%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP101-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Sun Sep 27 07:27:20 AM UTC 2026
% Result : Unsatisfiable 0.86s 0.68s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 5
% Syntax : Number of formulae : 109 ( 81 unt; 0 def)
% Number of atoms : 167 ( 166 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 154 ( 96 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 123 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,double_divide(double_divide(VAR_1,double_divide(VAR_2,VAR_0)),double_divide(VAR_2,identity))),double_divide(identity,identity)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = double_divide(double_divide(VAR_1,VAR_0),identity),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = double_divide(double_divide(B,A),identity),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = double_divide(VAR_0,identity),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = double_divide(A,identity),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = double_divide(VAR_0,inverse(VAR_0)),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = double_divide(A,inverse(A)),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_341,plain,
identity = double_divide(A,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_5,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(copy,[status(thm)],[c_341]) ).
fof(prove_these_axioms,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_6,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_342,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(double_divide(a1,identity),a1) != identity ),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_343,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_342]) ).
cnf(c_344,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_5,c_343]) ).
cnf(c_345,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_344]) ).
cnf(c_346,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(double_divide(double_divide(b3,a3),identity),c3) != multiply(a3,multiply(b3,c3))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_345]) ).
cnf(c_347,plain,
( multiply(a4,b4) != multiply(b4,a4)
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,multiply(b3,c3))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_346]) ).
cnf(c_348,plain,
( multiply(a4,b4) != multiply(b4,a4)
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,double_divide(double_divide(c3,b3),identity))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_347]) ).
cnf(c_349,plain,
( multiply(a4,b4) != multiply(b4,a4)
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_348]) ).
cnf(c_350,plain,
( double_divide(double_divide(b4,a4),identity) != multiply(b4,a4)
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_349]) ).
cnf(c_351,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_350]) ).
cnf(c_7,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(copy,[status(thm)],[c_351]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(C,double_divide(double_divide(B,double_divide(D,C)),double_divide(D,identity))),identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_352,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(C,double_divide(double_divide(B,double_divide(D,C)),double_divide(D,identity))),identity))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_12,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(C,double_divide(double_divide(B,double_divide(D,C)),double_divide(D,identity))),identity))) = double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)),
inference(copy,[status(thm)],[c_352]) ).
cnf(c_19,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_20,plain,
double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_22,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(C,double_divide(double_divide(B,double_divide(D,C)),double_divide(D,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_19,c_12]) ).
cnf(c_353,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_19,c_9]) ).
cnf(c_23,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(copy,[status(thm)],[c_353]) ).
cnf(c_24,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_23,c_22]) ).
cnf(c_26,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_354,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_355,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_20,c_354]) ).
cnf(c_27,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_355]) ).
cnf(c_28,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity) = A,
inference(paramod,[status(thm)],[c_27,c_26]) ).
cnf(c_30,plain,
double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_27,c_24]) ).
cnf(c_31,plain,
double_divide(double_divide(double_divide(A,identity),A),identity) = identity,
inference(paramod,[status(thm)],[c_27,c_20]) ).
cnf(c_34,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_27,c_11]) ).
cnf(c_356,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_27,c_7]) ).
cnf(c_36,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| double_divide(double_divide(a2,identity),identity) != a2 ),
inference(copy,[status(thm)],[c_356]) ).
cnf(c_37,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_34,c_30]) ).
cnf(c_41,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),identity)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_27,c_23]) ).
cnf(c_357,plain,
double_divide(double_divide(double_divide(identity,identity),identity),identity) = double_divide(double_divide(A,identity),A),
inference(paramod,[status(thm)],[c_31,c_28]) ).
cnf(c_358,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(double_divide(A,identity),A),
inference(paramod,[status(thm)],[c_27,c_357]) ).
cnf(c_359,plain,
double_divide(identity,identity) = double_divide(double_divide(A,identity),A),
inference(paramod,[status(thm)],[c_27,c_358]) ).
cnf(c_360,plain,
identity = double_divide(double_divide(A,identity),A),
inference(paramod,[status(thm)],[c_27,c_359]) ).
cnf(c_47,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(copy,[status(thm)],[c_360]) ).
cnf(c_361,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(B,A),identity),identity))),
inference(paramod,[status(thm)],[c_47,c_23]) ).
cnf(c_50,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),identity))) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(copy,[status(thm)],[c_361]) ).
cnf(c_54,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_34,c_28]) ).
cnf(c_362,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(double_divide(double_divide(A,identity),identity),identity),
inference(paramod,[status(thm)],[c_28,c_34]) ).
cnf(c_55,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_54,c_362]) ).
cnf(c_363,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_54,c_28]) ).
cnf(c_57,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_55,c_363]) ).
