%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP583-1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:30:25 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.64s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 5
% Syntax : Number of formulae : 122 ( 122 unt; 0 def)
% Number of atoms : 122 ( 121 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 24 ( 24 ~; 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 : 153 ( 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_288,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_288]) ).
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_289,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_290,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_289]) ).
cnf(c_291,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_290]) ).
cnf(c_292,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_291]) ).
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_292]) ).
cnf(c_8,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_11,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_12,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(C,double_divide(identity,identity)),double_divide(B,A)))) = C,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_15,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(B,double_divide(identity,double_divide(A,double_divide(double_divide(identity,identity),B)))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_17,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_5,c_8]) ).
cnf(c_293,plain,
double_divide(identity,double_divide(double_divide(identity,A),identity)) = double_divide(B,double_divide(identity,double_divide(A,double_divide(double_divide(identity,identity),B)))),
inference(paramod,[status(thm)],[c_17,c_15]) ).
cnf(c_21,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))) = double_divide(identity,double_divide(double_divide(identity,B),identity)),
inference(copy,[status(thm)],[c_293]) ).
cnf(c_294,plain,
double_divide(identity,double_divide(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_17,c_8]) ).
cnf(c_22,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(copy,[status(thm)],[c_294]) ).
cnf(c_24,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),identity)) = A,
inference(paramod,[status(thm)],[c_22,c_12]) ).
cnf(c_295,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_11]) ).
cnf(c_296,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_295]) ).
cnf(c_297,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_296]) ).
cnf(c_25,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_297]) ).
cnf(c_26,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_25,c_24]) ).
cnf(c_27,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(identity,double_divide(double_divide(identity,B),identity)),
inference(paramod,[status(thm)],[c_25,c_21]) ).
cnf(c_298,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_25,c_17]) ).
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_25,c_298]) ).
cnf(c_29,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(paramod,[status(thm)],[c_25,c_11]) ).
cnf(c_31,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
inference(paramod,[status(thm)],[c_29,c_5]) ).
cnf(c_299,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_26,c_28]) ).
cnf(c_32,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_26,c_299]) ).
cnf(c_300,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_26,c_28]) ).
cnf(c_301,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_32,c_300]) ).
cnf(c_34,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_32,c_301]) ).
cnf(c_36,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(paramod,[status(thm)],[c_32,c_31]) ).
cnf(c_38,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(paramod,[status(thm)],[c_32,c_27]) ).
cnf(c_39,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_32,c_22]) ).
cnf(c_41,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,identity))) = identity,
inference(paramod,[status(thm)],[c_32,c_5]) ).
cnf(c_302,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_41,c_38]) ).
cnf(c_303,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_25,c_302]) ).
cnf(c_304,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_32,c_303]) ).
cnf(c_42,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = double_divide(double_divide(A,identity),identity),
inference(copy,[status(thm)],[c_304]) ).
cnf(c_43,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),double_divide(identity,double_divide(B,A))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_34,c_38]) ).
cnf(c_305,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity)),
inference(paramod,[status(thm)],[c_42,c_32]) ).
cnf(c_306,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity))),
inference(paramod,[status(thm)],[c_32,c_305]) ).
cnf(c_307,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity)))),
inference(paramod,[status(thm)],[c_32,c_306]) ).
cnf(c_48,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_34,c_307]) ).
cnf(c_51,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),double_divide(B,double_divide(identity,double_divide(A,identity))))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_32,c_39]) ).
cnf(c_308,plain,
double_divide(A,double_divide(double_divide(identity,B),identity)) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(B,A),identity))),identity))),
inference(paramod,[status(thm)],[c_36,c_39]) ).
cnf(c_309,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(B,A),identity))),identity))),
inference(paramod,[status(thm)],[c_32,c_308]) ).
cnf(c_310,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(B,A),identity)),identity)))),
inference(paramod,[status(thm)],[c_32,c_309]) ).
cnf(c_311,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(B,A),identity),identity))))),
inference(paramod,[status(thm)],[c_32,c_310]) ).
cnf(c_312,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(paramod,[status(thm)],[c_34,c_311]) ).
cnf(c_54,plain,
double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(copy,[status(thm)],[c_312]) ).
cnf(c_313,plain,
multiply(double_divide(identity,double_divide(A,B)),identity) = double_divide(double_divide(B,double_divide(identity,double_divide(A,identity))),identity),
inference(paramod,[status(thm)],[c_54,c_2]) ).
cnf(c_314,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),identity) = double_divide(double_divide(B,double_divide(identity,double_divide(A,identity))),identity),
inference(paramod,[status(thm)],[c_2,c_313]) ).
cnf(c_315,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),identity)) = double_divide(double_divide(B,double_divide(identity,double_divide(A,identity))),identity),
inference(paramod,[status(thm)],[c_32,c_314]) ).
cnf(c_316,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,B),identity))) = double_divide(double_divide(B,double_divide(identity,double_divide(A,identity))),identity),
inference(paramod,[status(thm)],[c_32,c_315]) ).
cnf(c_61,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(B,A),identity))),
inference(copy,[status(thm)],[c_316]) ).
cnf(c_317,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity))),
inference(paramod,[status(thm)],[c_36,c_54]) ).
