%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP504-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 01:27:12 PM UTC 2026
% Result : Unsatisfiable 3.66s 0.92s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 3
% Syntax : Number of clauses : 76 ( 76 unt; 0 nHn; 3 RR)
% Number of literals : 76 ( 75 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 327 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t2,plain,
double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
inference(orient,[status(thm)],[t1]) ).
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(t6175,plain,
double_divide(double_divide(X1,multiply(X3,X2)),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t6176,plain,
double_divide(double_divide(X1,multiply(X3,X2)),double_divide(inverse(X2),multiply(double_divide(X1,X4),X4))) = X3,
inference(step,[status(thm)],[t6175,t5]) ).
cnf(t6,plain,
double_divide(double_divide(X1,multiply(X3,X2)),double_divide(inverse(X2),multiply(double_divide(X1,X4),X4))) = X3,
inference(rw,[status(thm)],[t6176]) ).
cnf(t7,plain,
double_divide(double_divide(X1,multiply(X2,X3)),double_divide(inverse(X3),multiply(double_divide(X1,X4),X4))) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t9,plain,
multiply(double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)),double_divide(X2,multiply(X4,X1))) = inverse(X4),
inference(cp,[status(thm)],[t5,t7]) ).
cnf(t11,plain,
multiply(double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)),double_divide(X2,multiply(X4,X1))) = inverse(X4),
inference(orient,[status(thm)],[t9]) ).
cnf(t14,plain,
double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)) = double_divide(double_divide(X4,inverse(Y4)),double_divide(inverse(double_divide(X2,multiply(Y4,X1))),multiply(double_divide(X4,Y5),Y5))),
inference(cp,[status(thm)],[t7,t11]) ).
cnf(t6177,plain,
double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)) = double_divide(double_divide(X4,inverse(Y4)),double_divide(multiply(multiply(Y4,X1),X2),multiply(double_divide(X4,Y5),Y5))),
inference(step,[status(thm)],[t14,t5]) ).
cnf(t71,plain,
double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)) = double_divide(double_divide(X4,inverse(Y4)),double_divide(multiply(multiply(Y4,X1),X2),multiply(double_divide(X4,Y5),Y5))),
inference(orient,[status(thm)],[t6177]) ).
cnf(t118,plain,
double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)) = double_divide(inverse(X1),multiply(double_divide(X2,X4),X4)),
inference(cp,[status(thm)],[t71,t71]) ).
cnf(t119,plain,
double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)) = double_divide(inverse(X1),multiply(double_divide(X2,X4),X4)),
inference(orient,[status(thm)],[t118]) ).
cnf(t127,plain,
multiply(multiply(double_divide(X1,X2),X2),inverse(X3)) = inverse(double_divide(inverse(X3),multiply(double_divide(X1,X4),X4))),
inference(cp,[status(thm)],[t5,t119]) ).
cnf(t6178,plain,
multiply(multiply(double_divide(X1,X2),X2),inverse(X3)) = multiply(multiply(double_divide(X1,X4),X4),inverse(X3)),
inference(step,[status(thm)],[t127,t5]) ).
cnf(t148,plain,
multiply(multiply(double_divide(X1,X2),X2),inverse(X3)) = multiply(multiply(double_divide(X1,X4),X4),inverse(X3)),
inference(orient,[status(thm)],[t6178]) ).
cnf(t156,plain,
multiply(double_divide(X1,X2),X2) = double_divide(double_divide(X3,multiply(multiply(double_divide(X1,X4),X4),inverse(Y4))),double_divide(inverse(inverse(Y4)),multiply(double_divide(X3,Y5),Y5))),
inference(cp,[status(thm)],[t7,t148]) ).
cnf(t6179,plain,
multiply(double_divide(X1,X2),X2) = multiply(double_divide(X1,X4),X4),
inference(step,[status(thm)],[t156,t7]) ).
cnf(t167,plain,
multiply(double_divide(X1,X2),X2) = multiply(double_divide(X1,X3),X3),
inference(orient,[status(thm)],[t6179]) ).
cnf(t169,plain,
multiply(double_divide(double_divide(X1,multiply(X2,X3)),X4),X4) = multiply(X2,double_divide(inverse(X3),multiply(double_divide(X1,Y4),Y4))),
inference(cp,[status(thm)],[t167,t7]) ).
