%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:30:24 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.55s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 5
% Syntax : Number of formulae : 109 ( 109 unt; 0 def)
% Number of atoms : 109 ( 108 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 157 ( 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_259,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_259]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_260,plain,
multiply(double_divide(double_divide(b3,a3),identity),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_261,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_260]) ).
cnf(c_262,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,double_divide(double_divide(c3,b3),identity)),
inference(paramod,[status(thm)],[c_2,c_261]) ).
cnf(c_263,plain,
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),
inference(paramod,[status(thm)],[c_2,c_262]) ).
cnf(c_7,plain,
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_263]) ).
cnf(c_8,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_9,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_264,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(B,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(identity,double_divide(A,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_1,c_264]) ).
cnf(c_12,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(A,double_divide(double_divide(identity,double_divide(B,A)),double_divide(B,identity)))),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_265,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),double_divide(B,identity))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_266,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),double_divide(B,identity))),
inference(paramod,[status(thm)],[c_11,c_265]) ).
cnf(c_15,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,double_divide(identity,identity)),double_divide(identity,identity))),
inference(copy,[status(thm)],[c_266]) ).
cnf(c_267,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_5,c_8]) ).
cnf(c_16,plain,
double_divide(identity,double_divide(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_267]) ).
cnf(c_268,plain,
double_divide(identity,double_divide(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_11,c_8]) ).
cnf(c_269,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_16,c_268]) ).
cnf(c_21,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_269]) ).
cnf(c_270,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(identity,double_divide(identity,identity)))),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_21,c_12]) ).
cnf(c_271,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_270]) ).
cnf(c_272,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_11,c_271]) ).
cnf(c_273,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_272]) ).
cnf(c_274,plain,
double_divide(identity,double_divide(identity,double_divide(identity,identity))) = identity,
inference(paramod,[status(thm)],[c_11,c_273]) ).
cnf(c_22,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_5,c_274]) ).
cnf(c_275,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_22,c_15]) ).
cnf(c_23,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),identity)),
inference(paramod,[status(thm)],[c_22,c_275]) ).
cnf(c_276,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_22,c_11]) ).
cnf(c_28,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_22,c_276]) ).
cnf(c_277,plain,
double_divide(double_divide(identity,double_divide(double_divide(B,identity),identity)),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_278,plain,
double_divide(double_divide(identity,double_divide(double_divide(B,identity),identity)),identity) = B,
inference(paramod,[status(thm)],[c_22,c_277]) ).
cnf(c_29,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A,
inference(paramod,[status(thm)],[c_28,c_278]) ).
cnf(c_279,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_5,c_21]) ).
cnf(c_30,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_23,c_279]) ).
cnf(c_280,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_30,c_29]) ).
cnf(c_31,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_30,c_280]) ).
cnf(c_33,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_22,c_21]) ).
cnf(c_34,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,identity))) = identity,
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_281,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_21,c_28]) ).
cnf(c_282,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_28,c_281]) ).
cnf(c_283,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_28,c_282]) ).
cnf(c_284,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_30,c_283]) ).
cnf(c_285,plain,
A = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_31,c_284]) ).
cnf(c_37,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)) = A,
inference(copy,[status(thm)],[c_285]) ).
cnf(c_286,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(double_divide(B,identity),double_divide(double_divide(identity,A),identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_34,c_21]) ).
cnf(c_38,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(double_divide(B,identity),double_divide(identity,double_divide(A,identity)))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_28,c_286]) ).
cnf(c_287,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(identity,identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(paramod,[status(thm)],[c_34,c_21]) ).
cnf(c_288,plain,
double_divide(double_divide(A,identity),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(paramod,[status(thm)],[c_22,c_287]) ).
cnf(c_289,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(paramod,[status(thm)],[c_22,c_288]) ).
cnf(c_290,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(paramod,[status(thm)],[c_28,c_289]) ).
cnf(c_39,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_31,c_290]) ).
cnf(c_291,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity))) = identity,
inference(paramod,[status(thm)],[c_21,c_34]) ).
cnf(c_40,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(paramod,[status(thm)],[c_37,c_291]) ).
cnf(c_292,plain,
double_divide(identity,A) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_39,c_30]) ).
cnf(c_42,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(identity,A),
inference(copy,[status(thm)],[c_292]) ).
