%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP102-1 : 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 : 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 : Sun Sep 27 07:27:20 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 142 ( 114 unt; 0 def)
% Number of atoms : 201 ( 200 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 89 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 11 ( 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 : 235 ( 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(double_divide(VAR_1,VAR_0),VAR_2),double_divide(VAR_1,identity))),double_divide(identity,identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
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_241,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_241]) ).
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_242,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_243,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_242]) ).
cnf(c_244,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_243]) ).
cnf(c_245,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_244]) ).
cnf(c_246,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_245]) ).
cnf(c_247,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_246]) ).
cnf(c_248,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_247]) ).
cnf(c_249,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_248]) ).
cnf(c_250,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_249]) ).
cnf(c_251,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_250]) ).
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_251]) ).
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(double_divide(D,C),A),double_divide(D,identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_12,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_15,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(B,A),double_divide(double_divide(C,double_divide(double_divide(double_divide(D,C),B),double_divide(D,identity))),identity)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_18,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_21,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(A,B),B),double_divide(A,identity)),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_29,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_35,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_37,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(C,A),double_divide(double_divide(double_divide(double_divide(identity,C),identity),identity),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_29,c_8]) ).
cnf(c_252,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(A,B),B),double_divide(A,identity)),
inference(paramod,[status(thm)],[c_35,c_21]) ).
cnf(c_39,plain,
double_divide(double_divide(double_divide(A,B),B),double_divide(A,identity)) = double_divide(identity,identity),
inference(copy,[status(thm)],[c_252]) ).
cnf(c_40,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(identity,identity),B),double_divide(double_divide(double_divide(A,C),C),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_39,c_1]) ).
cnf(c_42,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_39,c_1]) ).
cnf(c_45,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),double_divide(double_divide(C,D),D)),double_divide(B,identity))),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_39,c_8]) ).
cnf(c_253,plain,
double_divide(A,double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(double_divide(C,B),A),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_1,c_42]) ).
cnf(c_55,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(C,double_divide(identity,identity)),
inference(copy,[status(thm)],[c_253]) ).
cnf(c_56,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(C,A),double_divide(double_divide(C,double_divide(identity,identity)),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_42,c_8]) ).
cnf(c_254,plain,
double_divide(A,double_divide(identity,identity)) = double_divide(double_divide(B,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),
inference(paramod,[status(thm)],[c_11,c_42]) ).
cnf(c_59,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))) = double_divide(B,double_divide(identity,identity)),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_255,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(A,double_divide(identity,identity)),identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_42,c_39]) ).
cnf(c_256,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_255]) ).
cnf(c_61,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_256]) ).
cnf(c_257,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),double_divide(double_divide(C,D),D)),double_divide(B,identity))),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_61,c_45]) ).
cnf(c_258,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),double_divide(double_divide(C,D),D)),double_divide(B,identity))),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_61,c_257]) ).
cnf(c_259,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(C,D),D),double_divide(identity,identity)),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_55,c_258]) ).
cnf(c_260,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(C,D),D),identity),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_61,c_259]) ).
cnf(c_64,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(A,B),B),identity),identity))),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_61,c_260]) ).
cnf(c_261,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_61,c_18]) ).
cnf(c_262,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(C,double_divide(identity,identity)),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_55,c_261]) ).
cnf(c_263,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(C,identity),identity))),double_divide(identity,identity)) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_61,c_262]) ).
cnf(c_70,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_61,c_263]) ).
cnf(c_264,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),double_divide(double_divide(C,double_divide(double_divide(double_divide(D,C),B),double_divide(D,identity))),identity)),
inference(paramod,[status(thm)],[c_61,c_15]) ).
cnf(c_265,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),double_divide(double_divide(B,double_divide(identity,identity)),identity)),
inference(paramod,[status(thm)],[c_55,c_264]) ).
cnf(c_71,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),double_divide(double_divide(B,identity),identity)),
inference(paramod,[status(thm)],[c_61,c_265]) ).
cnf(c_266,plain,
double_divide(double_divide(C,double_divide(identity,identity)),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_55,c_1]) ).
cnf(c_267,plain,
double_divide(double_divide(C,identity),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_61,c_266]) ).
cnf(c_75,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_61,c_267]) ).
cnf(c_268,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(C,A),double_divide(double_divide(C,double_divide(identity,identity)),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_61,c_56]) ).
