%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP075-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:27:06 AM UTC 2026
% Result : Unsatisfiable 1.10s 0.57s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 5
% Syntax : Number of formulae : 116 ( 96 unt; 0 def)
% Number of atoms : 148 ( 147 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 58 ~; 32 |; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : double_divide(double_divide(double_divide(VAR_0,double_divide(VAR_1,identity)),double_divide(double_divide(VAR_2,double_divide(VAR_3,double_divide(VAR_3,identity))),double_divide(VAR_0,identity))),VAR_1) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = 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_181,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_181]) ).
fof(prove_these_axioms,axiom,
( 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(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_182,plain,
( 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_183,plain,
( 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_182]) ).
cnf(c_184,plain,
( 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_183]) ).
cnf(c_185,plain,
( 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_184]) ).
cnf(c_186,plain,
( 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_185]) ).
cnf(c_187,plain,
( 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_186]) ).
cnf(c_188,plain,
( 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_187]) ).
cnf(c_189,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)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_188]) ).
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)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,identity),double_divide(A,identity))),B) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))),B) = identity,
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_10,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),B) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_14,plain,
double_divide(double_divide(identity,identity),double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_16,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(identity,double_divide(double_divide(C,identity),double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_10,c_8]) ).
cnf(c_19,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,identity)),double_divide(B,double_divide(A,identity))),double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity)))) = identity,
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_22,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_23,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity)))) = A,
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_24,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(identity,identity))) = A,
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_25,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_14,c_5]) ).
cnf(c_190,plain,
double_divide(double_divide(identity,identity),A) = double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_191,plain,
double_divide(identity,A) = double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_25,c_190]) ).
cnf(c_192,plain,
double_divide(identity,A) = double_divide(identity,double_divide(double_divide(A,identity),identity)),
inference(paramod,[status(thm)],[c_25,c_191]) ).
cnf(c_30,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,A),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A,
inference(paramod,[status(thm)],[c_25,c_24]) ).
cnf(c_31,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_30,c_193]) ).
cnf(c_194,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(identity,double_divide(double_divide(B,identity),identity))) = A,
inference(paramod,[status(thm)],[c_25,c_23]) ).
cnf(c_32,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(B,identity)) = A,
inference(paramod,[status(thm)],[c_31,c_194]) ).
cnf(c_195,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(identity,double_divide(double_divide(A,identity),identity)),
inference(paramod,[status(thm)],[c_25,c_22]) ).
cnf(c_33,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_31,c_195]) ).
cnf(c_196,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(A,identity))),double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity)))) = identity,
inference(paramod,[status(thm)],[c_25,c_19]) ).
cnf(c_197,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(A,identity))),double_divide(identity,double_divide(double_divide(B,identity),identity))) = identity,
inference(paramod,[status(thm)],[c_25,c_196]) ).
cnf(c_36,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(A,identity))),double_divide(B,identity)) = identity,
inference(paramod,[status(thm)],[c_31,c_197]) ).
cnf(c_198,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(identity,double_divide(double_divide(C,identity),identity)),
inference(paramod,[status(thm)],[c_25,c_16]) ).
cnf(c_39,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_31,c_198]) ).
cnf(c_199,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)
| double_divide(double_divide(a2,identity),identity) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_25,c_7]) ).
cnf(c_42,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)
| double_divide(double_divide(a2,identity),identity) != a2 ),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_200,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_31,c_30]) ).
cnf(c_43,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_201,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)
| double_divide(double_divide(identity,a2),identity) != a2 ),
inference(paramod,[status(thm)],[c_43,c_42]) ).
cnf(c_202,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)
| double_divide(identity,double_divide(identity,a2)) != a2 ),
inference(paramod,[status(thm)],[c_43,c_201]) ).
cnf(c_203,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)
| double_divide(identity,double_divide(identity,a2)) != a2 ),
inference(paramod,[status(thm)],[c_43,c_202]) ).
cnf(c_204,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)
| double_divide(identity,double_divide(identity,a2)) != a2 ),
inference(paramod,[status(thm)],[c_43,c_203]) ).
