TSTP Solution File: SET103+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET103+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 : n024.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 09:11:14 EDT 2024

% Result   : Theorem 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   43 (  13 unt;   0 def)
%            Number of atoms       :  123 (  42 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  122 (  42   ~;  38   |;  32   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   75 (  64   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1837,plain,
    $false,
    inference(trivial_inequality_removal,[],[f1829]) ).

fof(f1829,plain,
    ordered_pair(sK0,sK1) != ordered_pair(sK0,sK1),
    inference(superposition,[],[f135,f1721]) ).

fof(f1721,plain,
    ! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,sK1),
    inference(superposition,[],[f165,f1708]) ).

fof(f1708,plain,
    null_class = singleton(sK1),
    inference(resolution,[],[f1698,f350]) ).

fof(f350,plain,
    ! [X0] : ~ member(sK1,X0),
    inference(resolution,[],[f348,f140]) ).

fof(f140,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f348,plain,
    ! [X0] :
      ( ~ subclass(X0,universal_class)
      | ~ member(sK1,X0) ),
    inference(resolution,[],[f173,f136]) ).

fof(f136,plain,
    ~ member(sK1,universal_class),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ( ~ member(sK1,universal_class)
    & ordered_pair(sK0,sK1) != unordered_pair(singleton(sK0),unordered_pair(sK0,null_class)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f71,f85]) ).

fof(f85,plain,
    ( ? [X0,X1] :
        ( ~ member(X1,universal_class)
        & ordered_pair(X0,X1) != unordered_pair(singleton(X0),unordered_pair(X0,null_class)) )
   => ( ~ member(sK1,universal_class)
      & ordered_pair(sK0,sK1) != unordered_pair(singleton(sK0),unordered_pair(sK0,null_class)) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ? [X0,X1] :
      ( ~ member(X1,universal_class)
      & ordered_pair(X0,X1) != unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0,X1] :
        ( member(X1,universal_class)
        | ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0,X1] :
      ( member(X1,universal_class)
      | ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).

fof(f173,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subclass(X0,X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( subclass(X0,X1)
        | ( ~ member(sK4(X0,X1),X1)
          & member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subclass(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f100,f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK4(X0,X1),X1)
        & member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ( subclass(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subclass(X0,X1) ) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ( subclass(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subclass(X0,X1) ) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).

fof(f1698,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class ),
    inference(duplicate_literal_removal,[],[f1697]) ).

fof(f1697,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class
      | singleton(X0) = null_class ),
    inference(superposition,[],[f147,f1689]) ).

fof(f1689,plain,
    ! [X0] :
      ( sK2(singleton(X0)) = X0
      | singleton(X0) = null_class ),
    inference(resolution,[],[f1684,f148]) ).

fof(f148,plain,
    ! [X0] :
      ( member(sK2(X0),X0)
      | null_class = X0 ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ( disjoint(sK2(X0),X0)
        & member(sK2(X0),X0)
        & member(sK2(X0),universal_class) )
      | null_class = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f72,f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ? [X1] :
          ( disjoint(X1,X0)
          & member(X1,X0)
          & member(X1,universal_class) )
     => ( disjoint(sK2(X0),X0)
        & member(sK2(X0),X0)
        & member(sK2(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(f1684,plain,
    ! [X0,X1] :
      ( ~ member(X1,singleton(X0))
      | X0 = X1 ),
    inference(duplicate_literal_removal,[],[f1682]) ).

fof(f1682,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(sK2(X0),universal_class)
      | null_class = X0 ),
    inference(cnf_transformation,[],[f88]) ).

fof(f165,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).

fof(f135,plain,
    ordered_pair(sK0,sK1) != unordered_pair(singleton(sK0),unordered_pair(sK0,null_class)),
    inference(cnf_transformation,[],[f86]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SET103+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri May  3 16:45:53 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.34  % (6701)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35  % (6704)WARNING: value z3 for option sas not known
% 0.12/0.35  % (6705)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35  % (6706)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)
% 0.12/0.35  % (6704)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)
% 0.12/0.35  % (6703)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35  % (6707)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)
% 0.12/0.35  % (6702)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35  % (6708)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)
% 0.12/0.38  TRYING [1]
% 0.12/0.38  TRYING [2]
% 0.12/0.38  TRYING [1]
% 0.12/0.38  TRYING [2]
% 0.18/0.40  % (6707)First to succeed.
% 0.18/0.41  % (6707)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6701"
% 0.18/0.41  % (6707)Refutation found. Thanks to Tanya!
% 0.18/0.41  % SZS status Theorem for theBenchmark
% 0.18/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.41  % (6707)------------------------------
% 0.18/0.41  % (6707)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.41  % (6707)Termination reason: Refutation
% 0.18/0.41  
% 0.18/0.41  % (6707)Memory used [KB]: 1553
% 0.18/0.41  % (6707)Time elapsed: 0.053 s
% 0.18/0.41  % (6707)Instructions burned: 92 (million)
% 0.18/0.41  % (6701)Success in time 0.069 s
%------------------------------------------------------------------------------