%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 01:27:35 PM UTC 2026
% Result : Unsatisfiable 3.34s 6.07s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 5
% Syntax : Number of clauses : 114 ( 114 unt; 0 nHn; 9 RR)
% Number of literals : 114 ( 113 equ; 2 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 163 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
inference(orient,[status(thm)],[t3]) ).
cnf(t0,axiom,
double_divide(X1,identity) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
double_divide(X1,identity) = inverse(X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t732,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),inverse(X2))),double_divide(identity,identity)) = X3,
inference(step,[status(thm)],[t4,t8]) ).
cnf(t733,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),inverse(X2))),inverse(identity)) = X3,
inference(step,[status(thm)],[t732,t8]) ).
cnf(t9,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),inverse(X2))),inverse(identity)) = X3,
inference(rw,[status(thm)],[t733]) ).
cnf(t70,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),inverse(X2))),inverse(identity)) = X3,
inference(orient,[status(thm)],[t9]) ).
cnf(t1,axiom,
double_divide(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
double_divide(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t1]) ).
cnf(t2,axiom,
double_divide(double_divide(X1,X2),identity) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t734,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(step,[status(thm)],[t2,t8]) ).
cnf(t11,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t734]) ).
cnf(t14,plain,
identity = double_divide(double_divide(X1,X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t10,t11]) ).
cnf(t35,plain,
double_divide(double_divide(X1,X2),multiply(X2,X1)) = identity,
inference(orient,[status(thm)],[t14]) ).
cnf(t71,plain,
multiply(X1,X2) = double_divide(double_divide(X1,double_divide(identity,inverse(X2))),inverse(identity)),
inference(cp,[status(thm)],[t70,t35]) ).
cnf(t91,plain,
double_divide(double_divide(X1,double_divide(identity,inverse(X2))),inverse(identity)) = multiply(X1,X2),
inference(orient,[status(thm)],[t71]) ).
cnf(t72,plain,
identity = double_divide(double_divide(X1,double_divide(inverse(double_divide(X2,X1)),inverse(X2))),inverse(identity)),
inference(cp,[status(thm)],[t70,t8]) ).
cnf(t736,plain,
identity = double_divide(double_divide(X1,double_divide(multiply(X1,X2),inverse(X2))),inverse(identity)),
inference(step,[status(thm)],[t72,t11]) ).
cnf(t166,plain,
double_divide(double_divide(X1,double_divide(multiply(X1,X2),inverse(X2))),inverse(identity)) = identity,
inference(orient,[status(thm)],[t736]) ).
cnf(t188,plain,
double_divide(multiply(double_divide(identity,X1),X2),inverse(X2)) = double_divide(double_divide(X1,identity),inverse(identity)),
inference(cp,[status(thm)],[t70,t166]) ).
cnf(t751,plain,
double_divide(multiply(double_divide(identity,X1),X2),inverse(X2)) = double_divide(inverse(X1),inverse(identity)),
inference(step,[status(thm)],[t188,t8]) ).
cnf(t92,plain,
multiply(X1,identity) = double_divide(double_divide(X1,identity),inverse(identity)),
inference(cp,[status(thm)],[t91,t10]) ).
cnf(t735,plain,
multiply(X1,identity) = double_divide(inverse(X1),inverse(identity)),
inference(step,[status(thm)],[t92,t8]) ).
cnf(t103,plain,
double_divide(inverse(X1),inverse(identity)) = multiply(X1,identity),
inference(orient,[status(thm)],[t735]) ).
cnf(t752,plain,
double_divide(multiply(double_divide(identity,X1),X2),inverse(X2)) = multiply(X1,identity),
inference(step,[status(thm)],[t751,t103]) ).
cnf(t280,plain,
double_divide(multiply(double_divide(identity,X1),X2),inverse(X2)) = multiply(X1,identity),
inference(orient,[status(thm)],[t752]) ).
cnf(t283,plain,
multiply(inverse(identity),identity) = double_divide(multiply(identity,X1),inverse(X1)),
inference(cp,[status(thm)],[t280,t10]) ).
cnf(t13,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(cp,[status(thm)],[t11,t10]) ).
cnf(t19,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(orient,[status(thm)],[t13]) ).
