%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP586-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 01:27:36 PM UTC 2026
% Result : Unsatisfiable 1.46s 1.19s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 3
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 3 RR)
% Number of literals : 84 ( 83 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 : 248 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X3))),X2))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t2,plain,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),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(t972,plain,
double_divide(X1,multiply(X2,inverse(double_divide(double_divide(X1,X2),inverse(X3))))) = X3,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t973,plain,
double_divide(X1,multiply(X2,multiply(inverse(X3),double_divide(X1,X2)))) = X3,
inference(step,[status(thm)],[t972,t5]) ).
cnf(t6,plain,
double_divide(X1,multiply(X2,multiply(inverse(X3),double_divide(X1,X2)))) = X3,
inference(rw,[status(thm)],[t973]) ).
cnf(t7,plain,
double_divide(X1,multiply(X2,multiply(inverse(X3),double_divide(X1,X2)))) = X3,
inference(orient,[status(thm)],[t6]) ).
cnf(t9,plain,
multiply(multiply(X1,multiply(inverse(X2),double_divide(X3,X1))),X3) = inverse(X2),
inference(cp,[status(thm)],[t5,t7]) ).
cnf(t11,plain,
multiply(multiply(X1,multiply(inverse(X2),double_divide(X3,X1))),X3) = inverse(X2),
inference(orient,[status(thm)],[t9]) ).
cnf(t12,plain,
inverse(double_divide(X1,X2)) = multiply(multiply(X3,multiply(multiply(X2,X1),double_divide(Y3,X3))),Y3),
inference(cp,[status(thm)],[t11,t5]) ).
cnf(t974,plain,
multiply(X2,X1) = multiply(multiply(X3,multiply(multiply(X2,X1),double_divide(Y3,X3))),Y3),
inference(step,[status(thm)],[t12,t5]) ).
cnf(t21,plain,
multiply(multiply(X1,multiply(multiply(X2,X3),double_divide(Y3,X1))),Y3) = multiply(X2,X3),
inference(orient,[status(thm)],[t974]) ).
cnf(t22,plain,
multiply(X1,multiply(inverse(X2),double_divide(double_divide(X3,Y3),X1))) = multiply(multiply(Y3,inverse(X2)),X3),
inference(cp,[status(thm)],[t21,t11]) ).
cnf(t39,plain,
multiply(X1,multiply(inverse(X2),double_divide(double_divide(X3,Y3),X1))) = multiply(multiply(Y3,inverse(X2)),X3),
inference(orient,[status(thm)],[t22]) ).
cnf(t46,plain,
X1 = double_divide(double_divide(X2,X3),multiply(multiply(X3,inverse(X1)),X2)),
inference(cp,[status(thm)],[t7,t39]) ).
cnf(t48,plain,
double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(X3)),X1)) = X3,
inference(orient,[status(thm)],[t46]) ).
cnf(t47,plain,
inverse(X1) = multiply(multiply(multiply(X2,inverse(X1)),X3),double_divide(X3,X2)),
inference(cp,[status(thm)],[t11,t39]) ).
cnf(t66,plain,
multiply(multiply(multiply(X1,inverse(X2)),X3),double_divide(X3,X1)) = inverse(X2),
inference(orient,[status(thm)],[t47]) ).
cnf(t70,plain,
inverse(double_divide(X1,X2)) = multiply(multiply(multiply(X3,multiply(X2,X1)),Y3),double_divide(Y3,X3)),
inference(cp,[status(thm)],[t66,t5]) ).
cnf(t975,plain,
multiply(X2,X1) = multiply(multiply(multiply(X3,multiply(X2,X1)),Y3),double_divide(Y3,X3)),
inference(step,[status(thm)],[t70,t5]) ).
cnf(t99,plain,
multiply(multiply(multiply(X1,multiply(X2,X3)),Y3),double_divide(Y3,X1)) = multiply(X2,X3),
inference(orient,[status(thm)],[t975]) ).