cnf(c_205,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)
| double_divide(identity,double_divide(identity,a2)) != a2 ),
inference(paramod,[status(thm)],[c_43,c_204]) ).
cnf(c_44,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))))
| double_divide(identity,double_divide(identity,a2)) != a2 ),
inference(paramod,[status(thm)],[c_43,c_205]) ).
cnf(c_45,plain,
multiply(A,B) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_43,c_2]) ).
cnf(c_47,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_43,c_31]) ).
cnf(c_206,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))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_47,c_44]) ).
cnf(c_48,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(copy,[status(thm)],[c_206]) ).
cnf(c_207,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),identity),
inference(paramod,[status(thm)],[c_32,c_33]) ).
cnf(c_208,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),B))),
inference(paramod,[status(thm)],[c_43,c_207]) ).
cnf(c_52,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(paramod,[status(thm)],[c_47,c_208]) ).
cnf(c_209,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),B)),double_divide(B,identity)) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_52,c_32]) ).
cnf(c_210,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),B)),double_divide(B,identity)) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_43,c_209]) ).
cnf(c_53,plain,
double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity)) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_31,c_210]) ).
cnf(c_211,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),double_divide(B,double_divide(double_divide(identity,A),identity))),double_divide(B,identity)) = identity,
inference(paramod,[status(thm)],[c_52,c_36]) ).
cnf(c_212,plain,
double_divide(double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,double_divide(double_divide(identity,A),identity))),double_divide(B,identity)) = identity,
inference(paramod,[status(thm)],[c_43,c_211]) ).
cnf(c_213,plain,
double_divide(double_divide(A,double_divide(B,double_divide(double_divide(identity,A),identity))),double_divide(B,identity)) = identity,
inference(paramod,[status(thm)],[c_31,c_212]) ).
cnf(c_214,plain,
double_divide(double_divide(A,double_divide(B,double_divide(identity,double_divide(identity,A)))),double_divide(B,identity)) = identity,
inference(paramod,[status(thm)],[c_43,c_213]) ).
cnf(c_61,plain,
double_divide(double_divide(A,double_divide(B,A)),double_divide(B,identity)) = identity,
inference(paramod,[status(thm)],[c_47,c_214]) ).
cnf(c_215,plain,
double_divide(double_divide(identity,identity),A) = double_divide(double_divide(B,double_divide(A,B)),identity),
inference(paramod,[status(thm)],[c_61,c_33]) ).
cnf(c_216,plain,
double_divide(identity,A) = double_divide(double_divide(B,double_divide(A,B)),identity),
inference(paramod,[status(thm)],[c_25,c_215]) ).
cnf(c_217,plain,
double_divide(identity,A) = double_divide(identity,double_divide(B,double_divide(A,B))),
inference(paramod,[status(thm)],[c_43,c_216]) ).
cnf(c_64,plain,
double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(identity,B),
inference(copy,[status(thm)],[c_217]) ).
cnf(c_218,plain,
double_divide(identity,double_divide(identity,A)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_64,c_47]) ).
cnf(c_219,plain,
A = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_47,c_218]) ).
cnf(c_69,plain,
double_divide(A,double_divide(B,A)) = B,
inference(copy,[status(thm)],[c_219]) ).
cnf(c_220,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,double_divide(A,identity)))),
inference(paramod,[status(thm)],[c_33,c_64]) ).
cnf(c_70,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_47,c_220]) ).
cnf(c_221,plain,
A = double_divide(double_divide(B,identity),double_divide(A,double_divide(identity,B))),
inference(paramod,[status(thm)],[c_69,c_52]) ).
cnf(c_74,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(copy,[status(thm)],[c_221]) ).
cnf(c_76,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_69,c_69]) ).
cnf(c_78,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = B,
inference(paramod,[status(thm)],[c_52,c_76]) ).
cnf(c_222,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_74,c_76]) ).
cnf(c_79,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(copy,[status(thm)],[c_222]) ).
cnf(c_223,plain,
multiply(double_divide(identity,A),B) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_79,c_45]) ).
cnf(c_224,plain,
double_divide(identity,double_divide(B,double_divide(identity,A))) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_45,c_223]) ).