cnf(t253,plain,
multiply(double_divide(double_divide(X1,multiply(X2,X3)),X4),X4) = multiply(X2,double_divide(inverse(X3),multiply(double_divide(X1,Y4),Y4))),
inference(orient,[status(thm)],[t169]) ).
cnf(t179,plain,
inverse(double_divide(X1,X2)) = multiply(double_divide(inverse(X2),multiply(double_divide(X3,X4),X4)),double_divide(X3,multiply(double_divide(X1,Y4),Y4))),
inference(cp,[status(thm)],[t11,t167]) ).
cnf(t6180,plain,
multiply(X2,X1) = multiply(double_divide(inverse(X2),multiply(double_divide(X3,X4),X4)),double_divide(X3,multiply(double_divide(X1,Y4),Y4))),
inference(step,[status(thm)],[t179,t5]) ).
cnf(t224,plain,
multiply(double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)),double_divide(X2,multiply(double_divide(X4,Y4),Y4))) = multiply(X1,X4),
inference(orient,[status(thm)],[t6180]) ).
cnf(t289,plain,
multiply(double_divide(double_divide(X1,multiply(double_divide(inverse(X2),multiply(double_divide(inverse(X3),X4),X4)),X3)),Y4),Y4) = multiply(X2,X1),
inference(cp,[status(thm)],[t253,t224]) ).
cnf(t391,plain,
multiply(double_divide(double_divide(X1,multiply(double_divide(inverse(X2),multiply(double_divide(inverse(X3),X4),X4)),X3)),Y4),Y4) = multiply(X2,X1),
inference(orient,[status(thm)],[t289]) ).
cnf(t12,plain,
inverse(X1) = multiply(double_divide(multiply(X2,X3),multiply(double_divide(X4,Y4),Y4)),double_divide(X4,multiply(X1,double_divide(X3,X2)))),
inference(cp,[status(thm)],[t11,t5]) ).
cnf(t24,plain,
multiply(double_divide(multiply(X1,X2),multiply(double_divide(X3,X4),X4)),double_divide(X3,multiply(Y4,double_divide(X2,X1)))) = inverse(Y4),
inference(orient,[status(thm)],[t12]) ).
cnf(t312,plain,
multiply(X1,X2) = multiply(double_divide(inverse(X1),multiply(double_divide(X3,X4),X4)),double_divide(X3,multiply(double_divide(double_divide(Y4,multiply(double_divide(X2,double_divide(inverse(Y5),multiply(double_divide(Y4,Y6),Y6))),Y5)),Y7),Y7))),
inference(cp,[status(thm)],[t224,t253]) ).
cnf(t6181,plain,
multiply(X1,X2) = multiply(X1,double_divide(Y4,multiply(double_divide(X2,double_divide(inverse(Y5),multiply(double_divide(Y4,Y6),Y6))),Y5))),
inference(step,[status(thm)],[t312,t224]) ).
cnf(t325,plain,
multiply(X1,double_divide(X2,multiply(double_divide(X3,double_divide(inverse(X4),multiply(double_divide(X2,Y4),Y4))),X4))) = multiply(X1,X3),
inference(orient,[status(thm)],[t6181]) ).
cnf(t176,plain,
inverse(double_divide(X1,double_divide(X2,X3))) = multiply(double_divide(multiply(X3,X2),multiply(double_divide(X4,Y4),Y4)),double_divide(X4,multiply(double_divide(X1,Y5),Y5))),
inference(cp,[status(thm)],[t24,t167]) ).
cnf(t6183,plain,
multiply(double_divide(X2,X3),X1) = multiply(double_divide(multiply(X3,X2),multiply(double_divide(X4,Y4),Y4)),double_divide(X4,multiply(double_divide(X1,Y5),Y5))),
inference(step,[status(thm)],[t176,t5]) ).
cnf(t422,plain,
multiply(double_divide(multiply(X1,X2),multiply(double_divide(X3,X4),X4)),double_divide(X3,multiply(double_divide(Y4,Y5),Y5))) = multiply(double_divide(X2,X1),Y4),
inference(orient,[status(thm)],[t6183]) ).
cnf(t427,plain,
multiply(double_divide(X1,double_divide(X2,X1)),X3) = multiply(double_divide(multiply(double_divide(X2,X4),X4),multiply(double_divide(Y4,Y5),Y5)),double_divide(Y4,multiply(double_divide(X3,Y6),Y6))),
inference(cp,[status(thm)],[t422,t167]) ).