cnf(c_269,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),double_divide(double_divide(C,double_divide(identity,identity)),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_61,c_268]) ).
cnf(c_270,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),double_divide(double_divide(C,identity),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_61,c_269]) ).
cnf(c_271,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),C)),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_75,c_270]) ).
cnf(c_76,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),C)),identity))),identity) = B,
inference(paramod,[status(thm)],[c_61,c_271]) ).
cnf(c_272,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(C,A),double_divide(double_divide(double_divide(double_divide(identity,C),identity),identity),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_61,c_37]) ).
cnf(c_273,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),double_divide(double_divide(double_divide(double_divide(identity,C),identity),identity),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_61,c_272]) ).
cnf(c_274,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),double_divide(double_divide(identity,C),identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_75,c_273]) ).
cnf(c_81,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),double_divide(double_divide(identity,C),identity))),identity))),identity) = B,
inference(paramod,[status(thm)],[c_61,c_274]) ).
cnf(c_275,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_75,c_29]) ).
cnf(c_84,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(paramod,[status(thm)],[c_61,c_275]) ).
cnf(c_85,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_88,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_61,c_55]) ).
cnf(c_276,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(double_divide(double_divide(A,C),C),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_61,c_40]) ).
cnf(c_94,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(double_divide(double_divide(A,C),C),identity))),identity) = B,
inference(paramod,[status(thm)],[c_61,c_276]) ).
cnf(c_101,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_61,c_12]) ).
cnf(c_277,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_61,c_7]) ).
cnf(c_278,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
| identity != identity ),
inference(paramod,[status(thm)],[c_75,c_277]) ).
cnf(c_279,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(copy,[status(thm)],[c_278]) ).
cnf(c_104,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_279]) ).
cnf(c_280,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(A,B),B))),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_75,c_64]) ).
cnf(c_105,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_84,c_280]) ).
cnf(c_281,plain,
A = double_divide(double_divide(B,A),double_divide(double_divide(B,identity),identity)),
inference(paramod,[status(thm)],[c_84,c_71]) ).
cnf(c_282,plain,
A = double_divide(double_divide(B,A),B),
inference(paramod,[status(thm)],[c_75,c_281]) ).
cnf(c_108,plain,
double_divide(double_divide(A,B),A) = B,
inference(copy,[status(thm)],[c_282]) ).
cnf(c_283,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_75,c_70]) ).
cnf(c_109,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_108,c_283]) ).
cnf(c_284,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,A),identity))),identity) = B,
inference(paramod,[status(thm)],[c_108,c_76]) ).
cnf(c_285,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(identity,double_divide(identity,A)))),identity) = B,
inference(paramod,[status(thm)],[c_109,c_284]) ).
cnf(c_113,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,B),double_divide(identity,double_divide(identity,A))))) = B,
inference(paramod,[status(thm)],[c_109,c_285]) ).
cnf(c_286,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(double_divide(C,A),double_divide(identity,double_divide(identity,C)))),identity))),identity) = B,
inference(paramod,[status(thm)],[c_109,c_81]) ).
cnf(c_287,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(identity,double_divide(identity,double_divide(double_divide(C,A),double_divide(identity,double_divide(identity,C))))))),identity) = B,
inference(paramod,[status(thm)],[c_109,c_286]) ).
cnf(c_288,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),identity) = B,
inference(paramod,[status(thm)],[c_113,c_287]) ).
cnf(c_289,plain,
double_divide(double_divide(identity,B),identity) = B,
inference(paramod,[status(thm)],[c_108,c_288]) ).
cnf(c_115,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_109,c_289]) ).
cnf(c_290,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_109,c_104]) ).
cnf(c_291,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_109,c_290]) ).
cnf(c_292,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_109,c_291]) ).
cnf(c_293,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_109,c_292]) ).
cnf(c_294,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_109,c_293]) ).
cnf(c_121,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_109,c_294]) ).
cnf(c_295,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,identity)))) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_109,c_101]) ).
cnf(c_124,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,identity)))) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_109,c_295]) ).
cnf(c_296,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(identity,double_divide(double_divide(A,C),C)))),identity) = B,
inference(paramod,[status(thm)],[c_109,c_94]) ).
cnf(c_297,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),identity) = B,
inference(paramod,[status(thm)],[c_105,c_296]) ).
cnf(c_298,plain,
double_divide(double_divide(B,identity),identity) = B,
inference(paramod,[status(thm)],[c_85,c_297]) ).
