%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 5.34s 1.12s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 9
% Syntax : Number of clauses : 105 ( 105 unt; 0 nHn; 60 RR)
% Number of literals : 105 ( 104 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
sF0 = inverse(b1),
introduced(definition) ).
cnf(t7,plain,
inverse(b1) = sF0,
inference(orient,[status(thm)],[t1]) ).
cnf(t2,axiom,
sF1 = double_divide(b1,inverse(b1)),
introduced(definition) ).
cnf(t940,plain,
sF1 = double_divide(b1,sF0),
inference(step,[status(thm)],[t2,t7]) ).
cnf(t9,plain,
double_divide(b1,sF0) = sF1,
inference(orient,[status(thm)],[t940]) ).
cnf(t4,axiom,
sF3 = inverse(a1),
introduced(definition) ).
cnf(t8,plain,
inverse(a1) = sF3,
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
sF4 = double_divide(a1,inverse(a1)),
introduced(definition) ).
cnf(t941,plain,
sF4 = double_divide(a1,sF3),
inference(step,[status(thm)],[t5,t8]) ).
cnf(t10,plain,
double_divide(a1,sF3) = sF4,
inference(orient,[status(thm)],[t941]) ).
cnf(t0,axiom,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X3))),X2))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t13,plain,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X3))),X2))) = X3,
inference(orient,[status(thm)],[t0]) ).
cnf(t6,axiom,
sF5 = inverse(double_divide(a1,inverse(a1))),
introduced(definition) ).
cnf(t944,plain,
sF5 = inverse(double_divide(a1,sF3)),
inference(step,[status(thm)],[t6,t8]) ).
cnf(t945,plain,
sF5 = inverse(sF4),
inference(step,[status(thm)],[t944,t10]) ).
cnf(t12,plain,
inverse(sF4) = sF5,
inference(orient,[status(thm)],[t945]) ).
cnf(t19,plain,
sF4 = double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF5)),X2))),
inference(cp,[status(thm)],[t13,t12]) ).
cnf(t337,plain,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF5)),X2))) = sF4,
inference(orient,[status(thm)],[t19]) ).
cnf(t16,plain,
X1 = double_divide(b1,inverse(double_divide(inverse(double_divide(sF1,inverse(X1))),sF0))),
inference(cp,[status(thm)],[t13,t9]) ).
cnf(t22,plain,
double_divide(b1,inverse(double_divide(inverse(double_divide(sF1,inverse(X1))),sF0))) = X1,
inference(orient,[status(thm)],[t16]) ).
cnf(t28,plain,
X1 = double_divide(b1,inverse(double_divide(inverse(double_divide(X2,inverse(X1))),inverse(double_divide(inverse(double_divide(sF1,inverse(X2))),sF0))))),
inference(cp,[status(thm)],[t13,t22]) ).
cnf(t833,plain,
double_divide(b1,inverse(double_divide(inverse(double_divide(X1,inverse(X2))),inverse(double_divide(inverse(double_divide(sF1,inverse(X1))),sF0))))) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t17,plain,
X1 = double_divide(a1,inverse(double_divide(inverse(double_divide(sF4,inverse(X1))),sF3))),
inference(cp,[status(thm)],[t13,t10]) ).
cnf(t129,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(sF4,inverse(X1))),sF3))) = X1,
inference(orient,[status(thm)],[t17]) ).
cnf(t3,axiom,
sF2 = inverse(double_divide(b1,inverse(b1))),
introduced(definition) ).
cnf(t942,plain,
sF2 = inverse(double_divide(b1,sF0)),
inference(step,[status(thm)],[t3,t7]) ).
cnf(t943,plain,
sF2 = inverse(sF1),
inference(step,[status(thm)],[t942,t9]) ).
cnf(t11,plain,
inverse(sF1) = sF2,
inference(orient,[status(thm)],[t943]) ).
cnf(t130,plain,
sF1 = double_divide(a1,inverse(double_divide(inverse(double_divide(sF4,sF2)),sF3))),
inference(cp,[status(thm)],[t129,t11]) ).
cnf(t154,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(sF4,sF2)),sF3))) = sF1,
inference(orient,[status(thm)],[t130]) ).
cnf(t850,plain,
double_divide(inverse(double_divide(sF4,sF2)),sF3) = double_divide(b1,inverse(double_divide(inverse(sF1),inverse(double_divide(inverse(double_divide(sF1,inverse(a1))),sF0))))),
inference(cp,[status(thm)],[t833,t154]) ).
