%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP594-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:27:37 PM UTC 2026
% Result : Unsatisfiable 5.24s 1.14s
% Output : CNFRefutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 3
% Syntax : Number of clauses : 71 ( 71 unt; 0 nHn; 4 RR)
% Number of literals : 71 ( 70 equ; 3 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 : 168 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t2,plain,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = 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(t625,plain,
multiply(inverse(double_divide(X1,inverse(double_divide(X3,X2)))),double_divide(X1,X2)) = X3,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t626,plain,
multiply(multiply(inverse(double_divide(X3,X2)),X1),double_divide(X1,X2)) = X3,
inference(step,[status(thm)],[t625,t5]) ).
cnf(t627,plain,
multiply(multiply(multiply(X2,X3),X1),double_divide(X1,X2)) = X3,
inference(step,[status(thm)],[t626,t5]) ).
cnf(t6,plain,
multiply(multiply(multiply(X2,X3),X1),double_divide(X1,X2)) = X3,
inference(rw,[status(thm)],[t627]) ).
cnf(t7,plain,
multiply(multiply(multiply(X1,X2),X3),double_divide(X3,X1)) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t9,plain,
double_divide(X1,X2) = multiply(multiply(X3,Y3),double_divide(Y3,multiply(multiply(X2,X3),X1))),
inference(cp,[status(thm)],[t7,t7]) ).
cnf(t15,plain,
multiply(multiply(X1,X2),double_divide(X2,multiply(multiply(X3,X1),Y3))) = double_divide(Y3,X3),
inference(orient,[status(thm)],[t9]) ).
cnf(t8,plain,
X1 = multiply(X2,double_divide(double_divide(X1,X3),multiply(X3,X2))),
inference(cp,[status(thm)],[t7,t7]) ).
cnf(t10,plain,
multiply(X1,double_divide(double_divide(X2,X3),multiply(X3,X1))) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t16,plain,
double_divide(multiply(X1,double_divide(X2,multiply(X3,X1))),X3) = X2,
inference(cp,[status(thm)],[t15,t10]) ).
cnf(t29,plain,
double_divide(multiply(X1,double_divide(X2,multiply(X3,X1))),X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t30,plain,
X1 = double_divide(double_divide(multiply(X2,X1),X3),multiply(X3,X2)),
inference(cp,[status(thm)],[t29,t15]) ).
cnf(t39,plain,
double_divide(double_divide(multiply(X1,X2),X3),multiply(X3,X1)) = X2,
inference(orient,[status(thm)],[t30]) ).
cnf(t46,plain,
multiply(multiply(X1,X2),double_divide(multiply(X2,X3),X1)) = inverse(X3),
inference(cp,[status(thm)],[t5,t39]) ).
cnf(t66,plain,
multiply(multiply(X1,X2),double_divide(multiply(X2,X3),X1)) = inverse(X3),
inference(orient,[status(thm)],[t46]) ).
cnf(t75,plain,
X1 = multiply(inverse(X2),double_divide(double_divide(multiply(X1,X2),X3),X3)),
inference(cp,[status(thm)],[t7,t66]) ).
cnf(t87,plain,
multiply(inverse(X1),double_divide(double_divide(multiply(X2,X1),X3),X3)) = X2,
inference(orient,[status(thm)],[t75]) ).
cnf(t105,plain,
double_divide(multiply(X1,X2),multiply(X3,inverse(X2))) = double_divide(X1,X3),
inference(cp,[status(thm)],[t29,t87]) ).
cnf(t128,plain,
double_divide(multiply(X1,X2),multiply(X3,inverse(X2))) = double_divide(X1,X3),
inference(orient,[status(thm)],[t105]) ).
cnf(t142,plain,
multiply(X1,X2) = double_divide(multiply(inverse(X2),double_divide(X1,X3)),X3),
inference(cp,[status(thm)],[t29,t128]) ).
cnf(t143,plain,
double_divide(multiply(inverse(X1),double_divide(X2,X3)),X3) = multiply(X2,X1),
inference(orient,[status(thm)],[t142]) ).
cnf(t34,plain,
multiply(X1,multiply(X2,double_divide(X3,multiply(X1,X2)))) = inverse(X3),
inference(cp,[status(thm)],[t5,t29]) ).
cnf(t50,plain,
multiply(X1,multiply(X2,double_divide(X3,multiply(X1,X2)))) = inverse(X3),
inference(orient,[status(thm)],[t34]) ).
cnf(t144,plain,
multiply(double_divide(multiply(X1,X2),X3),X2) = double_divide(X1,X3),
inference(cp,[status(thm)],[t143,t87]) ).
cnf(t175,plain,
multiply(double_divide(multiply(X1,X2),X3),X2) = double_divide(X1,X3),
inference(orient,[status(thm)],[t144]) ).
