## TSTP Solution File: SYN969+1 by Metis---2.4

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 : Thu Jul 21 09:12:31 EDT 2022

% Result   : Theorem 0.11s 0.33s
% Output   : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   20 (   7 unt;   0 def)
%            Number of atoms       :   53 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   50 (  17   ~;  12   |;  11   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   20 (   0 sgn  17   !;   1   ?)

%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [B] :
( ( ! [X] :
( p(X)
=> q(X) )
& r(B) )
=> ( ! [Y] :
( r(Y)
=> p(Y) )
=> q(B) ) ) ).

fof(subgoal_0,plain,
! [B] :
( ( ! [X] :
( p(X)
=> q(X) )
& r(B)
& ! [Y] :
( r(Y)
=> p(Y) ) )
=> q(B) ),
inference(strip,[],[prove_this]) ).

fof(negate_0_0,plain,
~ ! [B] :
( ( ! [X] :
( p(X)
=> q(X) )
& r(B)
& ! [Y] :
( r(Y)
=> p(Y) ) )
=> q(B) ),
inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
? [B] :
( ~ q(B)
& r(B)
& ! [X] :
( ~ p(X)
| q(X) )
& ! [Y] :
( ~ r(Y)
| p(Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
( ~ q(skolemFOFtoCNF_B)
& r(skolemFOFtoCNF_B)
& ! [X] :
( ~ p(X)
| q(X) )
& ! [Y] :
( ~ r(Y)
| p(Y) ) ),
inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
! [X] :
( ~ p(X)
| q(X) ),
inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
! [X] :
( ~ p(X)
| q(X) ),
inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
r(skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_5,plain,
! [Y] :
( ~ r(Y)
| p(Y) ),
inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_6,plain,
! [Y] :
( ~ r(Y)
| p(Y) ),
inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
~ q(skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
( ~ p(X)
| q(X) ),
inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
( ~ p(skolemFOFtoCNF_B)
| q(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(X,\$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_2,plain,
r(skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
( ~ r(Y)
| p(Y) ),
inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_4,plain,
( ~ r(skolemFOFtoCNF_B)
| p(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_3:[bind(Y,\$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_5,plain,
p(skolemFOFtoCNF_B),
inference(resolve,[\$cnf( r(skolemFOFtoCNF_B) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
q(skolemFOFtoCNF_B),
inference(resolve,[\$cnf( p(skolemFOFtoCNF_B) )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
~ q(skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_7]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.11/0.32  % Computer : n023.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Mon Jul 11 13:11:09 EDT 2022
% 0.11/0.33  % CPUTime  :
% 0.11/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.33  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.33
% 0.11/0.33  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.11/0.33
%------------------------------------------------------------------------------
```