cnf(c_364,plain,
double_divide(A,B) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_57,c_50]) ).
cnf(c_58,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(B,A),
inference(copy,[status(thm)],[c_364]) ).
cnf(c_59,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_58,c_57]) ).
cnf(c_65,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_58,c_41]) ).
cnf(c_66,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_58,c_37]) ).
cnf(c_68,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_58,c_23]) ).
cnf(c_365,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| a2 != a2 ),
inference(paramod,[status(thm)],[c_59,c_36]) ).
cnf(c_69,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(copy,[status(thm)],[c_365]) ).
cnf(c_366,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_5,c_58]) ).
cnf(c_70,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_366]) ).
cnf(c_367,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_59,c_58]) ).
cnf(c_368,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_70,c_367]) ).
cnf(c_72,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_58,c_368]) ).
cnf(c_369,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(paramod,[status(thm)],[c_70,c_69]) ).
cnf(c_370,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(paramod,[status(thm)],[c_70,c_369]) ).
cnf(c_371,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity) ),
inference(paramod,[status(thm)],[c_70,c_370]) ).
cnf(c_372,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_70,c_371]) ).
cnf(c_373,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(double_divide(a4,b4),identity)
| double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_70,c_372]) ).
cnf(c_73,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_70,c_373]) ).
cnf(c_74,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_70,c_65]) ).
cnf(c_79,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_72,c_58]) ).
cnf(c_374,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(double_divide(identity,double_divide(b3,c3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_79,c_73]) ).
cnf(c_375,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_79,c_374]) ).
cnf(c_376,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))) ),
inference(paramod,[status(thm)],[c_79,c_375]) ).
cnf(c_377,plain,
( double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))) ),
inference(paramod,[status(thm)],[c_79,c_376]) ).
cnf(c_378,plain,
( double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) ),
inference(copy,[status(thm)],[c_377]) ).
cnf(c_80,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(copy,[status(thm)],[c_378]) ).
cnf(c_81,plain,
double_divide(A,double_divide(double_divide(B,identity),double_divide(C,double_divide(B,A)))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_79,c_68]) ).
cnf(c_82,plain,
double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_79,c_66]) ).
cnf(c_87,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_79,c_72]) ).
cnf(c_379,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_82,c_87]) ).
cnf(c_380,plain,
A = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_72,c_379]) ).
cnf(c_90,plain,
double_divide(A,double_divide(B,A)) = B,
inference(copy,[status(thm)],[c_380]) ).
cnf(c_91,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_79,c_90]) ).
cnf(c_381,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_74,c_91]) ).
cnf(c_97,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(A,identity)),
inference(copy,[status(thm)],[c_381]) ).
cnf(c_382,plain,
double_divide(double_divide(a3,b3),double_divide(c3,identity)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_97,c_80]) ).
cnf(c_383,plain,
double_divide(double_divide(a3,b3),double_divide(identity,c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_79,c_382]) ).
cnf(c_384,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_79,c_383]) ).
cnf(c_385,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),double_divide(a3,identity)),
inference(paramod,[status(thm)],[c_97,c_384]) ).
cnf(c_386,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),double_divide(identity,a3)),
inference(paramod,[status(thm)],[c_79,c_385]) ).
cnf(c_98,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_79,c_386]) ).
cnf(c_112,plain,
double_divide(double_divide(A,B),double_divide(double_divide(B,identity),double_divide(C,A))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_90,c_81]) ).
cnf(c_387,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(B,identity),double_divide(C,A)),
inference(paramod,[status(thm)],[c_112,c_91]) ).
cnf(c_185,plain,
double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(copy,[status(thm)],[c_387]) ).
cnf(c_211,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_79,c_185]) ).
cnf(c_388,plain,
double_divide(double_divide(b3,c3),double_divide(a3,identity)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_211,c_98]) ).
cnf(c_389,plain,
double_divide(double_divide(b3,c3),double_divide(identity,a3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_79,c_388]) ).
cnf(c_390,plain,
double_divide(double_divide(identity,a3),double_divide(b3,c3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_79,c_389]) ).
cnf(c_340,plain,
$false,
inference(copy,[status(thm)],[c_390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP101-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:22:18 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 416246 was started by sandbox2 on n014,
% 0.17/0.43 % Fri Sep 25 14:22:18 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.86/0.68
% 0.86/0.68 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 0.86/0.68
% 0.86/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.86/0.68
% 0.86/0.68 % Proof 1 at 0.16 (+ 0.06) seconds.
% 0.86/0.68 % Length of proof is 54.
% 0.86/0.68 % Level of proof is 18.
% 0.86/0.68 % Maximum clause weight is 99.000.
% 0.86/0.68 % Given clauses 64.
% 0.86/0.68
% 0.86/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------