t74,t5]) ).
cnf(t99,plain,
multiply(double_divide(X1,X2),multiply(X2,multiply(multiply(X3,Y3),X1))) = multiply(X3,Y3),
inference(orient,[status(thm)],[t1745]) ).
cnf(t113,plain,
X1 = double_divide(multiply(X2,X3),double_divide(multiply(multiply(X2,X3),Y3),double_divide(Y3,inverse(X1)))),
inference(cp,[status(thm)],[t48,t99]) ).
cnf(t276,plain,
double_divide(multiply(X1,X2),double_divide(multiply(multiply(X1,X2),X3),double_divide(X3,inverse(Y3)))) = Y3,
inference(orient,[status(thm)],[t113]) ).
cnf(t277,plain,
X1 = double_divide(multiply(double_divide(X2,double_divide(X2,inverse(X1))),inverse(X3)),X3),
inference(cp,[status(thm)],[t276,t7]) ).
cnf(t304,plain,
double_divide(multiply(double_divide(X1,double_divide(X1,inverse(X2))),inverse(X3)),X3) = X2,
inference(orient,[status(thm)],[t277]) ).
cnf(t309,plain,
multiply(X1,multiply(double_divide(X2,double_divide(X2,inverse(X3))),inverse(X1))) = inverse(X3),
inference(cp,[status(thm)],[t5,t304]) ).
cnf(t332,plain,
multiply(X1,multiply(double_divide(X2,double_divide(X2,inverse(X3))),inverse(X1))) = inverse(X3),
inference(orient,[status(thm)],[t309]) ).
cnf(t8,plain,
double_divide(X1,X2) = double_divide(multiply(multiply(double_divide(X3,Y3),multiply(X2,X1)),X3),Y3),
inference(cp,[status(thm)],[t7,t5]) ).
cnf(t14,plain,
double_divide(multiply(multiply(double_divide(X1,X2),multiply(X3,Y3)),X1),X2) = double_divide(Y3,X3),
inference(orient,[status(thm)],[t8]) ).
cnf(t15,plain,
double_divide(X1,multiply(double_divide(X1,double_divide(X2,X3)),inverse(Y3))) = double_divide(multiply(inverse(Y3),X2),X3),
inference(cp,[status(thm)],[t14,t11]) ).
cnf(t27,plain,
double_divide(X1,multiply(double_divide(X1,double_divide(X2,X3)),inverse(Y3))) = double_divide(multiply(inverse(Y3),X2),X3),
inference(orient,[status(thm)],[t15]) ).
cnf(t61,plain,
double_divide(multiply(inverse(X1),X2),X3) = double_divide(multiply(X3,multiply(inverse(Y3),X2)),multiply(Y3,inverse(X1))),
inference(cp,[status(thm)],[t27,t48]) ).
cnf(t164,plain,
double_divide(multiply(X1,multiply(inverse(X2),X3)),multiply(X2,inverse(Y3))) = double_divide(multiply(inverse(Y3),X3),X1),
inference(orient,[status(thm)],[t61]) ).
cnf(t351,plain,
multiply(double_divide(X1,double_divide(X1,inverse(X2))),inverse(double_divide(X3,Y3))) = multiply(Y3,multiply(inverse(X2),X3)),
inference(cp,[status(thm)],[t21,t332]) ).
cnf(t1747,plain,
multiply(double_divide(X1,double_divide(X1,inverse(X2))),multiply(Y3,X3)) = multiply(Y3,multiply(inverse(X2),X3)),
inference(step,[status(thm)],[t351,t5]) ).
cnf(t353,plain,
multiply(double_divide(X1,double_divide(X1,inverse(X2))),multiply(X3,Y3)) = multiply(X3,multiply(inverse(X2),Y3)),
inference(orient,[status(thm)],[t1747]) ).
cnf(t354,plain,
multiply(double_divide(X1,double_divide(X1,inverse(X2))),multiply(inverse(X3),inverse(double_divide(Y3,double_divide(Y3,inverse(X3)))))) = inverse(X2),
inference(cp,[status(thm)],[t353,t332]) ).
cnf(t1753,plain,
multiply(inverse(X3),multiply(inverse(X2),inverse(double_divide(Y3,double_divide(Y3,inverse(X3)))))) = inverse(X2),
inference(step,[status(thm)],[t354,t353]) ).
cnf(t1754,plain,
multiply(inverse(X3),multiply(inverse(X2),multiply(double_divide(Y3,inverse(X3)),Y3))) = inverse(X2),
inference(step,[status(thm)],[t1753,t5]) ).
