%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP103-1 : 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 : n002.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 0.78s 0.48s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 5
% Syntax : Number of formulae : 150 ( 117 unt; 0 def)
% Number of atoms : 221 ( 220 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 179 ( 108 ~; 71 |; 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 : 192 ( 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(identity,VAR_1),double_divide(VAR_2,double_divide(VAR_1,VAR_0)))),double_divide(identity,identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),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_273,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_273]) ).
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_274,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_275,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_274]) ).
cnf(c_276,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_275]) ).
cnf(c_277,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_276]) ).
cnf(c_278,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_277]) ).
cnf(c_279,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_278]) ).
cnf(c_280,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_279]) ).
cnf(c_281,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_280]) ).
cnf(c_282,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_281]) ).
cnf(c_283,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_282]) ).
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_283]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))),double_divide(identity,identity)) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_12,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_284,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(B,double_divide(double_divide(identity,C),double_divide(D,double_divide(C,B))))),double_divide(A,D))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_13,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),D)),double_divide(identity,identity)),
inference(copy,[status(thm)],[c_284]) ).
cnf(c_19,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(C,identity),double_divide(B,A))))),identity)),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_22,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(identity,double_divide(double_divide(identity,A),identity)),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_285,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_286,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_285]) ).
cnf(c_287,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_286]) ).
cnf(c_23,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_287]) ).
cnf(c_288,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),D)),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_23,c_13]) ).
cnf(c_289,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))) = double_divide(double_divide(identity,double_divide(identity,D)),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_23,c_288]) ).
cnf(c_26,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))) = double_divide(double_divide(identity,double_divide(identity,D)),identity),
inference(paramod,[status(thm)],[c_23,c_289]) ).
cnf(c_290,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_291,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(paramod,[status(thm)],[c_23,c_290]) ).
cnf(c_27,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(identity,C)),identity),
inference(copy,[status(thm)],[c_291]) ).
cnf(c_292,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,identity)) = double_divide(identity,double_divide(double_divide(identity,A),identity)),
inference(paramod,[status(thm)],[c_23,c_22]) ).
cnf(c_28,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(double_divide(identity,A),identity)),
inference(paramod,[status(thm)],[c_23,c_292]) ).
cnf(c_293,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(C,identity),double_divide(B,A))))),identity)),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_23,c_19]) ).
cnf(c_294,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(C,identity))),identity)),identity)),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_27,c_293]) ).
cnf(c_295,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),identity))),identity)),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_28,c_294]) ).
cnf(c_296,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),identity)),identity))),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_28,c_295]) ).
cnf(c_297,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),identity)),identity))),identity) = C,
inference(paramod,[status(thm)],[c_23,c_296]) ).
cnf(c_29,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)),identity)),identity)) = A,
inference(paramod,[status(thm)],[c_28,c_297]) ).
cnf(c_33,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(paramod,[status(thm)],[c_23,c_12]) ).
cnf(c_34,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_23,c_11]) ).
cnf(c_298,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_23,c_10]) ).
cnf(c_35,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),identity) = B,
inference(paramod,[status(thm)],[c_23,c_298]) ).
cnf(c_299,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_23,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_299]) ).
cnf(c_300,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,C)),identity)),double_divide(D,C))) = double_divide(double_divide(identity,double_divide(identity,D)),identity),
inference(paramod,[status(thm)],[c_27,c_26]) ).
cnf(c_301,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,C),identity))),double_divide(D,C))) = double_divide(double_divide(identity,double_divide(identity,D)),identity),
inference(paramod,[status(thm)],[c_28,c_300]) ).
cnf(c_37,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,A))) = double_divide(identity,double_divide(double_divide(identity,B),identity)),
inference(paramod,[status(thm)],[c_28,c_301]) ).
cnf(c_38,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(identity,double_divide(double_divide(identity,C),identity)),
inference(paramod,[status(thm)],[c_28,c_27]) ).
cnf(c_39,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_33,c_29]) ).
cnf(c_302,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)),identity)),
inference(paramod,[status(thm)],[c_39,c_28]) ).
cnf(c_42,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_39,c_302]) ).
cnf(c_303,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_39,c_28]) ).
cnf(c_304,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_42,c_303]) ).
cnf(c_44,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_42,c_304]) ).
cnf(c_48,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(identity,double_divide(identity,double_divide(C,identity))),
inference(paramod,[status(thm)],[c_42,c_38]) ).