cnf(c_318,plain,
double_divide(identity,identity) = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity))),
inference(paramod,[status(thm)],[c_25,c_317]) ).
cnf(c_319,plain,
identity = double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity))),
inference(paramod,[status(thm)],[c_25,c_318]) ).
cnf(c_320,plain,
identity = double_divide(A,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))))),
inference(paramod,[status(thm)],[c_61,c_319]) ).
cnf(c_321,plain,
identity = double_divide(A,double_divide(identity,A)),
inference(paramod,[status(thm)],[c_34,c_320]) ).
cnf(c_67,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(copy,[status(thm)],[c_321]) ).
cnf(c_322,plain,
double_divide(A,double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_67,c_38]) ).
cnf(c_323,plain,
double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_25,c_322]) ).
cnf(c_79,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(A,identity),
inference(copy,[status(thm)],[c_323]) ).
cnf(c_89,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_79,c_61]) ).
cnf(c_96,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),double_divide(B,double_divide(identity,double_divide(A,identity))))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_79,c_51]) ).
cnf(c_99,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),double_divide(identity,double_divide(B,A))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_79,c_43]) ).
cnf(c_101,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_79,c_39]) ).
cnf(c_104,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_79,c_34]) ).
cnf(c_105,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(B,A))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_104,c_99]) ).
cnf(c_324,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_104,c_48]) ).
cnf(c_116,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_324]) ).
cnf(c_118,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_116,c_104]) ).
cnf(c_325,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_118,c_89]) ).
cnf(c_326,plain,
double_divide(identity,double_divide(A,B)) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_116,c_325]) ).
cnf(c_119,plain,
double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_116,c_326]) ).
cnf(c_327,plain,
double_divide(identity,double_divide(identity,A)) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_116,c_32]) ).
cnf(c_123,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_118,c_327]) ).
cnf(c_328,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_116,c_7]) ).
cnf(c_329,plain,
double_divide(double_divide(double_divide(identity,double_divide(b3,c3)),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(paramod,[status(thm)],[c_119,c_328]) ).
cnf(c_330,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(b3,c3)),a3)) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(paramod,[status(thm)],[c_116,c_329]) ).
cnf(c_331,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(paramod,[status(thm)],[c_119,c_330]) ).
cnf(c_332,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity),
inference(paramod,[status(thm)],[c_116,c_331]) ).
cnf(c_333,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(double_divide(c3,double_divide(identity,double_divide(a3,b3))),identity),
inference(paramod,[status(thm)],[c_119,c_332]) ).
cnf(c_334,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_116,c_333]) ).
cnf(c_124,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_334]) ).
cnf(c_335,plain,
double_divide(identity,double_divide(A,double_divide(B,double_divide(identity,double_divide(A,identity))))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_123,c_96]) ).
cnf(c_128,plain,
double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_118,c_335]) ).
cnf(c_336,plain,
double_divide(A,B) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_123,c_54]) ).
cnf(c_130,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_118,c_336]) ).
cnf(c_337,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_128,c_123]) ).
cnf(c_338,plain,
A = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_118,c_337]) ).
cnf(c_141,plain,
double_divide(A,double_divide(B,A)) = B,
inference(copy,[status(thm)],[c_338]) ).
cnf(c_142,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_130,c_141]) ).
cnf(c_148,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_141,c_101]) ).
cnf(c_155,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_105,c_142]) ).
cnf(c_339,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_142,c_155]) ).
cnf(c_161,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(A,identity)),
inference(copy,[status(thm)],[c_339]) ).
cnf(c_340,plain,
double_divide(double_divide(a3,b3),double_divide(c3,identity)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_161,c_124]) ).
cnf(c_341,plain,
double_divide(double_divide(a3,b3),double_divide(identity,c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_130,c_340]) ).
cnf(c_342,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_130,c_341]) ).
cnf(c_343,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),double_divide(a3,identity)),
inference(paramod,[status(thm)],[c_161,c_342]) ).
cnf(c_344,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),double_divide(identity,a3)),
inference(paramod,[status(thm)],[c_130,c_343]) ).
cnf(c_163,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_130,c_344]) ).
cnf(c_345,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_148,c_142]) ).
cnf(c_248,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_345]) ).
cnf(c_346,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_248,c_163]) ).
cnf(c_347,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_130,c_346]) ).
cnf(c_348,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_130,c_347]) ).
cnf(c_287,plain,
$false,
inference(copy,[status(thm)],[c_348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP583-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n017.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 14:56:03 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 2577851 was started by sandbox2 on n017,
% 0.20/0.46 % Fri Sep 25 14:56:03 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.24/0.64
% 0.24/0.64 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.24/0.64
% 0.24/0.64 % SZS status Unsatisfiable for theBenchmark
% 0.24/0.64
% 0.24/0.64 % Proof 1 at 0.10 (+ 0.05) seconds.
% 0.24/0.64 % Length of proof is 56.
% 0.24/0.64 % Level of proof is 22.
% 0.24/0.64 % Maximum clause weight is 93.000.
% 0.24/0.64 % Given clauses 63.
% 0.24/0.64
% 0.24/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------