## TSTP Solution File: SYN721+1 by Metis---2.4

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```%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 09:05:01 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   25 (   7 unt;   0 def)
%            Number of atoms       :   63 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   62 (  24   ~;  17   |;  12   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   49 (   5 sgn  35   !;   6   ?)

%------------------------------------------------------------------------------
fof(lx1,conjecture,
( ( r(a,b)
& ! [X] :
( ? [Y] : r(X,Y)
=> q(X,X) )
& ! [U,V] :
( q(U,V)
=> ! [Z] : r(Z,V) ) )
=> ? [W] :
( r(b,W)
& q(W,a) ) ) ).

fof(subgoal_0,plain,
( ( r(a,b)
& ! [X] :
( ? [Y] : r(X,Y)
=> q(X,X) )
& ! [U,V] :
( q(U,V)
=> ! [Z] : r(Z,V) ) )
=> ? [W] :
( r(b,W)
& q(W,a) ) ),
inference(strip,[],[lx1]) ).

fof(negate_0_0,plain,
~ ( ( r(a,b)
& ! [X] :
( ? [Y] : r(X,Y)
=> q(X,X) )
& ! [U,V] :
( q(U,V)
=> ! [Z] : r(Z,V) ) )
=> ? [W] :
( r(b,W)
& q(W,a) ) ),
inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
( r(a,b)
& ! [W] :
( ~ q(W,a)
| ~ r(b,W) )
& ! [X] :
( q(X,X)
| ! [Y] : ~ r(X,Y) )
& ! [U,V] :
( ~ q(U,V)
| ! [Z] : r(Z,V) ) ),
inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
! [W] :
( ~ q(W,a)
| ~ r(b,W) ),
inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
! [W] :
( ~ q(W,a)
| ~ r(b,W) ),
inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
r(a,b),
inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_4,plain,
! [X] :
( q(X,X)
| ! [Y] : ~ r(X,Y) ),
inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_5,plain,
! [X] :
( q(X,X)
| ! [Y] : ~ r(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
! [X,Y] :
( ~ r(X,Y)
| q(X,X) ),
inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
! [U,V] :
( ~ q(U,V)
| ! [Z] : r(Z,V) ),
inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_8,plain,
! [U,V] :
( ~ q(U,V)
| ! [Z] : r(Z,V) ),
inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
! [U,V,Z] :
( ~ q(U,V)
| r(Z,V) ),
inference(clausify,[],[normalize_0_8]) ).

cnf(refute_0_0,plain,
( ~ q(W,a)
| ~ r(b,W) ),
inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
( ~ q(a,a)
| ~ r(b,a) ),
inference(subst,[],[refute_0_0:[bind(W,\$fot(a))]]) ).

cnf(refute_0_2,plain,
r(a,b),
inference(canonicalize,[],[normalize_0_3]) ).

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

cnf(refute_0_4,plain,
( ~ r(a,b)
| q(a,a) ),
inference(subst,[],[refute_0_3:[bind(X,\$fot(a)),bind(Y,\$fot(b))]]) ).

cnf(refute_0_5,plain,
q(a,a),
inference(resolve,[\$cnf( r(a,b) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
( ~ q(U,V)
| r(Z,V) ),
inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_7,plain,
( ~ q(a,a)
| r(X_5,a) ),
inference(subst,[],[refute_0_6:[bind(U,\$fot(a)),bind(V,\$fot(a)),bind(Z,\$fot(X_5))]]) ).

cnf(refute_0_8,plain,
r(X_5,a),
inference(resolve,[\$cnf( q(a,a) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
r(b,a),
inference(subst,[],[refute_0_8:[bind(X_5,\$fot(b))]]) ).

cnf(refute_0_10,plain,
~ q(a,a),
inference(resolve,[\$cnf( r(b,a) )],[refute_0_9,refute_0_1]) ).

cnf(refute_0_11,plain,
\$false,
inference(resolve,[\$cnf( q(a,a) )],[refute_0_5,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul 11 20:36:18 EDT 2022
% 0.12/0.34  % CPUTime  :
% 0.12/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------
```