TSTP Solution File: SET084+1 by SnakeForV---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET084+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n017.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 : Wed Aug 31 18:19:01 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   45 (  12 unt;   0 def)
%            Number of atoms       :  131 (  46 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  135 (  49   ~;  40   |;  34   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   65 (  54   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f619,plain,
    $false,
    inference(avatar_sat_refutation,[],[f424,f537,f616]) ).

fof(f616,plain,
    ~ spl8_14,
    inference(avatar_contradiction_clause,[],[f615]) ).

fof(f615,plain,
    ( $false
    | ~ spl8_14 ),
    inference(trivial_inequality_removal,[],[f614]) ).

fof(f614,plain,
    ( sK3 != sK3
    | ~ spl8_14 ),
    inference(superposition,[],[f211,f607]) ).

fof(f607,plain,
    ( sK4 = sK3
    | ~ spl8_14 ),
    inference(duplicate_literal_removal,[],[f600]) ).

fof(f600,plain,
    ( sK4 = sK3
    | sK4 = sK3
    | ~ spl8_14 ),
    inference(resolution,[],[f178,f420]) ).

fof(f420,plain,
    ( member(sK4,unordered_pair(sK3,sK3))
    | ~ spl8_14 ),
    inference(avatar_component_clause,[],[f418]) ).

fof(f418,plain,
    ( spl8_14
  <=> member(sK4,unordered_pair(sK3,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).

fof(f178,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,unordered_pair(X1,X0))
      | X1 = X2
      | X0 = X2 ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,unordered_pair(X1,X0))
        | ( X1 != X2
          & X0 != X2 )
        | ~ member(X2,universal_class) )
      & ( ( ( X1 = X2
            | X0 = X2 )
          & member(X2,universal_class) )
        | ~ member(X2,unordered_pair(X1,X0)) ) ),
    inference(rectify,[],[f106]) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,unordered_pair(X0,X2))
        | ( X0 != X1
          & X1 != X2 )
        | ~ member(X1,universal_class) )
      & ( ( ( X0 = X1
            | X1 = X2 )
          & member(X1,universal_class) )
        | ~ member(X1,unordered_pair(X0,X2)) ) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,unordered_pair(X0,X2))
        | ( X0 != X1
          & X1 != X2 )
        | ~ member(X1,universal_class) )
      & ( ( ( X0 = X1
            | X1 = X2 )
          & member(X1,universal_class) )
        | ~ member(X1,unordered_pair(X0,X2)) ) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( member(X1,unordered_pair(X0,X2))
    <=> ( ( X0 = X1
          | X1 = X2 )
        & member(X1,universal_class) ) ),
    inference(rectify,[],[f4]) ).

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

fof(f211,plain,
    sK4 != sK3,
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ( member(sK4,universal_class)
    & singleton(sK3) = singleton(sK4)
    & sK4 != sK3 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f130,f131]) ).

fof(f131,plain,
    ( ? [X0,X1] :
        ( member(X1,universal_class)
        & singleton(X0) = singleton(X1)
        & X0 != X1 )
   => ( member(sK4,universal_class)
      & singleton(sK3) = singleton(sK4)
      & sK4 != sK3 ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ? [X0,X1] :
      ( member(X1,universal_class)
      & singleton(X0) = singleton(X1)
      & X0 != X1 ),
    inference(rectify,[],[f78]) ).

fof(f78,plain,
    ? [X1,X0] :
      ( member(X0,universal_class)
      & singleton(X0) = singleton(X1)
      & X0 != X1 ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ? [X0,X1] :
      ( X0 != X1
      & singleton(X0) = singleton(X1)
      & member(X0,universal_class) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ~ ! [X0,X1] :
        ( ( singleton(X0) = singleton(X1)
          & member(X0,universal_class) )
       => X0 = X1 ),
    inference(rectify,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X1,X0] :
        ( ( member(X1,universal_class)
          & singleton(X0) = singleton(X1) )
       => X0 = X1 ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X1,X0] :
      ( ( member(X1,universal_class)
        & singleton(X0) = singleton(X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element2) ).

fof(f537,plain,
    spl8_12,
    inference(avatar_split_clause,[],[f529,f404]) ).

fof(f404,plain,
    ( spl8_12
  <=> member(sK4,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).

fof(f529,plain,
    member(sK4,universal_class),
    inference(resolution,[],[f518,f214]) ).

fof(f214,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[],[f2]) ).