cnf(t113,plain,
X1 = double_divide(double_divide(double_divide(inverse(X1),X2),multiply(X2,multiply(X3,Y3))),multiply(X3,Y3)),
inference(cp,[status(thm)],[t48,t99]) ).
cnf(t276,plain,
double_divide(double_divide(double_divide(inverse(X1),X2),multiply(X2,multiply(X3,Y3))),multiply(X3,Y3)) = X1,
inference(orient,[status(thm)],[t113]) ).
cnf(t25,plain,
multiply(X1,multiply(multiply(X2,X3),double_divide(double_divide(Y3,Y4),X1))) = multiply(multiply(Y4,multiply(X2,X3)),Y3),
inference(cp,[status(thm)],[t21,t21]) ).
cnf(t187,plain,
multiply(X1,multiply(multiply(X2,X3),double_divide(double_divide(Y3,Y4),X1))) = multiply(multiply(Y4,multiply(X2,X3)),Y3),
inference(orient,[status(thm)],[t25]) ).
cnf(t277,plain,
X1 = double_divide(X2,multiply(inverse(X2),double_divide(double_divide(inverse(X1),X3),X3))),
inference(cp,[status(thm)],[t276,t7]) ).
cnf(t304,plain,
double_divide(X1,multiply(inverse(X1),double_divide(double_divide(inverse(X2),X3),X3))) = X2,
inference(orient,[status(thm)],[t277]) ).
cnf(t309,plain,
multiply(multiply(inverse(X1),double_divide(double_divide(inverse(X2),X3),X3)),X1) = inverse(X2),
inference(cp,[status(thm)],[t5,t304]) ).
cnf(t332,plain,
multiply(multiply(inverse(X1),double_divide(double_divide(inverse(X2),X3),X3)),X1) = inverse(X2),
inference(orient,[status(thm)],[t309]) ).
cnf(t351,plain,
multiply(inverse(double_divide(X1,X2)),double_divide(double_divide(inverse(X3),Y3),Y3)) = multiply(multiply(X2,inverse(X3)),X1),
inference(cp,[status(thm)],[t21,t332]) ).
cnf(t977,plain,
multiply(multiply(X2,X1),double_divide(double_divide(inverse(X3),Y3),Y3)) = multiply(multiply(X2,inverse(X3)),X1),
inference(step,[status(thm)],[t351,t5]) ).
cnf(t353,plain,
multiply(multiply(X1,X2),double_divide(double_divide(inverse(X3),Y3),Y3)) = multiply(multiply(X1,inverse(X3)),X2),
inference(orient,[status(thm)],[t977]) ).
cnf(t374,plain,
multiply(multiply(X1,multiply(X2,X3)),inverse(Y3)) = multiply(X1,multiply(multiply(X2,inverse(Y3)),X3)),
inference(cp,[status(thm)],[t187,t353]) ).
cnf(t415,plain,
multiply(multiply(X1,multiply(X2,X3)),inverse(Y3)) = multiply(X1,multiply(multiply(X2,inverse(Y3)),X3)),
inference(orient,[status(thm)],[t374]) ).
cnf(t433,plain,
multiply(X1,multiply(multiply(multiply(X2,multiply(inverse(X3),double_divide(Y3,X2))),inverse(Y4)),Y3)) = multiply(multiply(X1,inverse(X3)),inverse(Y4)),
inference(cp,[status(thm)],[t415,t11]) ).
cnf(t978,plain,
multiply(X1,multiply(multiply(X2,multiply(multiply(inverse(X3),inverse(Y4)),double_divide(Y3,X2))),Y3)) = multiply(multiply(X1,inverse(X3)),inverse(Y4)),
inference(step,[status(thm)],[t433,t415]) ).
cnf(t979,plain,
multiply(X1,multiply(inverse(X3),inverse(Y4))) = multiply(multiply(X1,inverse(X3)),inverse(Y4)),
inference(step,[status(thm)],[t978,t21]) ).
