%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP078-1 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:27:06 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.52s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 5
% Syntax : Number of formulae : 100 ( 80 unt; 0 def)
% Number of atoms : 138 ( 137 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 101 ( 63 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 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 : 132 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(identity,VAR_0),double_divide(identity,double_divide(double_divide(double_divide(VAR_0,VAR_1),identity),double_divide(VAR_2,VAR_1)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,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_216,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_216]) ).
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_217,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_218,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_217]) ).
cnf(c_219,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_218]) ).
cnf(c_220,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_219]) ).
cnf(c_221,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_220]) ).
cnf(c_222,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_221]) ).
cnf(c_223,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_222]) ).
cnf(c_224,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_223]) ).
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_224]) ).
cnf(c_8,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,double_divide(identity,double_divide(double_divide(double_divide(A,D),identity),double_divide(B,D))))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,double_divide(double_divide(double_divide(B,C),identity),double_divide(D,C)))),identity),D))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_13,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_14,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(B,identity),B))) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_15,plain,
double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),C),identity),double_divide(A,C))))))) = B,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_20,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,identity)),identity),double_divide(double_divide(B,identity),identity)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_225,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,identity),identity),identity),
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_226,plain,
identity = double_divide(double_divide(double_divide(identity,identity),identity),identity),
inference(paramod,[status(thm)],[c_5,c_225]) ).
cnf(c_21,plain,
double_divide(double_divide(double_divide(identity,identity),identity),identity) = identity,
inference(copy,[status(thm)],[c_226]) ).
cnf(c_227,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_21,c_1]) ).
cnf(c_23,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_5,c_227]) ).
cnf(c_24,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity))) = double_divide(double_divide(identity,identity),identity),
inference(paramod,[status(thm)],[c_21,c_1]) ).
cnf(c_228,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),identity),identity),double_divide(B,double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)))))) = B,
inference(paramod,[status(thm)],[c_21,c_8]) ).
cnf(c_27,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(B,double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)))))) = B,
inference(paramod,[status(thm)],[c_21,c_228]) ).
cnf(c_229,plain,
double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(double_divide(identity,identity),identity),
inference(paramod,[status(thm)],[c_21,c_23]) ).
cnf(c_230,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),identity),
inference(paramod,[status(thm)],[c_5,c_229]) ).
cnf(c_31,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_33,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity))) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_31,c_24]) ).
cnf(c_231,plain,
double_divide(double_divide(identity,identity),identity) = identity,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_35,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_31,c_231]) ).
cnf(c_36,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity))) = identity,
inference(paramod,[status(thm)],[c_35,c_33]) ).
cnf(c_232,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(double_divide(B,identity),identity)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_35,c_20]) ).
cnf(c_233,plain,
double_divide(B,identity) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_1,c_232]) ).
cnf(c_39,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_234,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),C),identity),double_divide(A,C))))))) = B,
inference(paramod,[status(thm)],[c_35,c_15]) ).
cnf(c_235,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(double_divide(identity,C),identity),double_divide(A,C))))))) = B,
inference(paramod,[status(thm)],[c_35,c_234]) ).
cnf(c_42,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,C)),double_divide(A,C))))))) = B,
inference(paramod,[status(thm)],[c_39,c_235]) ).
cnf(c_236,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_35,c_7]) ).
cnf(c_237,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
| identity != identity ),
inference(paramod,[status(thm)],[c_39,c_236]) ).
cnf(c_238,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
| identity != identity ),
inference(paramod,[status(thm)],[c_39,c_237]) ).
cnf(c_239,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
| identity != identity ),
inference(paramod,[status(thm)],[c_39,c_238]) ).
cnf(c_240,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
| identity != identity ),
inference(paramod,[status(thm)],[c_39,c_239]) ).
cnf(c_241,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
| identity != identity ),
inference(paramod,[status(thm)],[c_39,c_240]) ).
cnf(c_242,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
| identity != identity ),
inference(paramod,[status(thm)],[c_39,c_241]) ).
cnf(c_46,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(copy,[status(thm)],[c_242]) ).
cnf(c_243,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity))) = identity,
inference(paramod,[status(thm)],[c_39,c_36]) ).