cnf(t6184,plain,
multiply(double_divide(X1,double_divide(X2,X1)),X3) = multiply(double_divide(X4,double_divide(X2,X4)),X3),
inference(step,[status(thm)],[t427,t422]) ).
cnf(t457,plain,
multiply(double_divide(X1,double_divide(X2,X1)),X3) = multiply(double_divide(X4,double_divide(X2,X4)),X3),
inference(orient,[status(thm)],[t6184]) ).
cnf(t460,plain,
multiply(double_divide(X1,double_divide(X2,X1)),double_divide(X2,X3)) = multiply(double_divide(X3,X4),X4),
inference(cp,[status(thm)],[t457,t167]) ).
cnf(t540,plain,
multiply(double_divide(X1,double_divide(X2,X1)),double_divide(X2,X3)) = multiply(double_divide(X3,X4),X4),
inference(orient,[status(thm)],[t460]) ).
cnf(t471,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(X3,multiply(double_divide(X4,double_divide(X2,X4)),Y4)),double_divide(inverse(Y4),multiply(double_divide(X3,Y5),Y5))),
inference(cp,[status(thm)],[t7,t457]) ).
cnf(t6185,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X4,double_divide(X2,X4)),
inference(step,[status(thm)],[t471,t7]) ).
cnf(t501,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(orient,[status(thm)],[t6185]) ).
cnf(t560,plain,
multiply(double_divide(double_divide(X1,X2),X3),X3) = multiply(double_divide(X4,double_divide(X2,X4)),double_divide(Y4,double_divide(X1,Y4))),
inference(cp,[status(thm)],[t540,t501]) ).
cnf(t727,plain,
multiply(double_divide(double_divide(X1,X2),X3),X3) = multiply(double_divide(X4,double_divide(X2,X4)),double_divide(Y4,double_divide(X1,Y4))),
inference(orient,[status(thm)],[t560]) ).
cnf(t829,plain,
multiply(X1,multiply(double_divide(X2,X3),X3)) = multiply(X1,double_divide(X2,multiply(double_divide(double_divide(X4,inverse(double_divide(Y4,double_divide(X4,Y4)))),Y5),Y5))),
inference(cp,[status(thm)],[t325,t727]) ).
cnf(t6189,plain,
multiply(X1,multiply(double_divide(X2,X3),X3)) = multiply(X1,double_divide(X2,multiply(double_divide(double_divide(X4,multiply(double_divide(X4,Y4),Y4)),Y5),Y5))),
inference(step,[status(thm)],[t829,t5]) ).
cnf(t4447,plain,
multiply(X1,multiply(double_divide(X2,X3),X3)) = multiply(X1,double_divide(X2,multiply(double_divide(double_divide(X4,multiply(double_divide(X4,Y4),Y4)),Y5),Y5))),
inference(orient,[status(thm)],[t6189]) ).
cnf(t171,plain,
multiply(double_divide(inverse(X1),X2),X2) = multiply(double_divide(inverse(X1),multiply(double_divide(X3,X4),X4)),multiply(double_divide(X3,Y4),Y4)),
inference(cp,[status(thm)],[t167,t119]) ).
cnf(t1674,plain,
multiply(double_divide(inverse(X1),X2),X2) = multiply(double_divide(inverse(X1),multiply(double_divide(X3,X4),X4)),multiply(double_divide(X3,Y4),Y4)),
inference(orient,[status(thm)],[t171]) ).
cnf(t4453,plain,
multiply(double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)),double_divide(X2,multiply(double_divide(double_divide(X4,multiply(double_divide(X4,Y4),Y4)),Y5),Y5))) = multiply(double_divide(inverse(X1),Y6),Y6),
inference(cp,[status(thm)],[t4447,t1674]) ).
cnf(t6190,plain,
multiply(X1,double_divide(X4,multiply(double_divide(X4,Y4),Y4))) = multiply(double_divide(inverse(X1),Y6),Y6),
inference(step,[status(thm)],[t4453,t224]) ).
cnf(t4761,plain,
multiply(X1,double_divide(X2,multiply(double_divide(X2,X3),X3))) = multiply(double_divide(inverse(X1),X4),X4),
inference(orient,[status(thm)],[t6190]) ).