cnf(t449,plain,
multiply(multiply(X1,inverse(X2)),inverse(X3)) = multiply(X1,multiply(inverse(X2),inverse(X3))),
inference(orient,[status(thm)],[t979]) ).
cnf(t473,plain,
X1 = double_divide(double_divide(inverse(X2),X3),multiply(X3,multiply(inverse(X1),inverse(X2)))),
inference(cp,[status(thm)],[t48,t449]) ).
cnf(t576,plain,
double_divide(double_divide(inverse(X1),X2),multiply(X2,multiply(inverse(X3),inverse(X1)))) = X3,
inference(orient,[status(thm)],[t473]) ).
cnf(t590,plain,
X1 = double_divide(X2,multiply(inverse(X2),inverse(X1))),
inference(cp,[status(thm)],[t276,t576]) ).
cnf(t606,plain,
double_divide(X1,multiply(inverse(X1),inverse(X2))) = X2,
inference(orient,[status(thm)],[t590]) ).
cnf(t613,plain,
multiply(multiply(inverse(X1),inverse(X2)),X1) = inverse(X2),
inference(cp,[status(thm)],[t5,t606]) ).
cnf(t639,plain,
multiply(multiply(inverse(X1),inverse(X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t613]) ).
cnf(t670,plain,
X1 = double_divide(double_divide(X2,inverse(X2)),inverse(X1)),
inference(cp,[status(thm)],[t48,t639]) ).
cnf(t696,plain,
double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = X2,
inference(orient,[status(thm)],[t670]) ).
cnf(t76,plain,
X1 = double_divide(double_divide(double_divide(inverse(X1),X2),multiply(X2,inverse(X3))),inverse(X3)),
inference(cp,[status(thm)],[t48,t66]) ).
cnf(t114,plain,
double_divide(double_divide(double_divide(inverse(X1),X2),multiply(X2,inverse(X3))),inverse(X3)) = X1,
inference(orient,[status(thm)],[t76]) ).
cnf(t41,plain,
multiply(multiply(X1,inverse(X2)),X3) = multiply(multiply(Y3,multiply(inverse(Y4),double_divide(double_divide(X3,X1),Y3))),multiply(inverse(X2),Y4)),
inference(cp,[status(thm)],[t39,t7]) ).
cnf(t976,plain,
multiply(multiply(X1,inverse(X2)),X3) = multiply(multiply(multiply(X1,inverse(Y4)),X3),multiply(inverse(X2),Y4)),
inference(step,[status(thm)],[t41,t39]) ).
cnf(t143,plain,
multiply(multiply(multiply(X1,inverse(X2)),X3),multiply(inverse(Y3),X2)) = multiply(multiply(X1,inverse(Y3)),X3),
inference(orient,[status(thm)],[t976]) ).
cnf(t662,plain,
multiply(multiply(inverse(X1),inverse(X2)),X1) = multiply(inverse(X3),multiply(inverse(X2),X3)),
inference(cp,[status(thm)],[t143,t639]) ).
cnf(t985,plain,
inverse(X2) = multiply(inverse(X3),multiply(inverse(X2),X3)),
inference(step,[status(thm)],[t662,t639]) ).
cnf(t720,plain,
multiply(inverse(X1),multiply(inverse(X2),X1)) = inverse(X2),
inference(orient,[status(thm)],[t985]) ).
cnf(t668,plain,
inverse(X1) = multiply(inverse(X1),double_divide(X2,inverse(X2))),
inference(cp,[status(thm)],[t66,t639]) ).
cnf(t739,plain,
multiply(inverse(X1),double_divide(X2,inverse(X2))) = inverse(X1),
inference(orient,[status(thm)],[t668]) ).
cnf(t747,plain,
inverse(X1) = multiply(inverse(double_divide(X2,inverse(X2))),inverse(X1)),
inference(cp,[status(thm)],[t720,t739]) ).
cnf(t987,plain,
inverse(X1) = multiply(multiply(inverse(X2),X2),inverse(X1)),
inference(step,[status(thm)],[t747,t5]) ).
