## TSTP Solution File: SYN969+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : n029.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 19:46:13 EDT 2022

% Result   : Theorem 0.23s 0.50s
% Output   : Refutation 0.23s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   14 (   5 unt;   0 def)
%            Number of atoms       :   57 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   67 (  24   ~;  14   |;  20   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 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   :   24 (  20   !;   4   ?)

%------------------------------------------------------------------------------
fof(f14,plain,
\$false,
inference(resolution,[],[f13,f8]) ).

fof(f8,plain,
r(sK0),
inference(cnf_transformation,[],[f7]) ).

fof(f7,plain,
( ! [X1] :
( ~ r(X1)
| p(X1) )
& ! [X2] :
( q(X2)
| ~ p(X2) )
& ~ q(sK0)
& r(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f5,f6]) ).

fof(f6,plain,
( ? [X0] :
( ! [X1] :
( ~ r(X1)
| p(X1) )
& ! [X2] :
( q(X2)
| ~ p(X2) )
& ~ q(X0)
& r(X0) )
=> ( ! [X1] :
( ~ r(X1)
| p(X1) )
& ! [X2] :
( q(X2)
| ~ p(X2) )
& ~ q(sK0)
& r(sK0) ) ),
introduced(choice_axiom,[]) ).

fof(f5,plain,
? [X0] :
( ! [X1] :
( ~ r(X1)
| p(X1) )
& ! [X2] :
( q(X2)
| ~ p(X2) )
& ~ q(X0)
& r(X0) ),
inference(rectify,[],[f4]) ).

fof(f4,plain,
? [X0] :
( ! [X2] :
( ~ r(X2)
| p(X2) )
& ! [X1] :
( q(X1)
| ~ p(X1) )
& ~ q(X0)
& r(X0) ),
inference(flattening,[],[f3]) ).

fof(f3,plain,
? [X0] :
( ~ q(X0)
& ! [X2] :
( ~ r(X2)
| p(X2) )
& r(X0)
& ! [X1] :
( q(X1)
| ~ p(X1) ) ),
inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
~ ! [X0] :
( ( r(X0)
& ! [X1] :
( p(X1)
=> q(X1) ) )
=> ( ! [X2] :
( r(X2)
=> p(X2) )
=> q(X0) ) ),
inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
! [X0] :
( ( r(X0)
& ! [X1] :
( p(X1)
=> q(X1) ) )
=> ( ! [X2] :
( r(X2)
=> p(X2) )
=> q(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

fof(f13,plain,
~ r(sK0),
inference(resolution,[],[f11,f12]) ).

fof(f12,plain,
~ p(sK0),
inference(resolution,[],[f10,f9]) ).

fof(f9,plain,
~ q(sK0),
inference(cnf_transformation,[],[f7]) ).

fof(f10,plain,
! [X2] :
( q(X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f7]) ).

fof(f11,plain,
! [X1] :
( p(X1)
| ~ r(X1) ),
inference(cnf_transformation,[],[f7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.36  % Computer : n029.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 30 22:43:12 EDT 2022
% 0.15/0.37  % CPUTime    :
% 0.23/0.48  % (6984)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.23/0.49  % (7000)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/500Mi)
% 0.23/0.49  % (6984)First to succeed.
% 0.23/0.50  % (6984)Refutation found. Thanks to Tanya!
% 0.23/0.50  % SZS status Theorem for theBenchmark
% 0.23/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.50  % (6984)------------------------------
% 0.23/0.50  % (6984)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.23/0.50  % (6984)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.23/0.50  % (6984)Termination reason: Refutation
% 0.23/0.50
% 0.23/0.50  % (6984)Memory used [KB]: 895
% 0.23/0.50  % (6984)Time elapsed: 0.061 s
% 0.23/0.50  % (6984)Instructions burned: 1 (million)
% 0.23/0.50  % (6984)------------------------------
% 0.23/0.50  % (6984)------------------------------
% 0.23/0.50  % (6973)Success in time 0.121 s
%------------------------------------------------------------------------------
```