## TSTP Solution File: LCL666+1.001 by Vampire---4.7

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Vampire---4.7
% Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Sep 18 04:40:43 EDT 2022

% Result   : Theorem 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   15 (   6 unt;   0 def)
%            Number of atoms       :   51 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   75 (  39   ~;  19   |;  16   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   17 (  11   !;   6   ?)

%------------------------------------------------------------------------------
fof(f15,plain,
\$false,
inference(subsumption_resolution,[],[f14,f11]) ).

fof(f11,plain,
p101(sK0),
inference(cnf_transformation,[],[f8]) ).

fof(f8,plain,
( p101(sK0)
& p201(sK0)
& ! [X1] :
( ~ p101(X1)
| ~ p201(X1)
| ~ r1(sK0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).

fof(f7,plain,
( ? [X0] :
( p101(X0)
& p201(X0)
& ! [X1] :
( ~ p101(X1)
| ~ p201(X1)
| ~ r1(X0,X1) ) )
=> ( p101(sK0)
& p201(sK0)
& ! [X1] :
( ~ p101(X1)
| ~ p201(X1)
| ~ r1(sK0,X1) ) ) ),
introduced(choice_axiom,[]) ).

fof(f6,plain,
? [X0] :
( p101(X0)
& p201(X0)
& ! [X1] :
( ~ p101(X1)
| ~ p201(X1)
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f5]) ).

fof(f5,plain,
? [X0] :
( p101(X0)
& p201(X0)
& ! [X1] :
( ~ p101(X1)
| ~ p201(X1)
| ~ r1(X0,X1) ) ),
inference(ennf_transformation,[],[f4]) ).

fof(f4,plain,
? [X0] :
~ ( ~ ( p101(X0)
& p201(X0) )
| ~ ! [X1] :
( ~ ( p101(X1)
& p201(X1) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f3]) ).

fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ( p101(X0)
& p201(X0) )
| ~ ! [X1] :
( ~ ( p101(X1)
& p201(X1) )
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[],[f2]) ).

fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ( p101(X0)
& p201(X0) )
| ~ ! [X1] :
( ~ ( p101(X1)
& p201(X1) )
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).

fof(f14,plain,
~ p101(sK0),
inference(subsumption_resolution,[],[f13,f10]) ).

fof(f10,plain,
p201(sK0),
inference(cnf_transformation,[],[f8]) ).

fof(f13,plain,
( ~ p201(sK0)
| ~ p101(sK0) ),
inference(resolution,[],[f12,f9]) ).

fof(f9,plain,
! [X1] :
( ~ r1(sK0,X1)
| ~ p201(X1)
| ~ p101(X1) ),
inference(cnf_transformation,[],[f8]) ).

fof(f12,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Thu Sep  1 23:37:04 EDT 2022
% 0.13/0.35  % CPUTime    :
% 0.13/0.35  This is a FOF_THM_EPR_NEQ problem
% 0.13/0.35  Running vampire --ignore_missing on --mode casc -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  % (25279)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (25280)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
% 0.20/0.42  % (25282)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
% 0.20/0.42  % (25281)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
% 0.20/0.42  % (25286)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
% 0.20/0.42  % (25280)First to succeed.
% 0.20/0.42  % (25286)Also succeeded, but the first one will report.
% 0.20/0.42  % (25285)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
% 0.20/0.42  WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 0.20/0.42  % (25280)Refutation found. Thanks to Tanya!
% 0.20/0.42  % SZS status Theorem for theBenchmark
% 0.20/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.42  % (25280)------------------------------
% 0.20/0.42  % (25280)Version: Vampire 4.7 (commit 2d02e4655 on 2022-07-11 21:15:24 +0200)
% 0.20/0.42  % (25280)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.42  % (25280)Termination reason: Refutation
% 0.20/0.42
% 0.20/0.42  % (25280)Memory used [KB]: 5373
% 0.20/0.42  % (25280)Time elapsed: 0.003 s
% 0.20/0.42  % (25280)------------------------------
% 0.20/0.42  % (25280)------------------------------
% 0.20/0.42  % (25279)Success in time 0.061 s
%------------------------------------------------------------------------------
```