TSTP Solution File: SET881+1 by SnakeForV---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n022.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 18:22:39 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   29 (  13 unt;   0 def)
%            Number of atoms       :  110 (  76 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  130 (  49   ~;  48   |;  25   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :   57 (  49   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f71,plain,
    $false,
    inference(subsumption_resolution,[],[f70,f50]) ).

fof(f50,plain,
    empty_set != sF7,
    inference(definition_folding,[],[f33,f49,f48,f47]) ).

fof(f47,plain,
    sF5 = singleton(sK1),
    introduced(function_definition,[]) ).

fof(f48,plain,
    unordered_pair(sK1,sK2) = sF6,
    introduced(function_definition,[]) ).

fof(f49,plain,
    set_difference(sF5,sF6) = sF7,
    introduced(function_definition,[]) ).

fof(f33,plain,
    empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f19]) ).

fof(f19,plain,
    ( ? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1))
   => empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1)),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X1,X0] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X1,X0] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).

fof(f70,plain,
    empty_set = sF7,
    inference(subsumption_resolution,[],[f68,f51]) ).

fof(f51,plain,
    in(sK1,sF6),
    inference(superposition,[],[f46,f48]) ).

fof(f46,plain,
    ! [X2,X3] : in(X3,unordered_pair(X3,X2)),
    inference(equality_resolution,[],[f45]) ).

fof(f45,plain,
    ! [X2,X3,X0] :
      ( in(X3,X0)
      | unordered_pair(X3,X2) != X0 ),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | X1 != X3
      | unordered_pair(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 )
      & ( unordered_pair(X1,X2) = X0
        | ( ( ~ in(sK4(X0,X1,X2),X0)
            | ( sK4(X0,X1,X2) != X2
              & sK4(X0,X1,X2) != X1 ) )
          & ( in(sK4(X0,X1,X2),X0)
            | sK4(X0,X1,X2) = X2
            | sK4(X0,X1,X2) = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X0)
            | ( X2 != X4
              & X1 != X4 ) )
          & ( in(X4,X0)
            | X2 = X4
            | X1 = X4 ) )
     => ( ( ~ in(sK4(X0,X1,X2),X0)
          | ( sK4(X0,X1,X2) != X2
            & sK4(X0,X1,X2) != X1 ) )
        & ( in(sK4(X0,X1,X2),X0)
          | sK4(X0,X1,X2) = X2
          | sK4(X0,X1,X2) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 )
      & ( unordered_pair(X1,X2) = X0
        | ? [X4] :
            ( ( ~ in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) )
            & ( in(X4,X0)
              | X2 = X4
              | X1 = X4 ) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( X0 = X3
              | X1 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X0 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ( X0 != X3
                & X1 != X3 ) )
            & ( in(X3,X2)
              | X0 = X3
              | X1 = X3 ) ) ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( X0 = X3
              | X1 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X0 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ( X0 != X3
                & X1 != X3 ) )
            & ( in(X3,X2)
              | X0 = X3
              | X1 = X3 ) ) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X2,X1,X0] :
      ( ! [X3] :
          ( ( X0 = X3
            | X1 = X3 )
        <=> in(X3,X2) )
    <=> unordered_pair(X1,X0) = X2 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( ( X1 = X3
            | X0 = X3 )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f68,plain,
    ( ~ in(sK1,sF6)
    | empty_set = sF7 ),
    inference(superposition,[],[f67,f49]) ).

fof(f67,plain,
    ! [X0] :
      ( empty_set = set_difference(sF5,X0)
      | ~ in(sK1,X0) ),
    inference(superposition,[],[f30,f47]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( empty_set = set_difference(singleton(X1),X0)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( in(X1,X0)
        | empty_set != set_difference(singleton(X1),X0) )
      & ( empty_set = set_difference(singleton(X1),X0)
        | ~ in(X1,X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( in(X1,X0)
    <=> empty_set = set_difference(singleton(X1),X0) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( empty_set = set_difference(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % 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 : n022.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 14:29:11 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (7822)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (7850)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.50  % (7826)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50  % (7822)First to succeed.
% 0.19/0.50  % (7822)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (7822)------------------------------
% 0.19/0.50  % (7822)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (7822)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (7822)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (7822)Memory used [KB]: 5884
% 0.19/0.50  % (7822)Time elapsed: 0.092 s
% 0.19/0.50  % (7822)Instructions burned: 3 (million)
% 0.19/0.50  % (7822)------------------------------
% 0.19/0.50  % (7822)------------------------------
% 0.19/0.50  % (7818)Success in time 0.156 s
%------------------------------------------------------------------------------