cnf(c_305,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A))) = double_divide(identity,double_divide(double_divide(identity,B),identity)),
inference(paramod,[status(thm)],[c_42,c_37]) ).
cnf(c_49,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_42,c_305]) ).
cnf(c_53,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_5,c_34]) ).
cnf(c_306,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),identity)),identity) = identity,
inference(paramod,[status(thm)],[c_23,c_34]) ).
cnf(c_54,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),identity) = identity,
inference(paramod,[status(thm)],[c_42,c_306]) ).
cnf(c_307,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity),double_divide(A,double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_44,c_34]) ).
cnf(c_308,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)),double_divide(A,double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_42,c_307]) ).
cnf(c_67,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,A)),double_divide(A,double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_53,c_308]) ).
cnf(c_309,plain,
double_divide(A,identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity)),
inference(paramod,[status(thm)],[c_44,c_42]) ).
cnf(c_310,plain,
double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity))),
inference(paramod,[status(thm)],[c_42,c_309]) ).
cnf(c_311,plain,
double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_53,c_310]) ).
cnf(c_69,plain,
double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(A,identity),
inference(copy,[status(thm)],[c_311]) ).
cnf(c_71,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(B,A))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_69,c_49]) ).
cnf(c_312,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(B,double_divide(identity,double_divide(A,double_divide(identity,B)))),
inference(paramod,[status(thm)],[c_35,c_44]) ).
cnf(c_74,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(copy,[status(thm)],[c_312]) ).
cnf(c_313,plain,
double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_54,c_44]) ).
cnf(c_314,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_23,c_313]) ).
cnf(c_315,plain,
double_divide(identity,identity) = double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_23,c_314]) ).
cnf(c_316,plain,
identity = double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_23,c_315]) ).
cnf(c_80,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))) = identity,
inference(copy,[status(thm)],[c_316]) ).
cnf(c_317,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity))) = identity,
inference(paramod,[status(thm)],[c_53,c_80]) ).
cnf(c_82,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(identity,A))) = identity,
inference(paramod,[status(thm)],[c_53,c_317]) ).
cnf(c_84,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),A) = identity,
inference(paramod,[status(thm)],[c_44,c_82]) ).
cnf(c_85,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(A,identity)) = identity,
inference(paramod,[status(thm)],[c_69,c_82]) ).
cnf(c_318,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(double_divide(identity,double_divide(identity,B)),double_divide(B,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_67,c_44]) ).
cnf(c_90,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(copy,[status(thm)],[c_318]) ).
cnf(c_319,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,A)))),identity),identity) = A,
inference(paramod,[status(thm)],[c_85,c_67]) ).
cnf(c_320,plain,
double_divide(double_divide(double_divide(identity,double_divide(A,identity)),identity),identity) = A,
inference(paramod,[status(thm)],[c_69,c_319]) ).
cnf(c_321,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity) = A,
inference(paramod,[status(thm)],[c_42,c_320]) ).
cnf(c_322,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A,
inference(paramod,[status(thm)],[c_42,c_321]) ).
cnf(c_91,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_53,c_322]) ).
cnf(c_323,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)))),identity),identity) = A,
inference(paramod,[status(thm)],[c_84,c_67]) ).
cnf(c_324,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,A)))),identity),identity) = A,
inference(paramod,[status(thm)],[c_53,c_323]) ).
cnf(c_325,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,A)),identity),identity) = A,
inference(paramod,[status(thm)],[c_91,c_324]) ).
cnf(c_94,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_91,c_325]) ).
cnf(c_326,plain,
double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_91,c_90]) ).
cnf(c_99,plain,
double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_91,c_326]) ).
cnf(c_102,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_99,c_74]) ).
cnf(c_327,plain,
double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_94,c_71]) ).
cnf(c_103,plain,
double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_99,c_327]) ).
cnf(c_105,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_91,c_69]) ).
cnf(c_109,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_99,c_48]) ).
cnf(c_328,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_105,c_44]) ).
cnf(c_110,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_99,c_328]) ).
cnf(c_329,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(identity,a2),identity) != a2 ),
inference(paramod,[status(thm)],[c_105,c_36]) ).
cnf(c_330,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(identity,double_divide(identity,a2)) != a2 ),
inference(paramod,[status(thm)],[c_105,c_329]) ).
cnf(c_331,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_91,c_330]) ).
cnf(c_332,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)
| a2 != a2 ),
inference(paramod,[status(thm)],[c_105,c_331]) ).
cnf(c_333,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)
| a2 != a2 ),
inference(paramod,[status(thm)],[c_105,c_332]) ).
