%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 07:27:20 AM UTC 2026
% Result : Unsatisfiable 0.77s 0.56s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 5
% Syntax : Number of formulae : 139 ( 111 unt; 0 def)
% Number of atoms : 198 ( 197 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 89 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 251 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,double_divide(double_divide(VAR_1,double_divide(VAR_0,VAR_2)),double_divide(VAR_2,identity))),double_divide(identity,identity)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity)) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = double_divide(double_divide(VAR_1,VAR_0),identity),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = double_divide(double_divide(B,A),identity),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = double_divide(VAR_0,identity),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = double_divide(A,identity),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = double_divide(VAR_0,inverse(VAR_0)),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = double_divide(A,inverse(A)),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_428,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_428]) ).
fof(prove_these_axioms,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| 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(a4,b4) != multiply(b4,a4)
| 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_429,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_430,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_429]) ).
cnf(c_431,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_430]) ).
cnf(c_432,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_431]) ).
cnf(c_433,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_432]) ).
cnf(c_434,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_433]) ).
cnf(c_435,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_434]) ).
cnf(c_436,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_435]) ).
cnf(c_437,plain,
( double_divide(double_divide(b4,a4),identity) != multiply(b4,a4)
| 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_436]) ).
cnf(c_438,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_437]) ).
cnf(c_7,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_438]) ).
cnf(c_8,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_439,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(A,identity),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_439]) ).
cnf(c_440,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(B,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(identity,double_divide(A,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_1,c_440]) ).
cnf(c_12,plain,
double_divide(A,double_divide(double_divide(double_divide(B,double_divide(identity,identity)),double_divide(A,C)),double_divide(C,identity))) = B,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_441,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(A,double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_442,plain,
identity = double_divide(A,double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity))),
inference(paramod,[status(thm)],[c_10,c_441]) ).
cnf(c_13,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity))) = identity,
inference(copy,[status(thm)],[c_442]) ).
cnf(c_443,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(A,double_divide(identity,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_444,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(A,double_divide(identity,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_11,c_443]) ).
cnf(c_15,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_5,c_444]) ).
cnf(c_445,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(double_divide(identity,double_divide(C,double_divide(identity,identity))),double_divide(identity,identity))),double_divide(double_divide(double_divide(C,double_divide(B,D)),double_divide(D,identity)),identity))),
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_446,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(B,double_divide(double_divide(A,double_divide(double_divide(identity,double_divide(C,double_divide(identity,identity))),double_divide(identity,identity))),double_divide(double_divide(double_divide(C,double_divide(B,D)),double_divide(D,identity)),identity))),
inference(paramod,[status(thm)],[c_11,c_445]) ).
cnf(c_447,plain,
double_divide(A,identity) = double_divide(B,double_divide(double_divide(A,double_divide(double_divide(identity,double_divide(C,double_divide(identity,identity))),double_divide(identity,identity))),double_divide(double_divide(double_divide(C,double_divide(B,D)),double_divide(D,identity)),identity))),
inference(paramod,[status(thm)],[c_15,c_446]) ).
cnf(c_448,plain,
double_divide(A,identity) = double_divide(B,double_divide(double_divide(A,double_divide(identity,double_divide(double_divide(C,double_divide(identity,identity)),double_divide(identity,identity)))),double_divide(double_divide(double_divide(C,double_divide(B,D)),double_divide(D,identity)),identity))),
inference(paramod,[status(thm)],[c_11,c_447]) ).
cnf(c_449,plain,
double_divide(A,identity) = double_divide(B,double_divide(double_divide(A,double_divide(C,identity)),double_divide(double_divide(double_divide(C,double_divide(B,D)),double_divide(D,identity)),identity))),
inference(paramod,[status(thm)],[c_15,c_448]) ).
cnf(c_18,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,identity)),double_divide(double_divide(double_divide(C,double_divide(A,D)),double_divide(D,identity)),identity))) = double_divide(B,identity),
inference(copy,[status(thm)],[c_449]) ).
