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

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SnakeForV---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_uns --cores 0 -t %d %s

% Computer : n021.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 19:26:24 EDT 2022

% Result   : Theorem 1.51s 0.57s
% Output   : Refutation 1.51s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   25 (   5 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   79 (  31   ~;  18   |;  22   &)
%                                         (   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   :   27 (  19   !;   8   ?)

%------------------------------------------------------------------------------
fof(f36,plain,
\$false,
inference(avatar_sat_refutation,[],[f23,f27,f31,f35]) ).

fof(f35,plain,
~ spl2_2,

fof(f33,plain,
( \$false
| ~ spl2_2 ),
inference(resolution,[],[f22,f15]) ).

fof(f15,plain,
~ big_q(sK0),
inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
( ~ big_q(sK0)
& ! [X1] :
( ( ~ p
& big_r(X1) )
| ( big_q(X1)
& p ) )
& ~ big_r(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).

fof(f7,plain,
( ? [X0] : ~ big_q(X0)
=> ~ big_q(sK0) ),
introduced(choice_axiom,[]) ).

fof(f8,plain,
( ? [X2] : ~ big_r(X2)
=> ~ big_r(sK1) ),
introduced(choice_axiom,[]) ).

fof(f6,plain,
( ? [X0] : ~ big_q(X0)
& ! [X1] :
( ( ~ p
& big_r(X1) )
| ( big_q(X1)
& p ) )
& ? [X2] : ~ big_r(X2) ),
inference(rectify,[],[f5]) ).

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

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

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

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

fof(f1,conjecture,
( ! [X0] :
( ( ~ p
& big_r(X0) )
| ( big_q(X0)
& p ) )
=> ( ! [X0] : big_r(X0)
| ! [X0] : big_q(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2118) ).

fof(f22,plain,
( ! [X1] : big_q(X1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f21]) ).

fof(f21,plain,
( spl2_2
<=> ! [X1] : big_q(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f31,plain,
~ spl2_3,

fof(f28,plain,
( \$false
| ~ spl2_3 ),
inference(unit_resulting_resolution,[],[f10,f26]) ).

fof(f26,plain,
( ! [X1] : big_r(X1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f25]) ).

fof(f25,plain,
( spl2_3
<=> ! [X1] : big_r(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f10,plain,
~ big_r(sK1),
inference(cnf_transformation,[],[f9]) ).

fof(f27,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f11,f25,f17]) ).

fof(f17,plain,
( spl2_1
<=> p ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f11,plain,
! [X1] :
( big_r(X1)
| p ),
inference(cnf_transformation,[],[f9]) ).

fof(f23,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f14,f21,f17]) ).

fof(f14,plain,
! [X1] :
( big_q(X1)
| ~ p ),
inference(cnf_transformation,[],[f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n021.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 21:44:56 EDT 2022
% 0.12/0.34  % CPUTime    :
% 1.51/0.56  % (5193)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.51/0.56  % (5185)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.51/0.56  % (5185)First to succeed.
% 1.51/0.56  % (5201)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.51/0.57  % (5185)Refutation found. Thanks to Tanya!
% 1.51/0.57  % SZS status Theorem for theBenchmark
% 1.51/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.51/0.57  % (5185)------------------------------
% 1.51/0.57  % (5185)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.51/0.57  % (5185)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.51/0.57  % (5185)Termination reason: Refutation
% 1.51/0.57
% 1.51/0.57  % (5185)Memory used [KB]: 5884
% 1.51/0.57  % (5185)Time elapsed: 0.124 s
% 1.51/0.57  % (5185)Instructions burned: 1 (million)
% 1.51/0.57  % (5185)------------------------------
% 1.51/0.57  % (5185)------------------------------
% 1.51/0.57  % (5177)Success in time 0.213 s
%------------------------------------------------------------------------------
```