cnf(t777,plain,
multiply(multiply(inverse(X1),X1),inverse(X2)) = inverse(X2),
inference(orient,[status(thm)],[t987]) ).
cnf(t797,plain,
X1 = double_divide(double_divide(double_divide(inverse(X1),multiply(inverse(X2),X2)),inverse(X3)),inverse(X3)),
inference(cp,[status(thm)],[t114,t777]) ).
cnf(t8,plain,
double_divide(X1,X2) = double_divide(X3,multiply(Y3,multiply(multiply(X2,X1),double_divide(X3,Y3)))),
inference(cp,[status(thm)],[t7,t5]) ).
cnf(t14,plain,
double_divide(X1,multiply(X2,multiply(multiply(X3,Y3),double_divide(X1,X2)))) = double_divide(Y3,X3),
inference(orient,[status(thm)],[t8]) ).
cnf(t15,plain,
double_divide(multiply(inverse(X1),double_divide(double_divide(X2,X3),Y3)),Y3) = double_divide(X2,multiply(X3,inverse(X1))),
inference(cp,[status(thm)],[t14,t11]) ).
cnf(t27,plain,
double_divide(multiply(inverse(X1),double_divide(double_divide(X2,X3),Y3)),Y3) = double_divide(X2,multiply(X3,inverse(X1))),
inference(orient,[status(thm)],[t15]) ).
cnf(t61,plain,
double_divide(X1,multiply(X2,inverse(X3))) = double_divide(multiply(inverse(X3),Y3),multiply(multiply(X2,inverse(Y3)),X1)),
inference(cp,[status(thm)],[t27,t48]) ).
cnf(t164,plain,
double_divide(multiply(inverse(X1),X2),multiply(multiply(X3,inverse(X2)),Y3)) = double_divide(Y3,multiply(X3,inverse(X1))),
inference(orient,[status(thm)],[t61]) ).
cnf(t660,plain,
double_divide(X1,multiply(inverse(X1),inverse(X2))) = double_divide(multiply(inverse(X2),X3),inverse(X3)),
inference(cp,[status(thm)],[t164,t639]) ).
cnf(t984,plain,
X2 = double_divide(multiply(inverse(X2),X3),inverse(X3)),
inference(step,[status(thm)],[t660,t606]) ).
cnf(t674,plain,
double_divide(multiply(inverse(X1),X2),inverse(X2)) = X1,
inference(orient,[status(thm)],[t984]) ).
cnf(t748,plain,
X1 = double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))),
inference(cp,[status(thm)],[t674,t739]) ).
cnf(t986,plain,
X1 = double_divide(inverse(X1),multiply(inverse(X2),X2)),
inference(step,[status(thm)],[t748,t5]) ).
cnf(t754,plain,
double_divide(inverse(X1),multiply(inverse(X2),X2)) = X1,
inference(orient,[status(thm)],[t986]) ).
cnf(t988,plain,
X1 = double_divide(double_divide(X1,inverse(X3)),inverse(X3)),
inference(step,[status(thm)],[t797,t754]) ).
cnf(t804,plain,
double_divide(double_divide(X1,inverse(X2)),inverse(X2)) = X1,
inference(orient,[status(thm)],[t988]) ).
cnf(t814,plain,
multiply(inverse(X1),X2) = double_divide(X1,inverse(X2)),
inference(cp,[status(thm)],[t804,t674]) ).
cnf(t835,plain,
double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t814]) ).
cnf(t992,plain,
multiply(inverse(double_divide(X1,inverse(X1))),X2) = X2,
inference(step,[status(thm)],[t696,t835]) ).
cnf(t993,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(step,[status(thm)],[t992,t5]) ).
cnf(t870,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(rw,[status(thm)],[t993]) ).
cnf(t924,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t870]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a2 != a2,
inference(rw,[status(thm)],[goal_0,t924]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP586-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 15:08:58 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.46/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.46/1.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------