cnf(c_80,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_70,c_224]) ).
cnf(c_225,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),double_divide(c3,identity)),
inference(paramod,[status(thm)],[c_80,c_48]) ).
cnf(c_83,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(paramod,[status(thm)],[c_43,c_225]) ).
cnf(c_226,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(double_divide(C,double_divide(double_divide(identity,A),identity)),double_divide(B,double_divide(C,identity))),
inference(paramod,[status(thm)],[c_39,c_74]) ).
cnf(c_227,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(double_divide(C,double_divide(identity,double_divide(identity,A))),double_divide(B,double_divide(C,identity))),
inference(paramod,[status(thm)],[c_43,c_226]) ).
cnf(c_228,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(double_divide(C,A),double_divide(B,double_divide(C,identity))),
inference(paramod,[status(thm)],[c_47,c_227]) ).
cnf(c_93,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(A,identity))) = double_divide(double_divide(B,identity),double_divide(C,identity)),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_229,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(double_divide(double_divide(C,double_divide(double_divide(D,identity),identity)),double_divide(A,double_divide(C,identity))),identity))),D) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_39,c_39]) ).
cnf(c_230,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(double_divide(double_divide(C,double_divide(identity,double_divide(D,identity))),double_divide(A,double_divide(C,identity))),identity))),D) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_43,c_229]) ).
cnf(c_231,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(double_divide(double_divide(C,D),double_divide(A,double_divide(C,identity))),identity))),D) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_69,c_230]) ).
cnf(c_232,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(double_divide(double_divide(D,identity),double_divide(A,identity)),identity))),D) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_93,c_231]) ).
cnf(c_233,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(D,identity),double_divide(A,identity))))),D) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_43,c_232]) ).
cnf(c_234,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(A,double_divide(double_divide(D,identity),identity)))),D) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_70,c_233]) ).
cnf(c_235,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(A,double_divide(identity,double_divide(D,identity))))),D) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_43,c_234]) ).
cnf(c_94,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(A,C))),C) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_69,c_235]) ).
cnf(c_236,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),identity)) = double_divide(identity,double_divide(double_divide(identity,B),A)),
inference(paramod,[status(thm)],[c_78,c_53]) ).
cnf(c_237,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(double_divide(identity,B),A)),
inference(paramod,[status(thm)],[c_43,c_236]) ).
cnf(c_238,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(double_divide(identity,B),A)),
inference(paramod,[status(thm)],[c_69,c_237]) ).
cnf(c_100,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(double_divide(identity,B),A),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_239,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(paramod,[status(thm)],[c_100,c_83]) ).
cnf(c_104,plain,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(copy,[status(thm)],[c_239]) ).
cnf(c_240,plain,
double_divide(A,double_divide(B,identity)) = double_divide(double_divide(C,identity),double_divide(B,double_divide(C,A))),
inference(paramod,[status(thm)],[c_94,c_69]) ).
cnf(c_132,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(A,C))) = double_divide(C,double_divide(B,identity)),
inference(copy,[status(thm)],[c_240]) ).
cnf(c_163,plain,
double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_69,c_132]) ).
cnf(c_167,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_43,c_163]) ).
cnf(c_179,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(identity,B)),
inference(paramod,[status(thm)],[c_43,c_167]) ).
cnf(c_241,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_180,plain,
$false,
inference(resolve,[status(thm)],[c_179,c_241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP075-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n015.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 14:24:27 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.42 % Process 1562193 was started by sandbox on n015,
% 0.14/0.42 % Fri Sep 25 14:24:27 2026
% 0.14/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.42
% 0.14/0.42 % From the command line: assign(max_seconds, 300).
% 1.10/0.57
% 1.10/0.57 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 1.10/0.57
% 1.10/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.10/0.57
% 1.10/0.57 % Proof 1 at 0.09 (+ 0.04) seconds.
% 1.10/0.57 % Length of proof is 50.
% 1.10/0.57 % Level of proof is 21.
% 1.10/0.57 % Maximum clause weight is 96.000.
% 1.10/0.57 % Given clauses 48.
% 1.10/0.57
% 1.10/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------