cnf(t1031,plain,
double_divide(inverse(double_divide(sF4,sF2)),sF3) = double_divide(b1,inverse(double_divide(sF2,inverse(double_divide(inverse(double_divide(sF1,inverse(a1))),sF0))))),
inference(step,[status(thm)],[t850,t11]) ).
cnf(t14,plain,
b1 = double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF0)),X2))),
inference(cp,[status(thm)],[t13,t7]) ).
cnf(t33,plain,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF0)),X2))) = b1,
inference(orient,[status(thm)],[t14]) ).
cnf(t40,plain,
double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),sF0)),X3) = double_divide(X1,inverse(double_divide(inverse(b1),X2))),
inference(cp,[status(thm)],[t13,t33]) ).
cnf(t966,plain,
double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),sF0)),X3) = double_divide(X1,inverse(double_divide(sF0,X2))),
inference(step,[status(thm)],[t40,t7]) ).
cnf(t265,plain,
double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),sF0)),X3) = double_divide(X1,inverse(double_divide(sF0,X2))),
inference(orient,[status(thm)],[t966]) ).
cnf(t271,plain,
double_divide(X1,inverse(double_divide(sF0,X2))) = double_divide(inverse(double_divide(b1,sF0)),inverse(double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),sF0)),X3))),
inference(cp,[status(thm)],[t265,t33]) ).
cnf(t967,plain,
double_divide(X1,inverse(double_divide(sF0,X2))) = double_divide(inverse(sF1),inverse(double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),sF0)),X3))),
inference(step,[status(thm)],[t271,t9]) ).
cnf(t968,plain,
double_divide(X1,inverse(double_divide(sF0,X2))) = double_divide(sF2,inverse(double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),sF0)),X3))),
inference(step,[status(thm)],[t967,t11]) ).
cnf(t969,plain,
double_divide(X1,inverse(double_divide(sF0,X2))) = double_divide(sF2,inverse(double_divide(X1,inverse(double_divide(sF0,X2))))),
inference(step,[status(thm)],[t968,t265]) ).
cnf(t310,plain,
double_divide(sF2,inverse(double_divide(X1,inverse(double_divide(sF0,X2))))) = double_divide(X1,inverse(double_divide(sF0,X2))),
inference(orient,[status(thm)],[t969]) ).
cnf(t316,plain,
double_divide(X1,inverse(double_divide(sF0,inverse(double_divide(inverse(double_divide(double_divide(sF0,X2),sF0)),X2))))) = double_divide(sF2,inverse(double_divide(X1,inverse(b1)))),
inference(cp,[status(thm)],[t310,t33]) ).
cnf(t972,plain,
double_divide(X1,inverse(b1)) = double_divide(sF2,inverse(double_divide(X1,inverse(b1)))),
inference(step,[status(thm)],[t316,t33]) ).
cnf(t973,plain,
double_divide(X1,sF0) = double_divide(sF2,inverse(double_divide(X1,inverse(b1)))),
inference(step,[status(thm)],[t972,t7]) ).
cnf(t974,plain,
double_divide(X1,sF0) = double_divide(sF2,inverse(double_divide(X1,sF0))),
inference(step,[status(thm)],[t973,t7]) ).
cnf(t326,plain,
double_divide(sF2,inverse(double_divide(X1,sF0))) = double_divide(X1,sF0),
inference(orient,[status(thm)],[t974]) ).
cnf(t1032,plain,
double_divide(inverse(double_divide(sF4,sF2)),sF3) = double_divide(b1,inverse(double_divide(inverse(double_divide(sF1,inverse(a1))),sF0))),
inference(step,[status(thm)],[t1031,t326]) ).
cnf(t1033,plain,
double_divide(inverse(double_divide(sF4,sF2)),sF3) = a1,
inference(step,[status(thm)],[t1032,t22]) ).
cnf(t895,plain,
double_divide(inverse(double_divide(sF4,sF2)),sF3) = a1,
inference(orient,[status(thm)],[t1033]) ).
cnf(t901,plain,
sF4 = double_divide(inverse(double_divide(sF4,sF2)),inverse(double_divide(inverse(double_divide(a1,sF5)),sF3))),
inference(cp,[status(thm)],[t337,t895]) ).