cnf(t4851,plain,
inverse(X1) = multiply(double_divide(multiply(multiply(double_divide(X2,X3),X3),X2),multiply(double_divide(X4,Y4),Y4)),double_divide(X4,multiply(double_divide(inverse(X1),Y5),Y5))),
inference(cp,[status(thm)],[t24,t4761]) ).
cnf(t6194,plain,
inverse(X1) = multiply(double_divide(X2,multiply(double_divide(X2,X3),X3)),inverse(X1)),
inference(step,[status(thm)],[t4851,t422]) ).
cnf(t5592,plain,
multiply(double_divide(X1,multiply(double_divide(X1,X2),X2)),inverse(X3)) = inverse(X3),
inference(orient,[status(thm)],[t6194]) ).
cnf(t5647,plain,
multiply(inverse(X1),X2) = multiply(double_divide(double_divide(X2,inverse(X1)),X3),X3),
inference(cp,[status(thm)],[t391,t5592]) ).
cnf(t5655,plain,
multiply(double_divide(double_divide(X1,inverse(X2)),X3),X3) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t5647]) ).
cnf(t5683,plain,
multiply(inverse(double_divide(X1,X2)),X3) = multiply(double_divide(double_divide(X3,multiply(X2,X1)),X4),X4),
inference(cp,[status(thm)],[t5655,t5]) ).
cnf(t6207,plain,
multiply(multiply(X2,X1),X3) = multiply(double_divide(double_divide(X3,multiply(X2,X1)),X4),X4),
inference(step,[status(thm)],[t5683,t5]) ).
cnf(t4837,plain,
X1 = double_divide(double_divide(X2,multiply(double_divide(inverse(X1),X3),X3)),double_divide(inverse(double_divide(X4,multiply(double_divide(X4,Y4),Y4))),multiply(double_divide(X2,Y5),Y5))),
inference(cp,[status(thm)],[t7,t4761]) ).
cnf(t174,plain,
double_divide(X1,X2) = double_divide(double_divide(X3,multiply(double_divide(X1,X4),X4)),double_divide(inverse(X2),multiply(double_divide(X3,Y4),Y4))),
inference(cp,[status(thm)],[t7,t167]) ).
cnf(t192,plain,
double_divide(double_divide(X1,multiply(double_divide(X2,X3),X3)),double_divide(inverse(X4),multiply(double_divide(X1,Y4),Y4))) = double_divide(X2,X4),
inference(orient,[status(thm)],[t174]) ).
cnf(t6191,plain,
X1 = double_divide(inverse(X1),double_divide(X4,multiply(double_divide(X4,Y4),Y4))),
inference(step,[status(thm)],[t4837,t192]) ).
cnf(t5005,plain,
double_divide(inverse(X1),double_divide(X2,multiply(double_divide(X2,X3),X3))) = X1,
inference(orient,[status(thm)],[t6191]) ).
cnf(t5076,plain,
multiply(X1,inverse(X2)) = multiply(X1,double_divide(inverse(X3),multiply(X2,X3))),
inference(cp,[status(thm)],[t325,t5005]) ).
cnf(t5132,plain,
multiply(X1,double_divide(inverse(X2),multiply(X3,X2))) = multiply(X1,inverse(X3)),
inference(orient,[status(thm)],[t5076]) ).
cnf(t5142,plain,
multiply(X1,inverse(double_divide(X2,X3))) = multiply(double_divide(double_divide(X2,multiply(X1,X3)),X4),X4),
inference(cp,[status(thm)],[t5132,t253]) ).
cnf(t6195,plain,
multiply(X1,multiply(X3,X2)) = multiply(double_divide(double_divide(X2,multiply(X1,X3)),X4),X4),
inference(step,[status(thm)],[t5142,t5]) ).
cnf(t5867,plain,
multiply(double_divide(double_divide(X1,multiply(X2,X3)),X4),X4) = multiply(X2,multiply(X3,X1)),
inference(orient,[status(thm)],[t6195]) ).
cnf(t6208,plain,
multiply(multiply(X2,X1),X3) = multiply(X2,multiply(X1,X3)),
inference(step,[status(thm)],[t6207,t5867]) ).
cnf(t6129,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t6208]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[goal_0,t6129]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP504-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:59:09 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.66/0.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/0.92 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------