## TSTP Solution File: LCL666+1.001 by Metis---2.4

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 12:54:12 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   21 (  11 unt;   0 def)
%            Number of atoms       :   50 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   67 (  38   ~;  17   |;  10   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   16 (   0 sgn  12   !;   2   ?)

%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X) ).

fof(main,conjecture,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p201(Y)
& p101(Y) ) )
| ~ ( p201(X)
& p101(X) ) ) ).

fof(subgoal_0,plain,
! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p201(Y)
& p101(Y) ) )
& p201(X) )
=> ~ p101(X) ),
inference(strip,[],[main]) ).

fof(negate_0_0,plain,
~ ! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p201(Y)
& p101(Y) ) )
& p201(X) )
=> ~ p101(X) ),
inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
! [X] : r1(X,X),
inference(canonicalize,[],[reflexivity]) ).

fof(normalize_0_1,plain,
! [X] : r1(X,X),
inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
? [X] :
( p101(X)
& p201(X)
& ! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(X,Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_3,plain,
( p101(skolemFOFtoCNF_X)
& p201(skolemFOFtoCNF_X)
& ! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ) ),
inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ),
inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ),
inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
p101(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_7,plain,
p201(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_3]) ).

cnf(refute_0_0,plain,
r1(X,X),
inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_0:[bind(X,\$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_2,plain,
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
( ~ p101(skolemFOFtoCNF_X)
| ~ p201(skolemFOFtoCNF_X)
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_2:[bind(Y,\$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_4,plain,
( ~ p101(skolemFOFtoCNF_X)
| ~ p201(skolemFOFtoCNF_X) ),
inference(resolve,[\$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
p101(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
~ p201(skolemFOFtoCNF_X),
inference(resolve,[\$cnf( p101(skolemFOFtoCNF_X) )],[refute_0_5,refute_0_4]) ).

cnf(refute_0_7,plain,
p201(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_8,plain,
\$false,
inference(resolve,[\$cnf( p201(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul  4 22:24:14 EDT 2022
% 0.12/0.33  % CPUTime  :
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34
%------------------------------------------------------------------------------
```