cnf(c_44,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_45,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(double_divide(B,identity),double_divide(identity,double_divide(A,identity)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_42,c_38]) ).
cnf(c_48,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),identity)) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_42,c_33]) ).
cnf(c_50,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_42,c_31]) ).
cnf(c_51,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_50,c_21]) ).
cnf(c_293,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_50,c_42]) ).
cnf(c_52,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_293]) ).
cnf(c_53,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_52,c_48]) ).
cnf(c_54,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_52,c_39]) ).
cnf(c_294,plain,
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_52,c_7]) ).
cnf(c_295,plain,
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_52,c_294]) ).
cnf(c_296,plain,
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_52,c_295]) ).
cnf(c_55,plain,
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_52,c_296]) ).
cnf(c_297,plain,
double_divide(A,double_divide(double_divide(B,identity),double_divide(identity,double_divide(A,identity)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_54,c_45]) ).
cnf(c_59,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_54,c_297]) ).
cnf(c_298,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(double_divide(identity,double_divide(B,A)),identity),
inference(paramod,[status(thm)],[c_44,c_51]) ).
cnf(c_299,plain,
double_divide(A,B) = double_divide(double_divide(identity,double_divide(B,A)),identity),
inference(paramod,[status(thm)],[c_54,c_298]) ).
cnf(c_300,plain,
double_divide(A,B) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(paramod,[status(thm)],[c_52,c_299]) ).
cnf(c_66,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_50,c_300]) ).
cnf(c_301,plain,
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_66,c_55]) ).
cnf(c_302,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(b3,a3)))),
inference(paramod,[status(thm)],[c_66,c_301]) ).
cnf(c_303,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(paramod,[status(thm)],[c_66,c_302]) ).
cnf(c_74,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_75,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(B,A))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_50,c_53]) ).
cnf(c_304,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,B),identity),A)) = B,
inference(paramod,[status(thm)],[c_50,c_59]) ).
cnf(c_305,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,B)),A)) = B,
inference(paramod,[status(thm)],[c_66,c_304]) ).
cnf(c_85,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_50,c_305]) ).
cnf(c_91,plain,
double_divide(double_divide(A,B),double_divide(double_divide(C,A),double_divide(B,identity))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_85,c_51]) ).
cnf(c_93,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_66,c_85]) ).
cnf(c_97,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_75,c_93]) ).
cnf(c_306,plain,
double_divide(identity,double_divide(A,B)) = double_divide(double_divide(identity,A),double_divide(identity,B)),
inference(paramod,[status(thm)],[c_97,c_66]) ).
cnf(c_135,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(identity,double_divide(A,B)),
inference(copy,[status(thm)],[c_306]) ).
cnf(c_145,plain,
double_divide(double_divide(A,identity),double_divide(identity,B)) = double_divide(identity,double_divide(A,B)),
inference(paramod,[status(thm)],[c_66,c_135]) ).
cnf(c_160,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(paramod,[status(thm)],[c_93,c_145]) ).
cnf(c_192,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_91,c_93]) ).
cnf(c_307,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(A,identity),double_divide(B,C)),
inference(paramod,[status(thm)],[c_192,c_66]) ).
cnf(c_256,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))),
inference(paramod,[status(thm)],[c_160,c_307]) ).
cnf(c_308,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_192,c_66]) ).
cnf(c_309,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(B,identity),double_divide(C,A)),
inference(paramod,[status(thm)],[c_256,c_308]) ).
cnf(c_310,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(C,A)))),
inference(paramod,[status(thm)],[c_160,c_309]) ).
cnf(c_257,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(copy,[status(thm)],[c_310]) ).
cnf(c_311,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_74]) ).
cnf(c_258,plain,
$false,
inference(resolve,[status(thm)],[c_257,c_311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 15:02:37 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 476204 was started by sandbox on n003,
% 0.16/0.43 % Fri Sep 25 15:02:37 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.20/0.55
% 0.20/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.55
% 0.20/0.55 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.20/0.55 % Length of proof is 51.
% 0.20/0.55 % Level of proof is 23.
% 0.20/0.55 % Maximum clause weight is 96.000.
% 0.20/0.55 % Given clauses 41.
% 0.20/0.55
% 0.20/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------