cnf(c_450,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,double_divide(A,C)),double_divide(double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),double_divide(double_divide(C,identity),identity))),
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_451,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(double_divide(B,double_divide(A,C)),double_divide(double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),double_divide(double_divide(C,identity),identity))),
inference(paramod,[status(thm)],[c_11,c_450]) ).
cnf(c_452,plain,
double_divide(A,identity) = double_divide(double_divide(B,double_divide(A,C)),double_divide(double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),double_divide(double_divide(C,identity),identity))),
inference(paramod,[status(thm)],[c_15,c_451]) ).
cnf(c_453,plain,
double_divide(A,identity) = double_divide(double_divide(B,double_divide(A,C)),double_divide(double_divide(identity,double_divide(double_divide(B,double_divide(identity,identity)),double_divide(identity,identity))),double_divide(double_divide(C,identity),identity))),
inference(paramod,[status(thm)],[c_11,c_452]) ).
cnf(c_454,plain,
double_divide(A,identity) = double_divide(double_divide(B,double_divide(A,C)),double_divide(double_divide(B,identity),double_divide(double_divide(C,identity),identity))),
inference(paramod,[status(thm)],[c_15,c_453]) ).
cnf(c_19,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(double_divide(A,identity),double_divide(double_divide(C,identity),identity))) = double_divide(B,identity),
inference(copy,[status(thm)],[c_454]) ).
cnf(c_455,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_456,plain,
double_divide(A,identity) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_15,c_455]) ).
cnf(c_20,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))) = double_divide(B,identity),
inference(copy,[status(thm)],[c_456]) ).
cnf(c_23,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_20,c_13]) ).
cnf(c_457,plain,
double_divide(A,double_divide(double_divide(double_divide(B,identity),double_divide(A,C)),double_divide(C,identity))) = B,
inference(paramod,[status(thm)],[c_23,c_12]) ).
cnf(c_24,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_20,c_457]) ).
cnf(c_458,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_23,c_11]) ).
cnf(c_27,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_23,c_458]) ).
cnf(c_459,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_23,c_7]) ).
cnf(c_460,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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)
| a2 != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_24,c_459]) ).
cnf(c_461,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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)
| a2 != a2 ),
inference(copy,[status(thm)],[c_460]) ).
cnf(c_28,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_461]) ).
cnf(c_30,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(double_divide(A,identity),C)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_24,c_19]) ).
cnf(c_462,plain,
double_divide(A,identity) = double_divide(double_divide(B,double_divide(A,B)),identity),
inference(paramod,[status(thm)],[c_5,c_18]) ).
cnf(c_34,plain,
double_divide(double_divide(A,double_divide(B,A)),identity) = double_divide(B,identity),
inference(copy,[status(thm)],[c_462]) ).
cnf(c_463,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(B,double_divide(C,D)),double_divide(D,identity)),identity),identity))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_36,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(A,identity),double_divide(double_divide(B,double_divide(C,D)),double_divide(D,identity)))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_24,c_463]) ).
cnf(c_464,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_23,c_20]) ).
cnf(c_465,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_23,c_464]) ).
cnf(c_40,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_24,c_465]) ).
cnf(c_44,plain,
double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_40,c_34]) ).
cnf(c_466,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_40,c_28]) ).
cnf(c_467,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_40,c_466]) ).
cnf(c_468,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_40,c_467]) ).
cnf(c_469,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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_40,c_468]) ).
cnf(c_470,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(double_divide(a4,b4),identity)
| 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_40,c_469]) ).
cnf(c_47,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| 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_40,c_470]) ).
cnf(c_48,plain,
double_divide(identity,double_divide(identity,A)) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_40,c_27]) ).
cnf(c_49,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_40,c_24]) ).
cnf(c_52,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_49,c_48]) ).
cnf(c_53,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(paramod,[status(thm)],[c_40,c_5]) ).
cnf(c_471,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),double_divide(identity,identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_40,c_20]) ).
cnf(c_472,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_23,c_471]) ).