cnf(t176,plain,
double_divide(X1,X2) = multiply(X3,double_divide(X3,multiply(X2,X1))),
inference(cp,[status(thm)],[t175,t29]) ).
cnf(t201,plain,
multiply(X1,double_divide(X1,multiply(X2,X3))) = double_divide(X3,X2),
inference(orient,[status(thm)],[t176]) ).
cnf(t229,plain,
inverse(X1) = multiply(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t50,t201]) ).
cnf(t264,plain,
multiply(X1,double_divide(X2,X1)) = inverse(X2),
inference(orient,[status(thm)],[t229]) ).
cnf(t272,plain,
multiply(X1,X2) = double_divide(inverse(X1),inverse(X2)),
inference(cp,[status(thm)],[t143,t264]) ).
cnf(t284,plain,
double_divide(inverse(X1),inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t272]) ).
cnf(t203,plain,
double_divide(X1,X2) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t201,t66]) ).
cnf(t233,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t203]) ).
cnf(t236,plain,
double_divide(multiply(X1,double_divide(X2,multiply(X3,X1))),X3) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t233,t50]) ).
cnf(t630,plain,
X2 = inverse(inverse(X2)),
inference(step,[status(thm)],[t236,t29]) ).
cnf(t246,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t630]) ).
cnf(t285,plain,
multiply(inverse(X1),X2) = double_divide(X1,inverse(X2)),
inference(cp,[status(thm)],[t284,t246]) ).
cnf(t297,plain,
double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t285]) ).
cnf(t301,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(cp,[status(thm)],[t297,t246]) ).
cnf(t312,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(orient,[status(thm)],[t301]) ).
cnf(t326,plain,
inverse(X1) = double_divide(double_divide(double_divide(X2,X1),X3),multiply(X3,inverse(X2))),
inference(cp,[status(thm)],[t39,t312]) ).
cnf(t145,plain,
multiply(double_divide(X1,X2),X3) = double_divide(X1,multiply(X2,inverse(X3))),
inference(cp,[status(thm)],[t143,t10]) ).
cnf(t157,plain,
double_divide(X1,multiply(X2,inverse(X3))) = multiply(double_divide(X1,X2),X3),
inference(orient,[status(thm)],[t145]) ).
cnf(t632,plain,
inverse(X1) = multiply(double_divide(double_divide(double_divide(X2,X1),X3),X3),X2),
inference(step,[status(thm)],[t326,t157]) ).
cnf(t202,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(cp,[status(thm)],[t201,t10]) ).
cnf(t251,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t202]) ).
cnf(t633,plain,
inverse(X1) = multiply(double_divide(X2,X1),X2),
inference(step,[status(thm)],[t632,t251]) ).
cnf(t346,plain,
multiply(double_divide(X1,X2),X1) = inverse(X2),
inference(orient,[status(thm)],[t633]) ).
cnf(t354,plain,
double_divide(X1,double_divide(X1,X2)) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t233,t346]) ).
cnf(t634,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(step,[status(thm)],[t354,t246]) ).
cnf(t370,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t634]) ).
cnf(t380,plain,
X1 = double_divide(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t251,t370]) ).
cnf(t409,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t380]) ).
cnf(t419,plain,
inverse(double_divide(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t346,t409]) ).
cnf(t635,plain,
multiply(X2,X1) = multiply(X1,X2),
inference(step,[status(thm)],[t419,t5]) ).
cnf(t490,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t635]) ).
cnf(t373,plain,
inverse(X1) = double_divide(X2,multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t370,t297]) ).
cnf(t584,plain,
double_divide(X1,multiply(inverse(X1),X2)) = inverse(X2),
inference(orient,[status(thm)],[t373]) ).
cnf(t585,plain,
inverse(inverse(X1)) = multiply(double_divide(X2,inverse(X2)),X1),
inference(cp,[status(thm)],[t584,t157]) ).
cnf(t638,plain,
X1 = multiply(double_divide(X2,inverse(X2)),X1),
inference(step,[status(thm)],[t585,t246]) ).
cnf(t639,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(step,[status(thm)],[t638,t297]) ).
cnf(t640,plain,
X1 = multiply(multiply(X2,inverse(X2)),X1),
inference(step,[status(thm)],[t639,t490]) ).
cnf(t601,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(orient,[status(thm)],[t640]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(multiply(inverse(b2),b2),a2) != multiply(multiply(b2,inverse(b2)),a2),
inference(rw,[status(thm)],[goal_0,t490]) ).
cnf(g0_1,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(rw,[status(thm)],[g0_0,t601]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP594-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n026.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 15:12:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.24/1.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.24/1.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------