## TSTP Solution File: SYN721+1 by Vampire---4.7

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Vampire---4.7
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n012.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 23:31:03 EDT 2022

% Result   : Theorem 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   23 (   4 unt;   0 def)
%            Number of atoms       :   72 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   78 (  29   ~;  20   |;  18   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   47 (  41   !;   6   ?)

%------------------------------------------------------------------------------
fof(f28,plain,
\$false,
inference(avatar_sat_refutation,[],[f19,f24,f27]) ).

fof(f27,plain,
~ spl0_1,

fof(f25,plain,
( \$false
| ~ spl0_1 ),
inference(resolution,[],[f14,f7]) ).

fof(f7,plain,
r(a,b),
inference(cnf_transformation,[],[f6]) ).

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

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

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

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

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

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

fof(f14,plain,
( ! [X0] : ~ r(a,X0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f13]) ).

fof(f13,plain,
( spl0_1
<=> ! [X0] : ~ r(a,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f24,plain,
spl0_2,

fof(f22,plain,
( \$false
| spl0_2 ),
inference(resolution,[],[f21,f7]) ).

fof(f21,plain,
( ! [X0] : ~ r(a,X0)
| spl0_2 ),
inference(resolution,[],[f20,f8]) ).

fof(f8,plain,
! [X4,X5] :
( q(X4,X4)
| ~ r(X4,X5) ),
inference(cnf_transformation,[],[f6]) ).

fof(f20,plain,
( ! [X0] : ~ q(X0,a)
| spl0_2 ),
inference(resolution,[],[f18,f9]) ).

fof(f9,plain,
! [X2,X3,X1] :
( r(X3,X2)
| ~ q(X1,X2) ),
inference(cnf_transformation,[],[f6]) ).

fof(f18,plain,
( ~ r(b,a)
| spl0_2 ),
inference(avatar_component_clause,[],[f16]) ).

fof(f16,plain,
( spl0_2
<=> r(b,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f19,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f11,f16,f13]) ).

fof(f11,plain,
! [X0] :
( ~ r(b,a)
| ~ r(a,X0) ),
inference(resolution,[],[f10,f8]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36  % Computer : n012.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   : Mon Sep  5 06:44:18 EDT 2022
% 0.15/0.36  % CPUTime    :
% 0.15/0.36  This is a FOF_THM_EPR_NEQ problem
% 0.15/0.36  Running vampire --ignore_missing on --mode casc -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36  % (20061)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 0.22/0.42  % (20065)lrs-11_4:1_afp=4000:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_3 on theBenchmark
% 0.22/0.42  % (20062)dis+1011_10_add=large:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence_2 on theBenchmark
% 0.22/0.42  % (20067)dis+1002_8_awrs=converge:awrsf=64:av=off:cond=fast:fsr=off:gsp=on:lma=on:nm=64:nwc=1.2:s2a=on:sos=on:sp=frequency:urr=on:updr=off:uhcvi=on_12 on theBenchmark
% 0.22/0.42  % (20066)dis+1_3_add=large:afp=4000:afq=1.0:anc=none:gs=on:gsem=off:inw=on:lcm=reverse:lwlo=on:nm=64:nwc=1:sas=z3:sos=all:sac=on:thi=all:uwa=all:updr=off:uhcvi=on_12 on theBenchmark
% 0.22/0.42  % (20063)dis+1002_8:1_awrs=converge:awrsf=256:anc=all_dependent:br=off:fsr=off:fde=none:gs=on:gsaa=from_current:gsem=on:irw=on:nm=64:nwc=1:sas=z3:s2a=on:sp=frequency:thf=on:uwa=interpreted_only:urr=on_7 on theBenchmark
% 0.22/0.42  % (20062)First to succeed.
% 0.22/0.42  % (20068)dis+1_8_afp=4000:afq=1.1:amm=sco:gsp=on:nm=64:newcnf=on:nwc=4:sac=on:sp=occurrence:updr=off_191 on theBenchmark
% 0.22/0.42  % (20065)Also succeeded, but the first one will report.
% 0.22/0.42  % (20064)lrs+1_3_awrs=decay:awrsf=4:afp=10000:afq=1.0:amm=off:anc=none:bd=off:cond=on:fsr=off:fde=unused:gs=on:lwlo=on:nm=16:nwc=1:sas=z3:stl=30:ss=axioms:s2a=on:st=1.2:sos=theory:sp=frequency_3 on theBenchmark
% 0.22/0.42  % (20069)dis+10_128_add=large:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=2:nwc=1:sp=reverse_arity_3 on theBenchmark
% 0.22/0.43  % (20067)Also succeeded, but the first one will report.
% 0.22/0.43  % (20062)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for theBenchmark
% 0.22/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43  % (20062)------------------------------
% 0.22/0.43  % (20062)Version: Vampire 4.7 (commit 2d02e4655 on 2022-07-11 21:15:24 +0200)
% 0.22/0.43  % (20062)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.43  % (20062)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43  % (20062)Memory used [KB]: 5500
% 0.22/0.43  % (20062)Time elapsed: 0.004 s
% 0.22/0.43  % (20062)------------------------------
% 0.22/0.43  % (20062)------------------------------
% 0.22/0.43  % (20061)Success in time 0.061 s
%------------------------------------------------------------------------------
```