cnf(c_54,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_40,c_472]) ).
cnf(c_58,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(paramod,[status(thm)],[c_49,c_53]) ).
cnf(c_473,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(C,identity))) = double_divide(double_divide(A,double_divide(B,C)),identity),
inference(paramod,[status(thm)],[c_30,c_20]) ).
cnf(c_64,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(C,identity))) = double_divide(identity,double_divide(A,double_divide(B,C))),
inference(paramod,[status(thm)],[c_40,c_473]) ).
cnf(c_474,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(C,identity)))) = double_divide(double_divide(C,identity),identity),
inference(paramod,[status(thm)],[c_58,c_36]) ).
cnf(c_475,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,double_divide(A,double_divide(B,C)))) = double_divide(double_divide(C,identity),identity),
inference(paramod,[status(thm)],[c_64,c_474]) ).
cnf(c_476,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,double_divide(A,double_divide(B,C)))) = double_divide(identity,double_divide(C,identity)),
inference(paramod,[status(thm)],[c_40,c_475]) ).
cnf(c_88,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,double_divide(A,double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_49,c_476]) ).
cnf(c_477,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_44,c_52]) ).
cnf(c_478,plain,
A = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_49,c_477]) ).
cnf(c_100,plain,
double_divide(A,double_divide(B,A)) = B,
inference(copy,[status(thm)],[c_478]) ).
cnf(c_479,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,identity),double_divide(A,B))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_44,c_30]) ).
cnf(c_102,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_23,c_479]) ).
cnf(c_115,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_100,c_100]) ).
cnf(c_116,plain,
double_divide(double_divide(A,B),double_divide(double_divide(C,B),double_divide(A,identity))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_115,c_20]) ).
cnf(c_480,plain,
double_divide(A,double_divide(A,B)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_115,c_20]) ).
cnf(c_481,plain,
double_divide(A,double_divide(A,B)) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_40,c_480]) ).
cnf(c_119,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_100,c_481]) ).
cnf(c_140,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_100,c_119]) ).
cnf(c_482,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(double_divide(identity,double_divide(b3,c3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_140,c_47]) ).
cnf(c_483,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(paramod,[status(thm)],[c_140,c_482]) ).
cnf(c_484,plain,
( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4))
| 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_140,c_483]) ).
cnf(c_485,plain,
( double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4))
| 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_140,c_484]) ).
cnf(c_486,plain,
( double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4))
| 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_485]) ).
cnf(c_149,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_486]) ).
cnf(c_487,plain,
double_divide(double_divide(A,identity),double_divide(identity,B)) = double_divide(double_divide(A,B),identity),
inference(paramod,[status(thm)],[c_119,c_102]) ).
cnf(c_196,plain,
double_divide(double_divide(A,identity),double_divide(identity,B)) = double_divide(identity,double_divide(A,B)),
inference(paramod,[status(thm)],[c_140,c_487]) ).
cnf(c_216,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(paramod,[status(thm)],[c_119,c_196]) ).
cnf(c_219,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(identity,double_divide(A,B)),
inference(paramod,[status(thm)],[c_140,c_196]) ).
cnf(c_263,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(paramod,[status(thm)],[c_119,c_219]) ).
cnf(c_488,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_54,c_119]) ).
cnf(c_272,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(A,identity)),
inference(copy,[status(thm)],[c_488]) ).
cnf(c_282,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(identity,double_divide(A,double_divide(B,C))),
inference(paramod,[status(thm)],[c_88,c_119]) ).
cnf(c_489,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,double_divide(B,identity))) = double_divide(B,double_divide(identity,A)),
inference(paramod,[status(thm)],[c_54,c_88]) ).
cnf(c_490,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,identity))) = double_divide(B,double_divide(identity,A)),
inference(paramod,[status(thm)],[c_23,c_489]) ).
cnf(c_491,plain,
double_divide(double_divide(A,identity),B) = double_divide(B,double_divide(identity,A)),
inference(paramod,[status(thm)],[c_100,c_490]) ).
