TSTP Solution File: SET082+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n015.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 May  5 09:11:02 EDT 2024

% Result   : Theorem 0.10s 0.37s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   28 (   6 unt;   0 def)
%            Number of atoms       :   83 (  38 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   81 (  26   ~;  23   |;  24   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   39 (  33   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1109,plain,
    $false,
    inference(subsumption_resolution,[],[f1105,f136]) ).

fof(f136,plain,
    null_class != singleton(sK0),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ( null_class != singleton(sK0)
    & ~ member(sK0,universal_class) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f71,f85]) ).

fof(f85,plain,
    ( ? [X0] :
        ( singleton(X0) != null_class
        & ~ member(X0,universal_class) )
   => ( null_class != singleton(sK0)
      & ~ member(sK0,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ? [X0] :
      ( singleton(X0) != null_class
      & ~ member(X0,universal_class) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0] :
        ( ~ member(X0,universal_class)
       => singleton(X0) = null_class ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0] :
      ( ~ member(X0,universal_class)
     => singleton(X0) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).

fof(f1105,plain,
    null_class = singleton(sK0),
    inference(resolution,[],[f1097,f135]) ).

fof(f135,plain,
    ~ member(sK0,universal_class),
    inference(cnf_transformation,[],[f86]) ).

fof(f1097,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class ),
    inference(duplicate_literal_removal,[],[f1096]) ).

fof(f1096,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class
      | singleton(X0) = null_class ),
    inference(superposition,[],[f147,f1090]) ).

fof(f1090,plain,
    ! [X0] :
      ( sK1(singleton(X0)) = X0
      | singleton(X0) = null_class ),
    inference(resolution,[],[f1081,f148]) ).

fof(f148,plain,
    ! [X0] :
      ( member(sK1(X0),X0)
      | null_class = X0 ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ( disjoint(sK1(X0),X0)
        & member(sK1(X0),X0)
        & member(sK1(X0),universal_class) )
      | null_class = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f72,f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ? [X1] :
          ( disjoint(X1,X0)
          & member(X1,X0)
          & member(X1,universal_class) )
     => ( disjoint(sK1(X0),X0)
        & member(sK1(X0),X0)
        & member(sK1(X0),universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0] :
      ( ? [X1] :
          ( disjoint(X1,X0)
          & member(X1,X0)
          & member(X1,universal_class) )
      | null_class = X0 ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( null_class != X0
     => ? [X1] :
          ( disjoint(X1,X0)
          & member(X1,X0)
          & member(X1,universal_class) ) ),
    inference(rectify,[],[f41]) ).

fof(f41,axiom,
    ! [X0] :
      ( null_class != X0
     => ? [X2] :
          ( disjoint(X2,X0)
          & member(X2,X0)
          & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).

fof(f1081,plain,
    ! [X0,X1] :
      ( ~ member(X1,singleton(X0))
      | X0 = X1 ),
    inference(duplicate_literal_removal,[],[f1079]) ).

fof(f1079,plain,
    ! [X0,X1] :
      ( ~ member(X1,singleton(X0))
      | X0 = X1
      | X0 = X1 ),
    inference(superposition,[],[f204,f142]) ).

fof(f142,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f204,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( ( X0 = X2
          | X0 = X1 )
        & member(X0,universal_class) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,unordered_pair(X0,X1))
    <=> ( ( X1 = X2
          | X0 = X2 )
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).

fof(f147,plain,
    ! [X0] :
      ( member(sK1(X0),universal_class)
      | null_class = X0 ),
    inference(cnf_transformation,[],[f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32  % Computer : n015.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Fri May  3 16:24:38 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (27252)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34  % (27255)WARNING: value z3 for option sas not known
% 0.10/0.34  % (27255)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.34  % (27258)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.34  % (27253)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34  % (27256)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.34  % (27254)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34  % (27257)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.10/0.34  % (27259)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.36  TRYING [1]
% 0.10/0.36  TRYING [2]
% 0.10/0.36  TRYING [1]
% 0.10/0.37  % (27255)First to succeed.
% 0.10/0.37  % (27255)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27252"
% 0.10/0.37  TRYING [2]
% 0.10/0.37  % (27255)Refutation found. Thanks to Tanya!
% 0.10/0.37  % SZS status Theorem for theBenchmark
% 0.10/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.37  % (27255)------------------------------
% 0.10/0.37  % (27255)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.37  % (27255)Termination reason: Refutation
% 0.10/0.37  
% 0.10/0.37  % (27255)Memory used [KB]: 1297
% 0.10/0.37  % (27255)Time elapsed: 0.031 s
% 0.10/0.37  % (27255)Instructions burned: 52 (million)
% 0.10/0.37  % (27252)Success in time 0.044 s
%------------------------------------------------------------------------------