%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 07:29:52 AM UTC 2026
% Result : Unsatisfiable 0.94s 0.58s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 107 ( 107 unt; 0 def)
% Number of atoms : 107 ( 106 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 14 ( 3 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 : 250 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(VAR_0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(VAR_0,identity),double_divide(VAR_1,VAR_2))),VAR_1),identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),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_293,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_293]) ).
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_294,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_295,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_294]) ).
cnf(c_296,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_295]) ).
cnf(c_297,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_296]) ).
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_297]) ).
cnf(c_298,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),C),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(C,identity),double_divide(D,B))),D),identity),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = double_divide(D,double_divide(double_divide(double_divide(identity,double_divide(double_divide(D,identity),C)),A),identity)),
inference(copy,[status(thm)],[c_298]) ).
cnf(c_10,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),B),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_21,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),identity),double_divide(C,D))),C),identity),identity),double_divide(E,B))),E),identity) = double_divide(A,double_divide(D,identity)),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_299,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity) = double_divide(B,double_divide(double_divide(double_divide(identity,double_divide(double_divide(B,identity),identity)),A),identity)),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_25,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_10,c_299]) ).
cnf(c_27,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),identity),identity),double_divide(C,B))),C),identity) = double_divide(A,double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_35,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(C,identity),identity),D)),E),identity)))),B),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F),identity)),A),identity)),
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_39,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C,
inference(paramod,[status(thm)],[c_25,c_1]) ).
cnf(c_300,plain,
double_divide(A,identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),double_divide(B,A))),B),identity),
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_41,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),double_divide(A,B))),A),identity) = double_divide(B,identity),
inference(copy,[status(thm)],[c_300]) ).
cnf(c_301,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),identity),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_43,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(copy,[status(thm)],[c_301]) ).
cnf(c_302,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),double_divide(double_divide(identity,identity),double_divide(B,identity))),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(C,identity),identity)),A),identity)),
inference(paramod,[status(thm)],[c_25,c_8]) ).
cnf(c_45,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),double_divide(double_divide(identity,identity),double_divide(B,identity))),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_10,c_302]) ).
cnf(c_303,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),C)),A),identity),
inference(paramod,[status(thm)],[c_8,c_25]) ).
cnf(c_48,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),A),identity),
inference(paramod,[status(thm)],[c_43,c_303]) ).
cnf(c_49,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(A,B))),A),identity) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_52,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,double_divide(double_divide(B,identity),C))),identity),double_divide(D,C))),D),identity) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_48,c_21]) ).
cnf(c_304,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(A,B))),A),identity)) = B,
inference(paramod,[status(thm)],[c_43,c_1]) ).
cnf(c_54,plain,
double_divide(double_divide(identity,identity),double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_49,c_304]) ).
cnf(c_305,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),A),identity)),
inference(paramod,[status(thm)],[c_43,c_8]) ).
cnf(c_58,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),A),
inference(paramod,[status(thm)],[c_54,c_305]) ).
cnf(c_306,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),B),identity) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),A),identity)),
inference(paramod,[status(thm)],[c_43,c_8]) ).
cnf(c_307,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),A) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),A),identity)),
inference(paramod,[status(thm)],[c_58,c_306]) ).
cnf(c_308,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),A) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),A),identity)),
inference(paramod,[status(thm)],[c_43,c_307]) ).
cnf(c_309,plain,
double_divide(identity,A) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),A),identity)),
inference(paramod,[status(thm)],[c_5,c_308]) ).
cnf(c_310,plain,
double_divide(identity,A) = double_divide(identity,double_divide(double_divide(identity,A),identity)),
inference(paramod,[status(thm)],[c_5,c_309]) ).
cnf(c_59,plain,
double_divide(identity,double_divide(double_divide(identity,A),identity)) = double_divide(identity,A),
inference(copy,[status(thm)],[c_310]) ).
cnf(c_311,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),B),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_54,c_45]) ).
