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

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n022.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 19:39:22 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   14 (   5 unt;   0 def)
%            Number of atoms       :   53 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   58 (  19   ~;  12   |;  18   &)
%                                         (   0 <=>;   9  =>;   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   :   43 (  37   !;   6   ?)

% Comments :
%------------------------------------------------------------------------------
fof(f15,plain,
\$false,
inference(subsumption_resolution,[],[f13,f11]) ).

fof(f11,plain,
q(a,a),
inference(resolution,[],[f8,f9]) ).

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

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

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

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

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

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

fof(f1,conjecture,
( ( r(a,b)
& ! [X0] :
( ? [X1] : r(X0,X1)
=> q(X0,X0) )
& ! [X3,X2] :
( q(X2,X3)
=> ! [X4] : r(X4,X3) ) )
=> ? [X5] :
( q(X5,a)
& r(b,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1) ).

fof(f8,plain,
! [X3,X4] :
( ~ r(X3,X4)
| q(X3,X3) ),
inference(cnf_transformation,[],[f6]) ).

fof(f13,plain,
~ q(a,a),
inference(resolution,[],[f12,f7]) ).

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

fof(f12,plain,
! [X0] : r(X0,a),
inference(resolution,[],[f11,f10]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n022.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    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 22:19:26 EDT 2022
% 0.12/0.34  % CPUTime    :
% 0.20/0.49  % (20184)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.20/0.50  % (20162)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.50  % (20170)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.20/0.50  % (20162)First to succeed.
% 0.20/0.50  % (20162)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (20162)------------------------------
% 0.20/0.50  % (20162)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (20162)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (20162)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50  % (20162)Memory used [KB]: 5373
% 0.20/0.50  % (20162)Time elapsed: 0.101 s
% 0.20/0.50  % (20162)Instructions burned: 1 (million)
% 0.20/0.50  % (20162)------------------------------
% 0.20/0.50  % (20162)------------------------------
% 0.20/0.50  % (20157)Success in time 0.158 s
%------------------------------------------------------------------------------
```