cnf(t18,plain,
sF1 = double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF2)),X2))),
inference(cp,[status(thm)],[t13,t11]) ).
cnf(t182,plain,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF2)),X2))) = sF1,
inference(orient,[status(thm)],[t18]) ).
cnf(t320,plain,
double_divide(X1,inverse(double_divide(sF0,inverse(double_divide(inverse(double_divide(double_divide(sF0,X2),sF2)),X2))))) = double_divide(sF2,inverse(double_divide(X1,inverse(sF1)))),
inference(cp,[status(thm)],[t310,t182]) ).
cnf(t982,plain,
double_divide(X1,inverse(sF1)) = double_divide(sF2,inverse(double_divide(X1,inverse(sF1)))),
inference(step,[status(thm)],[t320,t182]) ).
cnf(t983,plain,
double_divide(X1,sF2) = double_divide(sF2,inverse(double_divide(X1,inverse(sF1)))),
inference(step,[status(thm)],[t982,t11]) ).
cnf(t984,plain,
double_divide(X1,sF2) = double_divide(sF2,inverse(double_divide(X1,sF2))),
inference(step,[status(thm)],[t983,t11]) ).
cnf(t425,plain,
double_divide(sF2,inverse(double_divide(X1,sF2))) = double_divide(X1,sF2),
inference(orient,[status(thm)],[t984]) ).
cnf(t15,plain,
a1 = double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF3)),X2))),
inference(cp,[status(thm)],[t13,t8]) ).
cnf(t89,plain,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),sF3)),X2))) = a1,
inference(orient,[status(thm)],[t15]) ).
cnf(t428,plain,
double_divide(inverse(double_divide(double_divide(sF2,sF2),sF3)),sF2) = a1,
inference(cp,[status(thm)],[t425,t89]) ).
cnf(t327,plain,
double_divide(b1,sF0) = double_divide(sF2,inverse(sF1)),
inference(cp,[status(thm)],[t326,t9]) ).
cnf(t975,plain,
sF1 = double_divide(sF2,inverse(sF1)),
inference(step,[status(thm)],[t327,t9]) ).
cnf(t976,plain,
sF1 = double_divide(sF2,sF2),
inference(step,[status(thm)],[t975,t11]) ).
cnf(t398,plain,
double_divide(sF2,sF2) = sF1,
inference(orient,[status(thm)],[t976]) ).
cnf(t1001,plain,
double_divide(inverse(double_divide(sF1,sF3)),sF2) = a1,
inference(step,[status(thm)],[t428,t398]) ).
cnf(t485,plain,
double_divide(inverse(double_divide(sF1,sF3)),sF2) = a1,
inference(orient,[status(thm)],[t1001]) ).
cnf(t492,plain,
double_divide(inverse(double_divide(sF1,sF3)),sF2) = double_divide(sF2,inverse(a1)),
inference(cp,[status(thm)],[t425,t485]) ).
cnf(t1002,plain,
a1 = double_divide(sF2,inverse(a1)),
inference(step,[status(thm)],[t492,t485]) ).
cnf(t1003,plain,
a1 = double_divide(sF2,sF3),
inference(step,[status(thm)],[t1002,t8]) ).
cnf(t553,plain,
double_divide(sF2,sF3) = a1,
inference(orient,[status(thm)],[t1003]) ).
cnf(t562,plain,
sF4 = double_divide(sF2,inverse(double_divide(inverse(double_divide(a1,sF5)),sF3))),
inference(cp,[status(thm)],[t337,t553]) ).
cnf(t318,plain,
double_divide(X1,inverse(double_divide(sF0,inverse(double_divide(inverse(double_divide(double_divide(sF0,X2),sF3)),X2))))) = double_divide(sF2,inverse(double_divide(X1,inverse(a1)))),
inference(cp,[status(thm)],[t310,t89]) ).
cnf(t977,plain,
double_divide(X1,inverse(a1)) = double_divide(sF2,inverse(double_divide(X1,inverse(a1)))),
inference(step,[status(thm)],[t318,t89]) ).
cnf(t978,plain,
double_divide(X1,sF3) = double_divide(sF2,inverse(double_divide(X1,inverse(a1)))),
inference(step,[status(thm)],[t977,t8]) ).
cnf(t979,plain,
double_divide(X1,sF3) = double_divide(sF2,inverse(double_divide(X1,sF3))),
inference(step,[status(thm)],[t978,t8]) ).