cnf(c_312,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_58,c_311]) ).
cnf(c_313,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_43,c_312]) ).
cnf(c_61,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_5,c_313]) ).
cnf(c_314,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C,
inference(paramod,[status(thm)],[c_54,c_39]) ).
cnf(c_63,plain,
double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B))) = C,
inference(paramod,[status(thm)],[c_61,c_314]) ).
cnf(c_315,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,double_divide(double_divide(B,identity),C)))),double_divide(D,C))),D),identity) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_61,c_52]) ).
cnf(c_66,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,double_divide(double_divide(B,identity),C)))),double_divide(D,C))),D)) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_61,c_315]) ).
cnf(c_316,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),D)),E),identity)))),B),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F),identity)),A),identity)),
inference(paramod,[status(thm)],[c_61,c_35]) ).
cnf(c_317,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),D)),E))))),B),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F),identity)),A),identity)),
inference(paramod,[status(thm)],[c_61,c_316]) ).
cnf(c_318,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),D)),E))))),B)) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F),identity)),A),identity)),
inference(paramod,[status(thm)],[c_61,c_317]) ).
cnf(c_319,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),D)),E))))),B)) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F))),A),identity)),
inference(paramod,[status(thm)],[c_61,c_318]) ).
cnf(c_72,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,identity)),D)),E))))),B)) = double_divide(C,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F))),A))),
inference(paramod,[status(thm)],[c_61,c_319]) ).
cnf(c_320,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),B))),identity),double_divide(C,B))),C),identity) = double_divide(A,double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_61,c_27]) ).
cnf(c_321,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),B)))),double_divide(C,B))),C),identity) = double_divide(A,double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_61,c_320]) ).
cnf(c_77,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),B)))),double_divide(C,B))),C)) = double_divide(A,double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_61,c_321]) ).
cnf(c_94,plain,
double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_322,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),A),
inference(paramod,[status(thm)],[c_61,c_58]) ).
cnf(c_95,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),B) = double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,A))),C)),
inference(copy,[status(thm)],[c_322]) ).
cnf(c_323,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_61,c_43]) ).
cnf(c_324,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_323]) ).
cnf(c_97,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_324]) ).
cnf(c_325,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_61,c_7]) ).
cnf(c_326,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_61,c_325]) ).
cnf(c_327,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_61,c_326]) ).
cnf(c_99,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_61,c_327]) ).
cnf(c_328,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(C,B))),C)) = double_divide(A,double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_94,c_77]) ).
cnf(c_102,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(C,B))),C)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_97,c_328]) ).
cnf(c_329,plain,
double_divide(double_divide(identity,double_divide(identity,A)),B) = double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,A))),C)),
inference(paramod,[status(thm)],[c_97,c_95]) ).
cnf(c_104,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) = double_divide(double_divide(identity,double_divide(identity,C)),A),
inference(copy,[status(thm)],[c_329]) ).
cnf(c_112,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(B,identity),C)))),double_divide(D,C))),D)) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_97,c_66]) ).
cnf(c_114,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_97,c_54]) ).
cnf(c_330,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(C,D)),E))))),B)) = double_divide(C,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F))),A))),
inference(paramod,[status(thm)],[c_114,c_72]) ).
cnf(c_331,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(C,D)),E)))),A) = double_divide(C,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F))),A))),
inference(paramod,[status(thm)],[c_104,c_330]) ).
cnf(c_332,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(C,D)),E)),A) = double_divide(C,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(E,identity),double_divide(F,D))),F))),A))),
inference(paramod,[status(thm)],[c_94,c_331]) ).
cnf(c_125,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),C)),D) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,B)),C)),D))),
inference(paramod,[status(thm)],[c_104,c_332]) ).
cnf(c_126,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,B)),A)) = B,
inference(paramod,[status(thm)],[c_104,c_63]) ).
cnf(c_132,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_61,c_114]) ).
cnf(c_136,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_132,c_126]) ).