cnf(t753,plain,
inverse(identity) = double_divide(multiply(identity,X1),inverse(X1)),
inference(step,[status(thm)],[t283,t19]) ).
cnf(t295,plain,
double_divide(multiply(identity,X1),inverse(X1)) = inverse(identity),
inference(orient,[status(thm)],[t753]) ).
cnf(t306,plain,
multiply(inverse(X1),multiply(identity,X1)) = inverse(inverse(identity)),
inference(cp,[status(thm)],[t11,t295]) ).
cnf(t12,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t11,t8]) ).
cnf(t15,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t754,plain,
multiply(inverse(X1),multiply(identity,X1)) = multiply(identity,identity),
inference(step,[status(thm)],[t306,t15]) ).
cnf(t309,plain,
multiply(inverse(X1),multiply(identity,X1)) = multiply(identity,identity),
inference(orient,[status(thm)],[t754]) ).
cnf(t282,plain,
multiply(identity,identity) = double_divide(multiply(inverse(identity),X1),inverse(X1)),
inference(cp,[status(thm)],[t280,t8]) ).
cnf(t330,plain,
double_divide(multiply(inverse(identity),X1),inverse(X1)) = multiply(identity,identity),
inference(orient,[status(thm)],[t282]) ).
cnf(t334,plain,
multiply(identity,identity) = double_divide(multiply(identity,identity),inverse(multiply(identity,identity))),
inference(cp,[status(thm)],[t330,t309]) ).
cnf(t756,plain,
multiply(identity,identity) = identity,
inference(step,[status(thm)],[t334,t10]) ).
cnf(t346,plain,
multiply(identity,identity) = identity,
inference(orient,[status(thm)],[t756]) ).
cnf(t761,plain,
multiply(inverse(X1),multiply(identity,X1)) = identity,
inference(step,[status(thm)],[t309,t346]) ).
cnf(t351,plain,
multiply(inverse(X1),multiply(identity,X1)) = identity,
inference(orient,[status(thm)],[t761]) ).
cnf(t355,plain,
identity = multiply(inverse(identity),identity),
inference(cp,[status(thm)],[t351,t346]) ).
cnf(t770,plain,
identity = inverse(identity),
inference(step,[status(thm)],[t355,t19]) ).
cnf(t371,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t770]) ).
cnf(t804,plain,
double_divide(double_divide(X1,double_divide(identity,inverse(X2))),identity) = multiply(X1,X2),
inference(step,[status(thm)],[t91,t371]) ).
cnf(t805,plain,
inverse(double_divide(X1,double_divide(identity,inverse(X2)))) = multiply(X1,X2),
inference(step,[status(thm)],[t804,t8]) ).
cnf(t806,plain,
multiply(double_divide(identity,inverse(X2)),X1) = multiply(X1,X2),
inference(step,[status(thm)],[t805,t11]) ).
cnf(t401,plain,
multiply(double_divide(identity,inverse(X2)),X1) = multiply(X1,X2),
inference(rw,[status(thm)],[t806]) ).
cnf(t506,plain,
multiply(double_divide(identity,inverse(X1)),X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t401]) ).
cnf(t523,plain,
multiply(inverse(X1),identity) = double_divide(multiply(X2,X1),inverse(X2)),
inference(cp,[status(thm)],[t280,t506]) ).
cnf(t795,plain,
double_divide(inverse(X1),identity) = multiply(X1,identity),
inference(step,[status(thm)],[t103,t371]) ).
cnf(t796,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(step,[status(thm)],[t795,t8]) ).
cnf(t797,plain,
multiply(identity,X1) = multiply(X1,identity),
inference(step,[status(thm)],[t796,t15]) ).
cnf(t397,plain,
multiply(identity,X1) = multiply(X1,identity),
inference(rw,[status(thm)],[t797]) ).
cnf(t420,plain,
multiply(identity,X1) = multiply(X1,identity),
inference(orient,[status(thm)],[t397]) ).
cnf(t828,plain,
multiply(identity,inverse(X1)) = double_divide(multiply(X2,X1),inverse(X2)),
inference(step,[status(thm)],[t523,t420]) ).