cnf(c_334,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)
| a2 != a2 ),
inference(paramod,[status(thm)],[c_105,c_333]) ).
cnf(c_335,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))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_105,c_334]) ).
cnf(c_336,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))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_105,c_335]) ).
cnf(c_337,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))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_105,c_336]) ).
cnf(c_113,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(copy,[status(thm)],[c_337]) ).
cnf(c_338,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_103,c_91]) ).
cnf(c_339,plain,
A = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_110,c_338]) ).
cnf(c_120,plain,
double_divide(A,double_divide(B,A)) = B,
inference(copy,[status(thm)],[c_339]) ).
cnf(c_123,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_120,c_120]) ).
cnf(c_340,plain,
double_divide(A,double_divide(A,B)) = double_divide(double_divide(identity,B),identity),
inference(paramod,[status(thm)],[c_123,c_99]) ).
cnf(c_341,plain,
double_divide(A,double_divide(A,B)) = double_divide(identity,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_105,c_340]) ).
cnf(c_124,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_91,c_341]) ).
cnf(c_342,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(paramod,[status(thm)],[c_102,c_123]) ).
cnf(c_130,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(double_divide(A,identity),B),
inference(copy,[status(thm)],[c_342]) ).
cnf(c_343,plain,
double_divide(A,double_divide(identity,B)) = double_divide(double_divide(double_divide(identity,A),B),identity),
inference(paramod,[status(thm)],[c_123,c_102]) ).
cnf(c_344,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(double_divide(identity,A),B)),
inference(paramod,[status(thm)],[c_105,c_343]) ).
cnf(c_131,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(A,double_divide(identity,B)),
inference(copy,[status(thm)],[c_344]) ).
cnf(c_345,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(c3,b3),double_divide(identity,a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_131,c_113]) ).
cnf(c_346,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(c3,b3),double_divide(identity,a3)) != double_divide(double_divide(c3,identity),double_divide(b3,a3)) ),
inference(paramod,[status(thm)],[c_130,c_345]) ).
cnf(c_132,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(c3,b3),double_divide(identity,a3)) != double_divide(double_divide(identity,c3),double_divide(b3,a3)) ),
inference(paramod,[status(thm)],[c_105,c_346]) ).
cnf(c_134,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_120,c_124]) ).
cnf(c_347,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(b3,c3),double_divide(identity,a3)) != double_divide(double_divide(identity,c3),double_divide(b3,a3)) ),
inference(paramod,[status(thm)],[c_134,c_132]) ).
cnf(c_348,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(identity,a3),double_divide(b3,c3)) != double_divide(double_divide(identity,c3),double_divide(b3,a3)) ),
inference(paramod,[status(thm)],[c_134,c_347]) ).
cnf(c_349,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(identity,a3),double_divide(b3,c3)) != double_divide(double_divide(identity,c3),double_divide(a3,b3)) ),
inference(paramod,[status(thm)],[c_134,c_348]) ).
cnf(c_350,plain,
( double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(identity,a3),double_divide(b3,c3)) != double_divide(double_divide(identity,c3),double_divide(a3,b3)) ),
inference(paramod,[status(thm)],[c_134,c_349]) ).
cnf(c_351,plain,
( double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)) ),
inference(copy,[status(thm)],[c_350]) ).
cnf(c_135,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(copy,[status(thm)],[c_351]) ).
cnf(c_147,plain,
double_divide(double_divide(A,B),double_divide(double_divide(identity,B),double_divide(C,A))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_120,c_109]) ).
cnf(c_352,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(identity,B),double_divide(C,A)),
inference(paramod,[status(thm)],[c_147,c_124]) ).
cnf(c_207,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(copy,[status(thm)],[c_352]) ).
cnf(c_353,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_207,c_135]) ).
cnf(c_354,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_134,c_353]) ).
cnf(c_355,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_134,c_354]) ).
cnf(c_272,plain,
$false,
inference(copy,[status(thm)],[c_355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP103-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:25:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3487147 was started by sandbox2 on n002,
% 0.10/0.36 % Fri Sep 25 14:25:10 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.78/0.48
% 0.78/0.48 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 0.78/0.48
% 0.78/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.78/0.48
% 0.78/0.48 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.78/0.48 % Length of proof is 62.
% 0.78/0.48 % Level of proof is 20.
% 0.78/0.48 % Maximum clause weight is 99.000.
% 0.78/0.48 % Given clauses 74.
% 0.78/0.48
% 0.78/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------