## TSTP Solution File: SYN367+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : n002.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 19:37:42 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   24 (   5 unt;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   71 (  28   ~;  17   |;  18   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   5 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   24 (  18   !;   6   ?)

%------------------------------------------------------------------------------
fof(f32,plain,
\$false,
inference(avatar_sat_refutation,[],[f22,f26,f29,f31]) ).

fof(f31,plain,
~ spl2_2,

fof(f30,plain,
( \$false
| ~ spl2_2 ),
inference(resolution,[],[f21,f10]) ).

fof(f10,plain,
~ big_q(sK0),
inference(cnf_transformation,[],[f8]) ).

fof(f8,plain,
( ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) )
& ~ big_q(sK0)
& ~ big_r(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f7,f6]) ).

fof(f6,plain,
( ? [X1] : ~ big_q(X1)
=> ~ big_q(sK0) ),
introduced(choice_axiom,[]) ).

fof(f7,plain,
( ? [X2] : ~ big_r(X2)
=> ~ big_r(sK1) ),
introduced(choice_axiom,[]) ).

fof(f5,plain,
( ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) )
& ? [X1] : ~ big_q(X1)
& ? [X2] : ~ big_r(X2) ),
inference(flattening,[],[f4]) ).

fof(f4,plain,
( ? [X2] : ~ big_r(X2)
& ? [X1] : ~ big_q(X1)
& ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) ) ),
inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
~ ( ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) )
=> ( ! [X2] : big_r(X2)
| ! [X1] : big_q(X1) ) ),
inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) )
=> ( ! [X0] : big_q(X0)
| ! [X0] : big_r(X0) ) ),
inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
( ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) )
=> ( ! [X0] : big_q(X0)
| ! [X0] : big_r(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2118) ).

fof(f21,plain,
( ! [X0] : big_q(X0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).

fof(f20,plain,
( spl2_2
<=> ! [X0] : big_q(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f29,plain,
~ spl2_3,

fof(f28,plain,
( \$false
| ~ spl2_3 ),
inference(resolution,[],[f25,f9]) ).

fof(f9,plain,
~ big_r(sK1),
inference(cnf_transformation,[],[f8]) ).

fof(f25,plain,
( ! [X0] : big_r(X0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f24]) ).

fof(f24,plain,
( spl2_3
<=> ! [X0] : big_r(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f26,plain,
( spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f13,f16,f24]) ).

fof(f16,plain,
( spl2_1
<=> p ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f13,plain,
! [X0] :
( p
| big_r(X0) ),
inference(cnf_transformation,[],[f8]) ).

fof(f22,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f12,f20,f16]) ).

fof(f12,plain,
! [X0] :
( big_q(X0)
| ~ p ),
inference(cnf_transformation,[],[f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 22:01:14 EDT 2022
% 0.13/0.35  % CPUTime    :
% 0.20/0.50  % (2653)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/177Mi)
% 0.20/0.50  % (2637)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.51  % (2655)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/355Mi)
% 0.20/0.51  % (2655)First to succeed.
% 0.20/0.51  % (2655)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (2655)------------------------------
% 0.20/0.51  % (2655)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (2655)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (2655)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51  % (2655)Memory used [KB]: 5373
% 0.20/0.51  % (2655)Time elapsed: 0.098 s
% 0.20/0.51  % (2655)Instructions burned: 1 (million)
% 0.20/0.51  % (2655)------------------------------
% 0.20/0.51  % (2655)------------------------------
% 0.20/0.51  % (2625)Success in time 0.155 s
%------------------------------------------------------------------------------
```