cnf(t405,plain,
double_divide(sF2,inverse(double_divide(X1,sF3))) = double_divide(X1,sF3),
inference(orient,[status(thm)],[t979]) ).
cnf(t1018,plain,
sF4 = double_divide(inverse(double_divide(a1,sF5)),sF3),
inference(step,[status(thm)],[t562,t405]) ).
cnf(t807,plain,
double_divide(inverse(double_divide(a1,sF5)),sF3) = sF4,
inference(orient,[status(thm)],[t1018]) ).
cnf(t1034,plain,
sF4 = double_divide(inverse(double_divide(sF4,sF2)),inverse(sF4)),
inference(step,[status(thm)],[t901,t807]) ).
cnf(t1035,plain,
sF4 = double_divide(inverse(double_divide(sF4,sF2)),sF5),
inference(step,[status(thm)],[t1034,t12]) ).
cnf(t397,plain,
double_divide(X1,inverse(double_divide(sF0,inverse(double_divide(inverse(double_divide(double_divide(sF0,X2),sF5)),X2))))) = double_divide(sF2,inverse(double_divide(X1,inverse(sF4)))),
inference(cp,[status(thm)],[t310,t337]) ).
cnf(t985,plain,
double_divide(X1,inverse(sF4)) = double_divide(sF2,inverse(double_divide(X1,inverse(sF4)))),
inference(step,[status(thm)],[t397,t337]) ).
cnf(t986,plain,
double_divide(X1,sF5) = double_divide(sF2,inverse(double_divide(X1,inverse(sF4)))),
inference(step,[status(thm)],[t985,t12]) ).
cnf(t987,plain,
double_divide(X1,sF5) = double_divide(sF2,inverse(double_divide(X1,sF5))),
inference(step,[status(thm)],[t986,t12]) ).
cnf(t437,plain,
double_divide(sF2,inverse(double_divide(X1,sF5))) = double_divide(X1,sF5),
inference(orient,[status(thm)],[t987]) ).
cnf(t441,plain,
double_divide(inverse(double_divide(double_divide(sF2,sF5),sF2)),sF5) = sF1,
inference(cp,[status(thm)],[t437,t182]) ).
cnf(t406,plain,
double_divide(a1,sF3) = double_divide(sF2,inverse(sF4)),
inference(cp,[status(thm)],[t405,t10]) ).
cnf(t980,plain,
sF4 = double_divide(sF2,inverse(sF4)),
inference(step,[status(thm)],[t406,t10]) ).
cnf(t981,plain,
sF4 = double_divide(sF2,sF5),
inference(step,[status(thm)],[t980,t12]) ).
cnf(t418,plain,
double_divide(sF2,sF5) = sF4,
inference(orient,[status(thm)],[t981]) ).
cnf(t1011,plain,
double_divide(inverse(double_divide(sF4,sF2)),sF5) = sF1,
inference(step,[status(thm)],[t441,t418]) ).
cnf(t603,plain,
double_divide(inverse(double_divide(sF4,sF2)),sF5) = sF1,
inference(orient,[status(thm)],[t1011]) ).
cnf(t1036,plain,
sF4 = sF1,
inference(step,[status(thm)],[t1035,t603]) ).
cnf(t904,plain,
sF4 = sF1,
inference(orient,[status(thm)],[t1036]) ).
cnf(t1037,plain,
double_divide(a1,sF3) = sF1,
inference(step,[status(thm)],[t10,t904]) ).
cnf(t905,plain,
double_divide(a1,sF3) = sF1,
inference(orient,[status(thm)],[t1037]) ).
cnf(u0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
inverse(double_divide(b1,sF0)) != inverse(double_divide(a1,inverse(a1))),
inference(rw,[status(thm)],[goal_0,t7]) ).
cnf(g0_1,plain,
inverse(sF1) != inverse(double_divide(a1,inverse(a1))),
inference(rw,[status(thm)],[g0_0,t9]) ).
cnf(g0_2,plain,
inverse(sF1) != inverse(double_divide(a1,sF3)),
inference(rw,[status(thm)],[g0_1,t8]) ).
cnf(g0_3,plain,
inverse(sF1) != inverse(sF1),
inference(rw,[status(thm)],[g0_2,t905]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 15:08:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.34/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.34/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------