%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP559-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 01:27:32 PM UTC 2026
% Result : Unsatisfiable 4.29s 1.13s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 3
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 4 RR)
% Number of literals : 75 ( 74 equ; 3 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 : 177 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
divide(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t2,plain,
divide(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t0,axiom,
divide(X1,inverse(X2)) = multiply(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t0]) ).
cnf(t424,plain,
multiply(X1,divide(divide(X2,X3),divide(X1,X3))) = X2,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t6,plain,
multiply(X1,divide(divide(X2,X3),divide(X1,X3))) = X2,
inference(rw,[status(thm)],[t424]) ).
cnf(t7,plain,
multiply(X1,divide(divide(X2,X3),divide(X1,X3))) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t8,plain,
X1 = multiply(X2,divide(multiply(X1,X3),divide(X2,inverse(X3)))),
inference(cp,[status(thm)],[t7,t5]) ).
cnf(t425,plain,
X1 = multiply(X2,divide(multiply(X1,X3),multiply(X2,X3))),
inference(step,[status(thm)],[t8,t5]) ).
cnf(t10,plain,
multiply(X1,divide(multiply(X2,X3),multiply(X1,X3))) = X2,
inference(orient,[status(thm)],[t425]) ).
cnf(t11,plain,
X1 = multiply(X2,divide(X3,multiply(X2,divide(divide(X3,Y3),divide(X1,Y3))))),
inference(cp,[status(thm)],[t10,t7]) ).
cnf(t15,plain,
multiply(X1,divide(X2,multiply(X1,divide(divide(X2,X3),divide(Y3,X3))))) = Y3,
inference(orient,[status(thm)],[t11]) ).
cnf(t16,plain,
X1 = multiply(X1,divide(X2,X2)),
inference(cp,[status(thm)],[t15,t7]) ).
cnf(t21,plain,
multiply(X1,divide(X2,X2)) = X1,
inference(orient,[status(thm)],[t16]) ).
cnf(t23,plain,
X1 = multiply(X2,divide(X1,multiply(X2,divide(X3,X3)))),
inference(cp,[status(thm)],[t10,t21]) ).
cnf(t426,plain,
X1 = multiply(X2,divide(X1,X2)),
inference(step,[status(thm)],[t23,t21]) ).
cnf(t26,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t426]) ).
cnf(t27,plain,
X1 = multiply(inverse(X2),multiply(X1,X2)),
inference(cp,[status(thm)],[t26,t5]) ).
cnf(t34,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(orient,[status(thm)],[t27]) ).
cnf(t36,plain,
X1 = multiply(inverse(divide(X2,X1)),X2),
inference(cp,[status(thm)],[t34,t26]) ).
cnf(t48,plain,
multiply(inverse(divide(X1,X2)),X1) = X2,
inference(orient,[status(thm)],[t36]) ).
cnf(t53,plain,
inverse(divide(X1,X2)) = multiply(inverse(X1),X2),
inference(cp,[status(thm)],[t34,t48]) ).
cnf(t57,plain,
inverse(divide(X1,X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t53]) ).
cnf(t38,plain,
X1 = multiply(inverse(divide(X2,X2)),X1),
inference(cp,[status(thm)],[t34,t21]) ).
cnf(t428,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(step,[status(thm)],[t38,t57]) ).
cnf(t63,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t428]) ).
cnf(t69,plain,
divide(multiply(X1,X2),multiply(multiply(inverse(X3),X3),X2)) = X1,
inference(cp,[status(thm)],[t63,t10]) ).
cnf(t429,plain,
divide(multiply(X1,X2),X2) = X1,
inference(step,[status(thm)],[t69,t63]) ).
cnf(t76,plain,
divide(multiply(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t429]) ).
cnf(t79,plain,
X1 = divide(X2,divide(X2,X1)),
inference(cp,[status(thm)],[t76,t26]) ).
cnf(t92,plain,
divide(X1,divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t79]) ).
cnf(t96,plain,
X1 = multiply(divide(X1,X2),X2),
inference(cp,[status(thm)],[t26,t92]) ).
cnf(t124,plain,
multiply(divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t96]) ).
cnf(t128,plain,
divide(X1,X2) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t34,t124]) ).
cnf(t132,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(orient,[status(thm)],[t128]) ).
cnf(t430,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(step,[status(thm)],[t57,t132]) ).
cnf(t133,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(orient,[status(thm)],[t430]) ).
