## TSTP Solution File: SYN721+1 by SnakeForV---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n001.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 : Wed Aug 31 19:28:12 EDT 2022

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (   3 unt;   0 def)
%            Number of atoms       :   71 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   78 (  29   ~;  20   |;  18   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   47 (  41   !;   6   ?)

%------------------------------------------------------------------------------
fof(f26,plain,
\$false,
inference(avatar_sat_refutation,[],[f19,f22,f25]) ).

fof(f25,plain,
~ spl0_2,

fof(f23,plain,
( \$false
| ~ spl0_2 ),
inference(resolution,[],[f18,f9]) ).

fof(f9,plain,
r(a,b),
inference(cnf_transformation,[],[f6]) ).

fof(f6,plain,
( ! [X0,X1] :
( ! [X2] : r(X2,X1)
| ~ q(X0,X1) )
& r(a,b)
& ! [X3] :
( ~ q(X3,a)
| ~ r(b,X3) )
& ! [X4] :
( ! [X5] : ~ r(X4,X5)
| q(X4,X4) ) ),
inference(rectify,[],[f5]) ).

fof(f5,plain,
( ! [X1,X0] :
( ! [X2] : r(X2,X0)
| ~ q(X1,X0) )
& r(a,b)
& ! [X5] :
( ~ q(X5,a)
| ~ r(b,X5) )
& ! [X3] :
( ! [X4] : ~ r(X3,X4)
| q(X3,X3) ) ),
inference(flattening,[],[f4]) ).

fof(f4,plain,
( ! [X5] :
( ~ q(X5,a)
| ~ r(b,X5) )
& r(a,b)
& ! [X1,X0] :
( ! [X2] : r(X2,X0)
| ~ q(X1,X0) )
& ! [X3] :
( ! [X4] : ~ r(X3,X4)
| q(X3,X3) ) ),
inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
~ ( ( r(a,b)
& ! [X1,X0] :
( q(X1,X0)
=> ! [X2] : r(X2,X0) )
& ! [X3] :
( ? [X4] : r(X3,X4)
=> q(X3,X3) ) )
=> ? [X5] :
( r(b,X5)
& q(X5,a) ) ),
inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
~ ( ( ! [X3,X2] :
( q(X2,X3)
=> ! [X4] : r(X4,X3) )
& r(a,b)
& ! [X0] :
( ? [X1] : r(X0,X1)
=> q(X0,X0) ) )
=> ? [X5] :
( r(b,X5)
& q(X5,a) ) ),
inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
( ( ! [X3,X2] :
( q(X2,X3)
=> ! [X4] : r(X4,X3) )
& r(a,b)
& ! [X0] :
( ? [X1] : r(X0,X1)
=> q(X0,X0) ) )
=> ? [X5] :
( r(b,X5)
& q(X5,a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lx1) ).

fof(f18,plain,
( ! [X0] : ~ r(a,X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f17]) ).

fof(f17,plain,
( spl0_2
<=> ! [X0] : ~ r(a,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f22,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f21,f13,f17]) ).

fof(f13,plain,
( spl0_1
<=> r(b,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f21,plain,
( ! [X0] : ~ r(a,X0)
| spl0_1 ),
inference(resolution,[],[f20,f7]) ).

fof(f7,plain,
! [X4,X5] :
( q(X4,X4)
| ~ r(X4,X5) ),
inference(cnf_transformation,[],[f6]) ).

fof(f20,plain,
( ! [X0] : ~ q(X0,a)
| spl0_1 ),
inference(resolution,[],[f15,f10]) ).

fof(f10,plain,
! [X2,X0,X1] :
( r(X2,X1)
| ~ q(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).

fof(f15,plain,
( ~ r(b,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f13]) ).

fof(f19,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f11,f17,f13]) ).

fof(f11,plain,
! [X0] :
( ~ r(a,X0)
| ~ r(b,a) ),
inference(resolution,[],[f8,f7]) ).

fof(f8,plain,
! [X3] :
( ~ q(X3,a)
| ~ r(b,X3) ),
inference(cnf_transformation,[],[f6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.33  % Computer : n001.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue Aug 30 22:39:32 EDT 2022
% 0.14/0.33  % CPUTime    :
% 0.19/0.46  % (18917)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.47  % (18909)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.47  % (18917)First to succeed.
% 0.19/0.47  % (18917)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (18917)------------------------------
% 0.19/0.47  % (18917)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (18917)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (18917)Termination reason: Refutation
% 0.19/0.47
% 0.19/0.47  % (18917)Memory used [KB]: 5884
% 0.19/0.47  % (18917)Time elapsed: 0.077 s
% 0.19/0.47  % (18917)Instructions burned: 1 (million)
% 0.19/0.47  % (18917)------------------------------
% 0.19/0.47  % (18917)------------------------------
% 0.19/0.47  % (18887)Success in time 0.134 s
%------------------------------------------------------------------------------
```