cnf(c_137,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),C)),D) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),D))),
inference(paramod,[status(thm)],[c_132,c_125]) ).
cnf(c_333,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(B,identity),C)))),double_divide(D,C))),D)) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_132,c_112]) ).
cnf(c_334,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(B,identity),C)),double_divide(D,C))),D)))) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_137,c_333]) ).
cnf(c_335,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,double_divide(double_divide(identity,double_divide(C,double_divide(D,C))),D)))))) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_137,c_334]) ).
cnf(c_145,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,double_divide(double_divide(identity,C),C)))))) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_136,c_335]) ).
cnf(c_336,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,double_divide(double_divide(identity,double_divide(B,double_divide(C,B))),C)))) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_137,c_102]) ).
cnf(c_149,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,double_divide(double_divide(identity,B),B)))) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_136,c_336]) ).
cnf(c_150,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_149,c_145]) ).
cnf(c_337,plain,
inverse(double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),C))) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),identity))),
inference(paramod,[status(thm)],[c_137,c_3]) ).
cnf(c_338,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),C)),identity) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),identity))),
inference(paramod,[status(thm)],[c_3,c_337]) ).
cnf(c_339,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),C))) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),identity))),
inference(paramod,[status(thm)],[c_61,c_338]) ).
cnf(c_340,plain,
double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),identity))),
inference(paramod,[status(thm)],[c_132,c_339]) ).
cnf(c_341,plain,
double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(B,C))))),
inference(paramod,[status(thm)],[c_61,c_340]) ).
cnf(c_250,plain,
double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))),
inference(paramod,[status(thm)],[c_132,c_341]) ).
cnf(c_342,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,double_divide(B,C)),identity)),D) = double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(C,double_divide(A,identity))),D))),
inference(paramod,[status(thm)],[c_150,c_137]) ).
cnf(c_343,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(identity,double_divide(B,C)))),D) = double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(C,double_divide(A,identity))),D))),
inference(paramod,[status(thm)],[c_61,c_342]) ).
cnf(c_344,plain,
double_divide(double_divide(A,double_divide(B,C)),D) = double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(C,double_divide(A,identity))),D))),
inference(paramod,[status(thm)],[c_132,c_343]) ).
cnf(c_277,plain,
double_divide(double_divide(A,double_divide(B,C)),D) = double_divide(B,double_divide(identity,double_divide(C,double_divide(identity,double_divide(double_divide(A,identity),D))))),
inference(paramod,[status(thm)],[c_250,c_344]) ).
cnf(c_345,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,double_divide(identity,double_divide(double_divide(identity,identity),a3)))))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_277,c_99]) ).
cnf(c_346,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,double_divide(identity,double_divide(identity,a3)))))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_97,c_345]) ).
cnf(c_347,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_132,c_346]) ).
cnf(c_292,plain,
$false,
inference(copy,[status(thm)],[c_347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.44 % Computer : n020.cluster.edu
% 0.14/0.44 % Model : x86_64 x86_64
% 0.14/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.44 % Memory : 8046.5625MB
% 0.14/0.44 % OS : Linux 6.8.0-71-generic
% 0.14/0.44 % CPULimit : 300
% 0.14/0.44 % WCLimit : 300
% 0.14/0.44 % DateTime : Fri Sep 25 14:57:19 UTC 2026
% 0.14/0.44 % CPUTime :
% 0.14/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.44 % Process 3201610 was started by sandbox2 on n020,
% 0.14/0.44 % Fri Sep 25 14:57:19 2026
% 0.14/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.45
% 0.14/0.45 % From the command line: assign(max_seconds, 300).
% 0.94/0.58
% 0.94/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.94/0.58
% 0.94/0.58 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.94/0.58 % Length of proof is 47.
% 0.94/0.58 % Level of proof is 16.
% 0.94/0.58 % Maximum clause weight is 47.000.
% 0.94/0.58 % Given clauses 32.
% 0.94/0.58
% 0.94/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------