TSTP Solution File: SET065+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET065+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 : n003.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 : Tue Apr 30 15:05:24 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   26 (  10 unt;   0 def)
%            Number of atoms       :   80 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   86 (  32   ~;  24   |;  23   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   40 (  34   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f371,plain,
    $false,
    inference(resolution,[],[f362,f219]) ).

fof(f219,plain,
    inductive(sK5),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ( ! [X1] :
        ( subclass(sK5,X1)
        | ~ inductive(X1) )
    & inductive(sK5)
    & member(sK5,universal_class) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f84,f131]) ).

fof(f131,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( subclass(X0,X1)
            | ~ inductive(X1) )
        & inductive(X0)
        & member(X0,universal_class) )
   => ( ! [X1] :
          ( subclass(sK5,X1)
          | ~ inductive(X1) )
      & inductive(sK5)
      & member(sK5,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ? [X0] :
      ( ! [X1] :
          ( subclass(X0,X1)
          | ~ inductive(X1) )
      & inductive(X0)
      & member(X0,universal_class) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ? [X0] :
      ( ! [X1] :
          ( inductive(X1)
         => subclass(X0,X1) )
      & inductive(X0)
      & member(X0,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).

fof(f362,plain,
    ! [X0] : ~ inductive(X0),
    inference(resolution,[],[f355,f149]) ).

fof(f149,plain,
    ! [X0] :
      ( member(null_class,X0)
      | ~ inductive(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ( inductive(X0)
        | ~ subclass(image(successor_relation,X0),X0)
        | ~ member(null_class,X0) )
      & ( ( subclass(image(successor_relation,X0),X0)
          & member(null_class,X0) )
        | ~ inductive(X0) ) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ( inductive(X0)
        | ~ subclass(image(successor_relation,X0),X0)
        | ~ member(null_class,X0) )
      & ( ( subclass(image(successor_relation,X0),X0)
          & member(null_class,X0) )
        | ~ inductive(X0) ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ( inductive(X0)
    <=> ( subclass(image(successor_relation,X0),X0)
        & member(null_class,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).

fof(f355,plain,
    ! [X0] : ~ member(null_class,X0),
    inference(resolution,[],[f353,f137]) ).

fof(f137,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(f353,plain,
    ! [X0] :
      ( ~ subclass(X0,universal_class)
      | ~ member(null_class,X0) ),
    inference(resolution,[],[f170,f133]) ).

fof(f133,plain,
    ~ member(null_class,universal_class),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ~ member(null_class,universal_class),
    inference(flattening,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ member(null_class,universal_class),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    member(null_class,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).

fof(f170,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subclass(X0,X1) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ( subclass(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subclass(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f98,f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,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,[],[f97]) ).

fof(f97,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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 01:40:03 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (8655)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (8658)WARNING: value z3 for option sas not known
% 0.14/0.38  % (8658)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)
% 0.14/0.38  % (8661)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)
% 0.14/0.38  % (8657)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (8662)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)
% 0.14/0.38  % (8659)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (8660)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)
% 0.14/0.38  % (8656)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  % (8661)First to succeed.
% 0.14/0.39  % (8658)Also succeeded, but the first one will report.
% 0.14/0.39  % (8661)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (8661)------------------------------
% 0.14/0.39  % (8661)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (8661)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (8661)Memory used [KB]: 966
% 0.14/0.39  % (8661)Time elapsed: 0.009 s
% 0.14/0.39  % (8661)Instructions burned: 16 (million)
% 0.14/0.39  % (8661)------------------------------
% 0.14/0.39  % (8661)------------------------------
% 0.14/0.39  % (8655)Success in time 0.024 s
%------------------------------------------------------------------------------