cnf(c_289,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(identity,A)),
inference(paramod,[status(thm)],[c_216,c_491]) ).
cnf(c_492,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(identity,double_divide(double_divide(B,double_divide(identity,A)),double_divide(identity,C))),
inference(paramod,[status(thm)],[c_272,c_263]) ).
cnf(c_493,plain,
double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(identity,double_divide(double_divide(B,double_divide(identity,A)),double_divide(identity,C))),
inference(paramod,[status(thm)],[c_282,c_492]) ).
cnf(c_317,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,C))) = double_divide(identity,double_divide(B,double_divide(A,C))),
inference(copy,[status(thm)],[c_493]) ).
cnf(c_494,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(identity,double_divide(double_divide(B,double_divide(identity,A)),double_divide(identity,C))),
inference(paramod,[status(thm)],[c_289,c_263]) ).
cnf(c_323,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(identity,double_divide(A,double_divide(B,C))),
inference(paramod,[status(thm)],[c_317,c_494]) ).
cnf(c_495,plain,
double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(C,double_divide(identity,B))),double_divide(A,identity))) = double_divide(double_divide(C,identity),identity),
inference(paramod,[status(thm)],[c_216,c_116]) ).
cnf(c_496,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(double_divide(C,double_divide(identity,B)),double_divide(identity,double_divide(A,identity))))) = double_divide(double_divide(C,identity),identity),
inference(paramod,[status(thm)],[c_263,c_495]) ).
cnf(c_497,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(double_divide(C,double_divide(identity,B)),A))) = double_divide(double_divide(C,identity),identity),
inference(paramod,[status(thm)],[c_100,c_496]) ).
cnf(c_498,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(identity,double_divide(C,double_divide(B,A))))) = double_divide(double_divide(C,identity),identity),
inference(paramod,[status(thm)],[c_323,c_497]) ).
cnf(c_499,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(B,A))) = double_divide(double_divide(C,identity),identity),
inference(paramod,[status(thm)],[c_119,c_498]) ).
cnf(c_500,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(B,A))) = double_divide(identity,double_divide(C,identity)),
inference(paramod,[status(thm)],[c_140,c_499]) ).
cnf(c_348,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(B,A))) = C,
inference(paramod,[status(thm)],[c_100,c_500]) ).
cnf(c_394,plain,
double_divide(double_divide(A,B),double_divide(double_divide(B,A),C)) = C,
inference(paramod,[status(thm)],[c_140,c_348]) ).
cnf(c_409,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_116,c_394]) ).
cnf(c_501,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(A,identity),double_divide(B,C)),
inference(paramod,[status(thm)],[c_409,c_140]) ).
cnf(c_425,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))),
inference(paramod,[status(thm)],[c_216,c_501]) ).
cnf(c_502,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(B,identity),double_divide(C,A)),
inference(paramod,[status(thm)],[c_409,c_140]) ).
cnf(c_503,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(B,identity),double_divide(C,A)),
inference(paramod,[status(thm)],[c_425,c_502]) ).
cnf(c_504,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(C,A)))),
inference(paramod,[status(thm)],[c_216,c_503]) ).
cnf(c_426,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(identity,double_divide(C,double_divide(identity,double_divide(A,B)))),
inference(copy,[status(thm)],[c_504]) ).
cnf(c_505,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))),
inference(copy,[status(thm)],[c_149]) ).
cnf(c_427,plain,
$false,
inference(resolve,[status(thm)],[c_426,c_505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n020.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 14:23:03 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3106943 was started by sandbox2 on n020,
% 0.18/0.44 % Fri Sep 25 14:23:03 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.77/0.56
% 0.77/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.77/0.56
% 0.77/0.56 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.77/0.56 % Length of proof is 56.
% 0.77/0.56 % Level of proof is 24.
% 0.77/0.56 % Maximum clause weight is 112.000.
% 0.77/0.56 % Given clauses 52.
% 0.77/0.56
% 0.77/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------