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

fof(f518,plain,
    ! [X28] :
      ( ~ subclass(universal_class,X28)
      | member(sK4,X28) ),
    inference(resolution,[],[f224,f213]) ).

fof(f213,plain,
    member(sK4,universal_class),
    inference(cnf_transformation,[],[f132]) ).

fof(f224,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,X0)
      | ~ subclass(X1,X0) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subclass(X1,X0) )
      & ( subclass(X1,X0)
        | ( ~ member(sK6(X0,X1),X0)
          & member(sK6(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f138,f139]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X0)
          & member(X3,X1) )
     => ( ~ member(sK6(X0,X1),X0)
        & member(sK6(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subclass(X1,X0) )
      & ( subclass(X1,X0)
        | ? [X3] :
            ( ~ member(X3,X0)
            & member(X3,X1) ) ) ),
    inference(rectify,[],[f137]) ).

fof(f137,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subclass(X0,X1) )
      & ( subclass(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) )
    <=> subclass(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f424,plain,
    ( spl8_14
    | ~ spl8_12 ),
    inference(avatar_split_clause,[],[f423,f404,f418]) ).

fof(f423,plain,
    ( ~ member(sK4,universal_class)
    | member(sK4,unordered_pair(sK3,sK3)) ),
    inference(superposition,[],[f287,f271]) ).

fof(f271,plain,
    unordered_pair(sK3,sK3) = unordered_pair(sK4,sK4),
    inference(definition_unfolding,[],[f212,f161,f161]) ).

fof(f161,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/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f212,plain,
    singleton(sK3) = singleton(sK4),
    inference(cnf_transformation,[],[f132]) ).

fof(f287,plain,
    ! [X2,X1] :
      ( member(X2,unordered_pair(X1,X2))
      | ~ member(X2,universal_class) ),
    inference(equality_resolution,[],[f179]) ).

fof(f179,plain,
    ! [X2,X0,X1] :
      ( member(X2,unordered_pair(X1,X0))
      | X0 != X2
      | ~ member(X2,universal_class) ),
    inference(cnf_transformation,[],[f107]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET084+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 12:36:05 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (14887)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50  % (14882)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (14882)Instruction limit reached!
% 0.19/0.50  % (14882)------------------------------
% 0.19/0.50  % (14882)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (14879)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (14882)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (14882)Termination reason: Unknown
% 0.19/0.50  % (14882)Termination phase: Preprocessing 3
% 0.19/0.50  
% 0.19/0.50  % (14882)Memory used [KB]: 1535
% 0.19/0.50  % (14882)Time elapsed: 0.004 s
% 0.19/0.50  % (14882)Instructions burned: 3 (million)
% 0.19/0.50  % (14882)------------------------------
% 0.19/0.50  % (14882)------------------------------
% 0.19/0.50  % (14874)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.50  % (14887)First to succeed.
% 0.19/0.51  % (14870)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.51  % (14873)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.51  % (14887)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (14887)------------------------------
% 0.19/0.51  % (14887)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (14887)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (14887)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (14887)Memory used [KB]: 6268
% 0.19/0.51  % (14887)Time elapsed: 0.068 s
% 0.19/0.51  % (14887)Instructions burned: 11 (million)
% 0.19/0.51  % (14887)------------------------------
% 0.19/0.51  % (14887)------------------------------
% 0.19/0.51  % (14864)Success in time 0.16 s
%------------------------------------------------------------------------------