cnf(t629,plain,
multiply(inverse(X1),multiply(inverse(X2),multiply(double_divide(X3,inverse(X1)),X3))) = inverse(X2),
inference(orient,[status(thm)],[t1754]) ).
cnf(t651,plain,
double_divide(multiply(inverse(X1),multiply(double_divide(X2,inverse(X3)),X2)),inverse(X3)) = double_divide(inverse(Y3),multiply(Y3,inverse(X1))),
inference(cp,[status(thm)],[t164,t629]) ).
cnf(t352,plain,
double_divide(inverse(double_divide(X1,X2)),double_divide(X3,double_divide(X3,inverse(Y3)))) = double_divide(multiply(inverse(Y3),X1),X2),
inference(cp,[status(thm)],[t14,t332]) ).
cnf(t1748,plain,
double_divide(multiply(X2,X1),double_divide(X3,double_divide(X3,inverse(Y3)))) = double_divide(multiply(inverse(Y3),X1),X2),
inference(step,[status(thm)],[t352,t5]) ).
cnf(t479,plain,
double_divide(multiply(X1,X2),double_divide(X3,double_divide(X3,inverse(Y3)))) = double_divide(multiply(inverse(Y3),X2),X1),
inference(orient,[status(thm)],[t1748]) ).
cnf(t480,plain,
double_divide(multiply(inverse(X1),inverse(double_divide(X2,double_divide(X2,inverse(X1))))),double_divide(X3,double_divide(X3,inverse(Y3)))) = Y3,
inference(cp,[status(thm)],[t479,t304]) ).
cnf(t1749,plain,
double_divide(multiply(inverse(Y3),inverse(double_divide(X2,double_divide(X2,inverse(X1))))),inverse(X1)) = Y3,
inference(step,[status(thm)],[t480,t479]) ).
cnf(t1750,plain,
double_divide(multiply(inverse(Y3),multiply(double_divide(X2,inverse(X1)),X2)),inverse(X1)) = Y3,
inference(step,[status(thm)],[t1749,t5]) ).
cnf(t516,plain,
double_divide(multiply(inverse(X1),multiply(double_divide(X2,inverse(X3)),X2)),inverse(X3)) = X1,
inference(orient,[status(thm)],[t1750]) ).
cnf(t1755,plain,
X1 = double_divide(inverse(Y3),multiply(Y3,inverse(X1))),
inference(step,[status(thm)],[t651,t516]) ).
cnf(t661,plain,
double_divide(inverse(X1),multiply(X1,inverse(X2))) = X2,
inference(orient,[status(thm)],[t1755]) ).
cnf(t40,plain,
multiply(X1,multiply(inverse(X2),X3)) = multiply(multiply(Y3,inverse(X2)),multiply(multiply(double_divide(Y4,double_divide(X3,X1)),inverse(Y3)),Y4)),
inference(cp,[status(thm)],[t39,t7]) ).
cnf(t1746,plain,
multiply(X1,multiply(inverse(X2),X3)) = multiply(multiply(Y3,inverse(X2)),multiply(X1,multiply(inverse(Y3),X3))),
inference(step,[status(thm)],[t40,t39]) ).
cnf(t143,plain,
multiply(multiply(X1,inverse(X2)),multiply(X3,multiply(inverse(X1),Y3))) = multiply(X3,multiply(inverse(X2),Y3)),
inference(orient,[status(thm)],[t1746]) ).
cnf(t653,plain,
multiply(inverse(X1),multiply(inverse(X2),multiply(double_divide(X3,inverse(X1)),X3))) = multiply(multiply(Y3,inverse(X2)),inverse(Y3)),
inference(cp,[status(thm)],[t143,t629]) ).
cnf(t1756,plain,
inverse(X2) = multiply(multiply(Y3,inverse(X2)),inverse(Y3)),
inference(step,[status(thm)],[t653,t629]) ).
cnf(t685,plain,
multiply(multiply(X1,inverse(X2)),inverse(X1)) = inverse(X2),
inference(orient,[status(thm)],[t1756]) ).
cnf(t697,plain,
X1 = double_divide(inverse(multiply(X1,inverse(X2))),inverse(X2)),
inference(cp,[status(thm)],[t661,t685]) ).
cnf(t708,plain,
double_divide(inverse(multiply(X1,inverse(X2))),inverse(X2)) = X1,
inference(orient,[status(thm)],[t697]) ).