cnf(c_244,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity))))) = identity,
inference(paramod,[status(thm)],[c_39,c_243]) ).
cnf(c_47,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(paramod,[status(thm)],[c_23,c_244]) ).
cnf(c_245,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(B,double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)))))) = B,
inference(paramod,[status(thm)],[c_39,c_27]) ).
cnf(c_246,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(B,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))))))) = B,
inference(paramod,[status(thm)],[c_39,c_245]) ).
cnf(c_50,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_23,c_246]) ).
cnf(c_247,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),double_divide(D,C)))),identity),D))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_39,c_9]) ).
cnf(c_53,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),double_divide(D,C))))),D))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_39,c_247]) ).
cnf(c_56,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),double_divide(C,B)))) = C,
inference(paramod,[status(thm)],[c_39,c_1]) ).
cnf(c_58,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,A)))) = A,
inference(paramod,[status(thm)],[c_39,c_23]) ).
cnf(c_60,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(paramod,[status(thm)],[c_39,c_47]) ).
cnf(c_248,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,identity)) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_60,c_14]) ).
cnf(c_249,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_35,c_248]) ).
cnf(c_61,plain,
double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_39,c_249]) ).
cnf(c_62,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_61,c_58]) ).
cnf(c_250,plain,
double_divide(A,double_divide(identity,double_divide(identity,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_62,c_50]) ).
cnf(c_67,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_62,c_250]) ).
cnf(c_251,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_62,c_46]) ).
cnf(c_70,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_251]) ).
cnf(c_252,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(C,double_divide(A,C))))))) = B,
inference(paramod,[status(thm)],[c_62,c_42]) ).
cnf(c_253,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))))) = B,
inference(paramod,[status(thm)],[c_67,c_252]) ).
cnf(c_72,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(paramod,[status(thm)],[c_62,c_253]) ).
cnf(c_254,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,double_divide(B,identity))))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_5,c_53]) ).
cnf(c_255,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),double_divide(identity,double_divide(B,identity))))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_35,c_254]) ).
cnf(c_256,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,identity))))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_67,c_255]) ).
cnf(c_78,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,B))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_67,c_256]) ).
cnf(c_91,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_67,c_67]) ).
cnf(c_93,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),D)))),double_divide(C,D)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_91,c_53]) ).
cnf(c_103,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_91,c_56]) ).
cnf(c_109,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),C)),double_divide(B,C)) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_103,c_93]) ).
cnf(c_133,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_67,c_78]) ).
cnf(c_257,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_72,c_78]) ).
cnf(c_258,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_67,c_257]) ).
cnf(c_135,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(identity,A)),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_146,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_135,c_70]) ).
cnf(c_259,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(double_divide(identity,B),A)),
inference(paramod,[status(thm)],[c_62,c_133]) ).
cnf(c_149,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(double_divide(identity,B),A),
inference(copy,[status(thm)],[c_259]) ).
cnf(c_260,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_149,c_146]) ).
cnf(c_151,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_260]) ).
cnf(c_154,plain,
double_divide(double_divide(double_divide(identity,A),double_divide(B,C)),double_divide(C,A)) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_149,c_109]) ).
cnf(c_261,plain,
double_divide(double_divide(A,B),double_divide(identity,C)) = double_divide(double_divide(identity,B),double_divide(C,A)),
inference(paramod,[status(thm)],[c_154,c_67]) ).
cnf(c_214,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(identity,B)),
inference(copy,[status(thm)],[c_261]) ).
cnf(c_262,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_151]) ).
cnf(c_215,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.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 14:23:49 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3482717 was started by sandbox on n002,
% 0.16/0.42 % Fri Sep 25 14:23:49 2026
% 0.16/0.42 % 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).
% 0.16/0.52
% 0.16/0.52 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 0.16/0.52
% 0.16/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.52
% 0.16/0.52 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.16/0.52 % Length of proof is 48.
% 0.16/0.52 % Level of proof is 18.
% 0.16/0.52 % Maximum clause weight is 99.000.
% 0.16/0.52 % Given clauses 48.
% 0.16/0.52
% 0.16/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------