## TSTP Solution File: SYN367+1 by Vampire-SAT---4.7

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.7
% Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode casc_sat --cores 8 -t %d %s

% Computer : n008.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 : Thu Sep 29 23:42:07 EDT 2022

% Result   : Theorem 0.21s 0.42s
% Output   : Refutation 0.21s
% 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(f32,plain,
\$false,
inference(avatar_sat_refutation,[],[f23,f27,f29,f31]) ).

fof(f31,plain,
~ spl2_3,

fof(f30,plain,
( \$false
| ~ spl2_3 ),
inference(resolution,[],[f26,f14]) ).

fof(f14,plain,
~ big_q(sK1),
inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
( ~ big_r(sK0)
& ~ big_q(sK1)
& ! [X2] :
( ( big_r(X2)
& ~ p )
| ( big_q(X2)
& p ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).

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

fof(f8,plain,
( ? [X1] : ~ big_q(X1)
=> ~ big_q(sK1) ),
introduced(choice_axiom,[]) ).

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

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

fof(f4,plain,
( ? [X1] : ~ big_r(X1)
& ? [X2] : ~ big_q(X2)
& ! [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 ) )
=> ( ! [X1] : big_r(X1)
| ! [X2] : big_q(X2) ) ),
inference(rectify,[],[f2]) ).

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

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

fof(f26,plain,
( ! [X2] : big_q(X2)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f25]) ).

fof(f25,plain,
( spl2_3
<=> ! [X2] : big_q(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f29,plain,
~ spl2_2,

fof(f28,plain,
( \$false
| ~ spl2_2 ),
inference(resolution,[],[f22,f15]) ).

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

fof(f22,plain,
( ! [X2] : big_r(X2)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f21]) ).

fof(f21,plain,
( spl2_2
<=> ! [X2] : big_r(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

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

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

fof(f11,plain,
! [X2] :
( ~ p
| big_q(X2) ),
inference(cnf_transformation,[],[f9]) ).

fof(f23,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f12,f21,f17]) ).

fof(f12,plain,
! [X2] :
( big_r(X2)
| p ),
inference(cnf_transformation,[],[f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.14  % Command    : vampire --ignore_missing on --mode casc_sat --cores 8 -t %d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Sep  5 02:59:40 EDT 2022
% 0.14/0.35  % CPUTime    :
% 0.14/0.35  This is a FOF_THM_EPR_NEQ problem
% 0.14/0.36  % (7827)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  WARNING Broken Constraint: if avatar(off) has been set then saturation_algorithm(fmb) is equal to lrs or saturation_algorithm(fmb) is equal to otter or saturation_algorithm(fmb) is equal to discount
% 0.21/0.42  % (7833)ott+2_5_afp=4000:afq=2.0:anc=none:bce=on:fsr=off:gsp=on:lma=on:nm=32:nwc=1:sp=reverse_arity_315 on theBenchmark
% 0.21/0.42  % (7832)ott-3_5_awrs=decay:awrsf=128:afr=on:afp=40000:afq=1.0:amm=off:anc=none:bce=on:cond=fast:lma=on:nm=64:newcnf=on:nwc=1.1:sas=z3:sp=frequency:updr=off_146 on theBenchmark
% 0.21/0.42  WARNING Broken Constraint: if avatar(off) has been set then saturation_algorithm(fmb) is equal to lrs or saturation_algorithm(fmb) is equal to otter or saturation_algorithm(fmb) is equal to discount
% 0.21/0.42  % (7830)dis+10_3_add=large:afp=10000:afq=2.0:amm=sco:anc=none:cond=on:fsr=off:gsp=on:lma=on:nm=16:nwc=1:sac=on:updr=off_197 on theBenchmark
% 0.21/0.42  % (7834)fmb+10_1_av=off:bce=on:fmbes=smt:fmbsr=1.4:fde=none:ile=on:updr=off_600 on theBenchmark
% 0.21/0.42  % (7829)fmb+10_1_av=off:bce=on:nm=6_1461 on theBenchmark
% 0.21/0.42  % (7828)ott+10_128_av=off:bs=on:gsp=on:irw=on:lcm=predicate:lma=on:nm=0:nwc=1:sp=occurrence:urr=on:updr=off:uhcvi=on_4 on theBenchmark
% 0.21/0.42  WARNING Broken Constraint: if avatar(off) has been set then saturation_algorithm(fmb) is equal to lrs or saturation_algorithm(fmb) is equal to otter or saturation_algorithm(fmb) is equal to discount
% 0.21/0.42  % (7831)dis+1_3_av=off:cond=on:nm=64:newcnf=on:nwc=1_87 on theBenchmark
% 0.21/0.42  Detected maximum model sizes of [2]
% 0.21/0.42  TRYING [1]
% 0.21/0.42  % (7833)First to succeed.
% 0.21/0.42  % (7835)fmb+10_1_av=off:bce=on:fmbsr=1.3:nm=2:newcnf=on_1200 on theBenchmark
% 0.21/0.42  TRYING [2]
% 0.21/0.42  Detected maximum model sizes of [2]
% 0.21/0.42  TRYING [1]
% 0.21/0.42  % (7829)Also succeeded, but the first one will report.
% 0.21/0.42  TRYING [2]
% 0.21/0.42  % (7830)Also succeeded, but the first one will report.
% 0.21/0.42  % (7833)Refutation found. Thanks to Tanya!
% 0.21/0.42  % SZS status Theorem for theBenchmark
% 0.21/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.42  % (7833)------------------------------
% 0.21/0.42  % (7833)Version: Vampire 4.7 (commit 2d02e4655 on 2022-07-11 21:15:24 +0200)
% 0.21/0.42  % (7833)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.42  % (7833)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42  % (7833)Memory used [KB]: 5500
% 0.21/0.42  % (7833)Time elapsed: 0.004 s
% 0.21/0.42  % (7833)------------------------------
% 0.21/0.42  % (7833)------------------------------
% 0.21/0.42  % (7827)Success in time 0.062 s
%------------------------------------------------------------------------------
```