cnf(t713,plain,
multiply(X1,inverse(X2)) = double_divide(inverse(inverse(X2)),inverse(X1)),
inference(cp,[status(thm)],[t708,t685]) ).
cnf(t741,plain,
double_divide(inverse(inverse(X1)),inverse(X2)) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t713]) ).
cnf(t742,plain,
multiply(X1,inverse(double_divide(X2,X3))) = double_divide(inverse(multiply(X3,X2)),inverse(X1)),
inference(cp,[status(thm)],[t741,t5]) ).
cnf(t1757,plain,
multiply(X1,multiply(X3,X2)) = double_divide(inverse(multiply(X3,X2)),inverse(X1)),
inference(step,[status(thm)],[t742,t5]) ).
cnf(t812,plain,
double_divide(inverse(multiply(X1,X2)),inverse(X3)) = multiply(X3,multiply(X1,X2)),
inference(orient,[status(thm)],[t1757]) ).
cnf(t1758,plain,
multiply(X2,multiply(X1,inverse(X2))) = X1,
inference(step,[status(thm)],[t708,t812]) ).
cnf(t837,plain,
multiply(X2,multiply(X1,inverse(X2))) = X1,
inference(rw,[status(thm)],[t1758]) ).
cnf(t838,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(orient,[status(thm)],[t837]) ).
cnf(t1759,plain,
double_divide(X2,double_divide(X2,inverse(X3))) = inverse(X3),
inference(step,[status(thm)],[t332,t838]) ).
cnf(t896,plain,
double_divide(X2,double_divide(X2,inverse(X3))) = inverse(X3),
inference(rw,[status(thm)],[t1759]) ).
cnf(t1027,plain,
double_divide(X1,double_divide(X1,inverse(X2))) = inverse(X2),
inference(orient,[status(thm)],[t896]) ).
cnf(t853,plain,
multiply(X1,multiply(X2,multiply(X3,inverse(X2)))) = double_divide(inverse(X3),inverse(X1)),
inference(cp,[status(thm)],[t812,t838]) ).
cnf(t1760,plain,
multiply(X1,X3) = double_divide(inverse(X3),inverse(X1)),
inference(step,[status(thm)],[t853,t838]) ).
cnf(t897,plain,
double_divide(inverse(X1),inverse(X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t1760]) ).
cnf(t1031,plain,
inverse(X1) = double_divide(inverse(X2),multiply(X1,X2)),
inference(cp,[status(thm)],[t1027,t897]) ).
cnf(t1090,plain,
double_divide(inverse(X1),multiply(X2,X1)) = inverse(X2),
inference(orient,[status(thm)],[t1031]) ).
cnf(t1091,plain,
inverse(inverse(X1)) = X1,
inference(cp,[status(thm)],[t1090,t661]) ).
cnf(t1126,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t1091]) ).
cnf(t1135,plain,
inverse(inverse(X1)) = double_divide(X2,double_divide(X2,X1)),
inference(cp,[status(thm)],[t1027,t1126]) ).
cnf(t1769,plain,
X1 = double_divide(X2,double_divide(X2,X1)),
inference(step,[status(thm)],[t1135,t1126]) ).
cnf(t1213,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t1769]) ).
cnf(t1220,plain,
multiply(X1,inverse(X2)) = double_divide(inverse(X1),X2),
inference(cp,[status(thm)],[t1213,t661]) ).
cnf(t1465,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t1220]) ).
cnf(t1132,plain,
multiply(X1,inverse(X2)) = double_divide(X2,inverse(X1)),
inference(cp,[status(thm)],[t897,t1126]) ).
cnf(t1436,plain,
double_divide(X1,inverse(X2)) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t1132]) ).
cnf(t1466,plain,
multiply(X1,inverse(inverse(X2))) = multiply(X2,inverse(inverse(X1))),
inference(cp,[status(thm)],[t1465,t1436]) ).
cnf(t1783,plain,
multiply(X1,X2) = multiply(X2,inverse(inverse(X1))),
inference(step,[status(thm)],[t1466,t1126]) ).
cnf(t1784,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(step,[status(thm)],[t1783,t1126]) ).
cnf(t1707,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t1784]) ).
cnf(goal_0,negated_conjecture,
multiply(b,a) != multiply(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(b,a) != multiply(b,a),
inference(rw,[status(thm)],[goal_0,t1707]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP608-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 15:14:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.53/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.53/1.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------