cnf(t533,plain,
double_divide(multiply(X1,X2),inverse(X1)) = multiply(identity,inverse(X2)),
inference(orient,[status(thm)],[t828]) ).
cnf(t189,plain,
inverse(identity) = double_divide(double_divide(double_divide(multiply(X1,X2),inverse(X2)),double_divide(identity,inverse(X1))),inverse(identity)),
inference(cp,[status(thm)],[t70,t166]) ).
cnf(t737,plain,
inverse(identity) = multiply(double_divide(multiply(X1,X2),inverse(X2)),X1),
inference(step,[status(thm)],[t189,t91]) ).
cnf(t191,plain,
multiply(double_divide(multiply(X1,X2),inverse(X2)),X1) = inverse(identity),
inference(orient,[status(thm)],[t737]) ).
cnf(t785,plain,
multiply(double_divide(multiply(X1,X2),inverse(X2)),X1) = identity,
inference(step,[status(thm)],[t191,t371]) ).
cnf(t386,plain,
multiply(double_divide(multiply(X1,X2),inverse(X2)),X1) = identity,
inference(orient,[status(thm)],[t785]) ).
cnf(t393,plain,
identity = multiply(double_divide(multiply(X1,identity),identity),X1),
inference(cp,[status(thm)],[t386,t371]) ).
cnf(t818,plain,
identity = multiply(inverse(multiply(X1,identity)),X1),
inference(step,[status(thm)],[t393,t8]) ).
cnf(t110,plain,
multiply(inverse(identity),inverse(X1)) = inverse(multiply(X1,identity)),
inference(cp,[status(thm)],[t11,t103]) ).
cnf(t112,plain,
multiply(inverse(identity),inverse(X1)) = inverse(multiply(X1,identity)),
inference(orient,[status(thm)],[t110]) ).
cnf(t794,plain,
multiply(identity,inverse(X1)) = inverse(multiply(X1,identity)),
inference(step,[status(thm)],[t112,t371]) ).
cnf(t396,plain,
multiply(identity,inverse(X1)) = inverse(multiply(X1,identity)),
inference(rw,[status(thm)],[t794]) ).
cnf(t403,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t396]) ).
cnf(t819,plain,
identity = multiply(multiply(identity,inverse(X1)),X1),
inference(step,[status(thm)],[t818,t403]) ).
cnf(t471,plain,
multiply(multiply(identity,inverse(X1)),X1) = identity,
inference(orient,[status(thm)],[t819]) ).
cnf(t513,plain,
multiply(X1,inverse(X2)) = multiply(double_divide(identity,multiply(identity,X2)),X1),
inference(cp,[status(thm)],[t506,t15]) ).
cnf(t771,plain,
multiply(inverse(X1),X1) = identity,
inference(step,[status(thm)],[t19,t371]) ).
cnf(t372,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t771]) ).
cnf(t543,plain,
multiply(identity,inverse(X1)) = double_divide(identity,inverse(inverse(X1))),
inference(cp,[status(thm)],[t533,t372]) ).
cnf(t832,plain,
multiply(identity,inverse(X1)) = double_divide(identity,multiply(identity,X1)),
inference(step,[status(thm)],[t543,t15]) ).
cnf(t564,plain,
double_divide(identity,multiply(identity,X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t832]) ).
cnf(t843,plain,
multiply(X1,inverse(X2)) = multiply(multiply(identity,inverse(X2)),X1),
inference(step,[status(thm)],[t513,t564]) ).
cnf(t645,plain,
multiply(multiply(identity,inverse(X1)),X2) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t843]) ).
cnf(t844,plain,
multiply(X1,inverse(X1)) = identity,
inference(step,[status(thm)],[t471,t645]) ).
cnf(t658,plain,
multiply(X1,inverse(X1)) = identity,
inference(rw,[status(thm)],[t844]) ).
cnf(t659,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t658]) ).
cnf(t662,plain,
multiply(identity,inverse(inverse(X1))) = double_divide(identity,inverse(X1)),
inference(cp,[status(thm)],[t533,t659]) ).
cnf(t845,plain,
multiply(identity,multiply(identity,X1)) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t662,t15]) ).
