## TSTP Solution File: SYN721+1 by Drodi---3.3.3

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Drodi---3.3.3
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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  : 300s
% DateTime : Thu Sep 29 21:35:04 EDT 2022

% Result   : Theorem 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   12 (   5 unt;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   41 (  14   ~;   9   |;  12   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 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   :   31 (  27   !;   4   ?)

%------------------------------------------------------------------------------
fof(f1,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) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,negated_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) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,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(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f4,plain,
( r(a,b)
& ! [X] :
( ! [Y] : ~ r(X,Y)
| q(X,X) )
& ! [V] :
( ! [U] : ~ q(U,V)
| ! [Z] : r(Z,V) )
& ! [W] :
( ~ r(b,W)
| ~ q(W,a) ) ),
inference(miniscoping,[status(esa)],[f3]) ).

fof(f5,plain,
r(a,b),
inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f6,plain,
! [X0,X1] :
( ~ r(X0,X1)
| q(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f7,plain,
! [X0,X1,X2] :
( ~ q(X0,X1)
| r(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f8,plain,
! [X0] :
( ~ r(b,X0)
| ~ q(X0,a) ),
inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f9,plain,
q(a,a),
inference(resolution,[status(thm)],[f6,f5]) ).

fof(f10,plain,
! [X0] : r(X0,a),
inference(resolution,[status(thm)],[f9,f7]) ).

fof(f11,plain,
~ q(a,a),
inference(resolution,[status(thm)],[f10,f8]) ).

fof(f12,plain,
\$false,
inference(forward_subsumption_resolution,[status(thm)],[f11,f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Sep  5 06:45:59 EDT 2022
% 0.14/0.34  % CPUTime  :
% 0.14/0.35  % Drodi V3.3.3
% 0.20/0.57  % Refutation found
% 0.20/0.57  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.57  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.57  % Elapsed time: 0.013645 seconds
% 0.20/0.57  % CPU time: 0.017823 seconds
% 0.20/0.57  % Memory used: 16.662 MB
%------------------------------------------------------------------------------
```