cnf(t94,plain,
X1 = divide(multiply(X2,X1),X2),
inference(cp,[status(thm)],[t92,t76]) ).
cnf(t110,plain,
divide(multiply(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t94]) ).
cnf(t117,plain,
divide(multiply(X1,X2),multiply(X3,X2)) = divide(X1,X3),
inference(cp,[status(thm)],[t110,t10]) ).
cnf(t297,plain,
divide(multiply(X1,X2),multiply(X3,X2)) = divide(X1,X3),
inference(orient,[status(thm)],[t117]) ).
cnf(t93,plain,
inverse(X1) = divide(X2,multiply(X2,X1)),
inference(cp,[status(thm)],[t92,t5]) ).
cnf(t152,plain,
divide(X1,multiply(X1,X2)) = inverse(X2),
inference(orient,[status(thm)],[t93]) ).
cnf(t160,plain,
divide(multiply(X1,X2),X1) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t133,t152]) ).
cnf(t433,plain,
X2 = inverse(inverse(X2)),
inference(step,[status(thm)],[t160,t110]) ).
cnf(t167,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t433]) ).
cnf(t168,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(cp,[status(thm)],[t5,t167]) ).
cnf(t170,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(orient,[status(thm)],[t168]) ).
cnf(t300,plain,
divide(X1,X2) = divide(divide(X1,X3),multiply(X2,inverse(X3))),
inference(cp,[status(thm)],[t297,t170]) ).
cnf(t438,plain,
divide(X1,X2) = divide(divide(X1,X3),divide(X2,X3)),
inference(step,[status(thm)],[t300,t170]) ).
cnf(t139,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X3,X2),X1),
inference(cp,[status(thm)],[t132,t133]) ).
cnf(t247,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X3,X2),X1),
inference(orient,[status(thm)],[t139]) ).
cnf(t439,plain,
divide(X1,X2) = multiply(divide(X3,X2),divide(X1,X3)),
inference(step,[status(thm)],[t438,t247]) ).
cnf(t313,plain,
multiply(divide(X1,X2),divide(X3,X1)) = divide(X3,X2),
inference(orient,[status(thm)],[t439]) ).
cnf(t317,plain,
divide(X1,multiply(X2,X3)) = multiply(inverse(X3),divide(X1,X2)),
inference(cp,[status(thm)],[t313,t152]) ).
cnf(t440,plain,
divide(X1,multiply(X2,X3)) = divide(divide(X1,X2),X3),
inference(step,[status(thm)],[t317,t132]) ).
cnf(t337,plain,
divide(divide(X1,X2),X3) = divide(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t440]) ).
cnf(t355,plain,
divide(X1,divide(X2,X3)) = inverse(divide(X2,multiply(X3,X1))),
inference(cp,[status(thm)],[t133,t337]) ).
cnf(t442,plain,
multiply(divide(X3,X2),X1) = inverse(divide(X2,multiply(X3,X1))),
inference(step,[status(thm)],[t355,t247]) ).
cnf(t443,plain,
multiply(divide(X3,X2),X1) = divide(multiply(X3,X1),X2),
inference(step,[status(thm)],[t442,t133]) ).
cnf(t329,plain,
divide(multiply(X1,X2),X3) = multiply(divide(X2,X3),X1),
inference(cp,[status(thm)],[t313,t76]) ).
cnf(t357,plain,
divide(multiply(X1,X2),X3) = multiply(divide(X2,X3),X1),
inference(orient,[status(thm)],[t329]) ).
cnf(t444,plain,
multiply(divide(X3,X2),X1) = multiply(divide(X1,X2),X3),
inference(step,[status(thm)],[t443,t357]) ).
cnf(t377,plain,
multiply(divide(X1,X2),X3) = multiply(divide(X3,X2),X1),
inference(orient,[status(thm)],[t444]) ).
cnf(t87,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(cp,[status(thm)],[t26,t76]) ).
cnf(t212,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t87]) ).
cnf(t380,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(cp,[status(thm)],[t377,t212]) ).
cnf(t393,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t380]) ).
cnf(t403,plain,
multiply(X1,divide(X2,inverse(X3))) = multiply(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t393,t5]) ).
cnf(t453,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X3),X2),
inference(step,[status(thm)],[t403,t5]) ).
cnf(t413,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t453]) ).
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(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[goal_0,t413]) ).
cnf(g0_1,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(c3,b3)),
inference(rw,[status(thm)],[g0_0,t212]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP559-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Wed Sep 23 14:59:45 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.29/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.29/1.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------