cnf(t436,plain,
multiply(X1,identity) = double_divide(multiply(identity,double_divide(identity,X1)),inverse(identity)),
inference(cp,[status(thm)],[t280,t420]) ).
cnf(t453,plain,
multiply(identity,multiply(identity,X1)) = multiply(X1,identity),
inference(orient,[status(thm)],[t436]) ).
cnf(t846,plain,
multiply(X1,identity) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t845,t453]) ).
cnf(t664,plain,
double_divide(identity,inverse(X1)) = multiply(X1,identity),
inference(orient,[status(thm)],[t846]) ).
cnf(t848,plain,
multiply(multiply(X1,identity),X2) = multiply(X2,X1),
inference(step,[status(thm)],[t506,t664]) ).
cnf(t674,plain,
multiply(multiply(X1,identity),X2) = multiply(X2,X1),
inference(rw,[status(thm)],[t848]) ).
cnf(t675,plain,
multiply(multiply(X1,identity),X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t674]) ).
cnf(t682,plain,
multiply(X1,X2) = multiply(multiply(identity,X2),X1),
inference(cp,[status(thm)],[t675,t420]) ).
cnf(t693,plain,
multiply(multiply(identity,X1),X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t682]) ).
cnf(t392,plain,
multiply(X1,identity) = double_divide(multiply(double_divide(identity,X1),identity),identity),
inference(cp,[status(thm)],[t280,t371]) ).
cnf(t810,plain,
multiply(X1,identity) = inverse(multiply(double_divide(identity,X1),identity)),
inference(step,[status(thm)],[t392,t8]) ).
cnf(t114,plain,
inverse(multiply(double_divide(X1,X2),identity)) = multiply(inverse(identity),multiply(X2,X1)),
inference(cp,[status(thm)],[t112,t11]) ).
cnf(t129,plain,
inverse(multiply(double_divide(X1,X2),identity)) = multiply(inverse(identity),multiply(X2,X1)),
inference(orient,[status(thm)],[t114]) ).
cnf(t783,plain,
inverse(multiply(double_divide(X1,X2),identity)) = multiply(identity,multiply(X2,X1)),
inference(step,[status(thm)],[t129,t371]) ).
cnf(t384,plain,
inverse(multiply(double_divide(X1,X2),identity)) = multiply(identity,multiply(X2,X1)),
inference(orient,[status(thm)],[t783]) ).
cnf(t811,plain,
multiply(X1,identity) = multiply(identity,multiply(X1,identity)),
inference(step,[status(thm)],[t810,t384]) ).
cnf(t440,plain,
multiply(identity,multiply(X1,identity)) = multiply(X1,identity),
inference(orient,[status(thm)],[t811]) ).
cnf(t696,plain,
multiply(X1,multiply(X2,identity)) = multiply(multiply(X2,identity),X1),
inference(cp,[status(thm)],[t693,t440]) ).
cnf(t849,plain,
multiply(X1,multiply(X2,identity)) = multiply(X1,X2),
inference(step,[status(thm)],[t696,t675]) ).
cnf(t707,plain,
multiply(X1,multiply(X2,identity)) = multiply(X1,X2),
inference(orient,[status(thm)],[t849]) ).
cnf(t708,plain,
multiply(multiply(identity,X1),X2) = multiply(multiply(X2,identity),X1),
inference(cp,[status(thm)],[t707,t693]) ).
cnf(t851,plain,
multiply(X2,X1) = multiply(multiply(X2,identity),X1),
inference(step,[status(thm)],[t708,t693]) ).
cnf(t852,plain,
multiply(X2,X1) = multiply(X1,X2),
inference(step,[status(thm)],[t851,t675]) ).
cnf(t719,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t852]) ).
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,t719]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.61 % Computer : n008.cluster.edu
% 0.13/5.61 % Model : x86_64 x86_64
% 0.13/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.61 % Memory : 8046.5625MB
% 0.13/5.61 % OS : Linux 6.8.0-71-generic
% 0.13/5.61 % CPULimit : 300
% 0.13/5.61 % WCLimit : 300
% 0.13/5.61 % DateTime : Wed Sep 23 15:08:34 UTC 2026
% 0.13/5.61 % CPUTime :
% 0.13/5.61 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.34/6.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.34/6.07 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------