cnf(c_127,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_109,c_298]) ).
cnf(c_131,plain,
double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_127,c_124]) ).
cnf(c_299,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_131,c_121]) ).
cnf(c_300,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_131,c_299]) ).
cnf(c_301,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_131,c_300]) ).
cnf(c_302,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_131,c_301]) ).
cnf(c_303,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_302]) ).
cnf(c_134,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_303]) ).
cnf(c_135,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_108,c_108]) ).
cnf(c_304,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(double_divide(double_divide(B,A),identity),identity),
inference(paramod,[status(thm)],[c_5,c_88]) ).
cnf(c_305,plain,
double_divide(A,B) = double_divide(double_divide(double_divide(B,A),identity),identity),
inference(paramod,[status(thm)],[c_135,c_304]) ).
cnf(c_306,plain,
double_divide(A,B) = double_divide(double_divide(identity,double_divide(B,A)),identity),
inference(paramod,[status(thm)],[c_109,c_305]) ).
cnf(c_307,plain,
double_divide(A,B) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(paramod,[status(thm)],[c_109,c_306]) ).
cnf(c_137,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_115,c_307]) ).
cnf(c_308,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,A),B),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_61,c_88]) ).
cnf(c_138,plain,
double_divide(A,double_divide(identity,double_divide(double_divide(identity,A),B))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_137,c_308]) ).
cnf(c_309,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(double_divide(C,B),A),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_88,c_108]) ).
cnf(c_310,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(C,identity),double_divide(double_divide(C,B),A)),
inference(paramod,[status(thm)],[c_137,c_309]) ).
cnf(c_141,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(A,B),C)) = double_divide(double_divide(C,identity),B),
inference(copy,[status(thm)],[c_310]) ).
cnf(c_159,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_137,c_108]) ).
cnf(c_171,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),B)),double_divide(B,identity)) = A,
inference(paramod,[status(thm)],[c_138,c_135]) ).
cnf(c_311,plain,
double_divide(A,double_divide(identity,B)) = double_divide(double_divide(double_divide(identity,A),B),identity),
inference(paramod,[status(thm)],[c_159,c_138]) ).
cnf(c_312,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(double_divide(identity,A),B)),
inference(paramod,[status(thm)],[c_137,c_311]) ).
cnf(c_178,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(A,double_divide(identity,B)),
inference(copy,[status(thm)],[c_312]) ).
cnf(c_182,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(B,identity)) = A,
inference(paramod,[status(thm)],[c_178,c_171]) ).
cnf(c_198,plain,
double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(double_divide(C,identity),double_divide(A,B)),
inference(paramod,[status(thm)],[c_159,c_141]) ).
cnf(c_313,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = B,
inference(paramod,[status(thm)],[c_137,c_182]) ).
cnf(c_216,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),B)) = B,
inference(paramod,[status(thm)],[c_137,c_313]) ).
cnf(c_314,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(double_divide(double_divide(identity,A),B),identity),identity),
inference(paramod,[status(thm)],[c_216,c_141]) ).
cnf(c_315,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(identity,double_divide(double_divide(identity,A),B)),identity),
inference(paramod,[status(thm)],[c_137,c_314]) ).
cnf(c_316,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(A,double_divide(identity,B)),identity),
inference(paramod,[status(thm)],[c_178,c_315]) ).
cnf(c_221,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(paramod,[status(thm)],[c_137,c_316]) ).
cnf(c_317,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(C,identity),double_divide(A,B)),
inference(paramod,[status(thm)],[c_221,c_198]) ).
cnf(c_239,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(identity,double_divide(C,double_divide(identity,double_divide(A,B)))),
inference(paramod,[status(thm)],[c_221,c_317]) ).
cnf(c_318,plain,
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(copy,[status(thm)],[c_134]) ).
cnf(c_240,plain,
$false,
inference(resolve,[status(thm)],[c_239,c_318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP102-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n017.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 14:17:53 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.39 % Process 2458922 was started by sandbox2 on n017,
% 0.09/5.39 % Fri Sep 25 14:17:53 2026
% 0.09/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.45
% 0.15/5.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.45
% 0.15/5.45 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.15/5.45 % Length of proof is 59.
% 0.15/5.45 % Level of proof is 21.
% 0.15/5.45 % Maximum clause weight is 42.000.
% 0.15/5.45 % Given clauses 30.
% 0.15/5.45
% 0.15/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------