%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET086+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 : n016.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 18:19:02 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   19 (   6 unt;   0 def)
%            Number of atoms       :   57 (  34 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   65 (  27   ~;  17   |;  19   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   26 (  14   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f299,plain,
    $false,
    inference(resolution,[],[f298,f291]) ).

fof(f291,plain,
    member(sK5,universal_class),
    inference(equality_resolution,[],[f191]) ).

fof(f191,plain,
    ! [X1] :
      ( member(sK5,universal_class)
      | sK4 != X1 ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X1] :
      ( ( ( member(sK5,universal_class)
          & singleton(sK5) = sK4 )
        | sK4 != X1 )
      & ( ~ member(X1,universal_class)
        | singleton(X1) != sK4 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f78,f116,f115]) ).

fof(f115,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( ? [X2] :
              ( member(X2,universal_class)
              & singleton(X2) = X0 )
          | X0 != X1 )
        & ( ~ member(X1,universal_class)
          | singleton(X1) != X0 ) )
   => ! [X1] :
        ( ( ? [X2] :
              ( member(X2,universal_class)
              & singleton(X2) = sK4 )
          | sK4 != X1 )
        & ( ~ member(X1,universal_class)
          | singleton(X1) != sK4 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ( ? [X2] :
        ( member(X2,universal_class)
        & singleton(X2) = sK4 )
   => ( member(sK5,universal_class)
      & singleton(sK5) = sK4 ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ? [X0] :
    ! [X1] :
      ( ( ? [X2] :
            ( member(X2,universal_class)
            & singleton(X2) = X0 )
        | X0 != X1 )
      & ( ~ member(X1,universal_class)
        | singleton(X1) != X0 ) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,plain,
    ~ ! [X0] :
      ? [X1] :
        ( ( singleton(X1) = X0
          & member(X1,universal_class) )
        | ( ~ ? [X2] :
                ( member(X2,universal_class)
                & singleton(X2) = X0 )
          & X0 = X1 ) ),
    inference(rectify,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0] :
      ? [X2] :
        ( ( member(X2,universal_class)
          & singleton(X2) = X0 )
        | ( X0 = X2
          & ~ ? [X1] :
                ( singleton(X1) = X0
                & member(X1,universal_class) ) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0] :
    ? [X2] :
      ( ( member(X2,universal_class)
        & singleton(X2) = X0 )
      | ( X0 = X2
        & ~ ? [X1] :
              ( singleton(X1) = X0
              & member(X1,universal_class) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_substitution) ).

fof(f298,plain,
    ~ member(sK5,universal_class),
    inference(trivial_inequality_removal,[],[f297]) ).

fof(f297,plain,
    ( ~ member(sK5,universal_class)
    | sK4 != sK4 ),
    inference(superposition,[],[f267,f292]) ).

fof(f292,plain,
    unordered_pair(sK5,sK5) = sK4,
    inference(equality_resolution,[],[f266]) ).

fof(f266,plain,
    ! [X1] :
      ( unordered_pair(sK5,sK5) = sK4
      | sK4 != X1 ),
    inference(definition_unfolding,[],[f190,f204]) ).

fof(f204,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(f190,plain,
    ! [X1] :
      ( singleton(sK5) = sK4
      | sK4 != X1 ),
    inference(cnf_transformation,[],[f117]) ).

fof(f267,plain,
    ! [X1] :
      ( unordered_pair(X1,X1) != sK4
      | ~ member(X1,universal_class) ),
    inference(definition_unfolding,[],[f189,f204]) ).

fof(f189,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | singleton(X1) != sK4 ),
    inference(cnf_transformation,[],[f117]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 13:34:46 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (3676)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  % (3668)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)
% 0.19/0.51  % (3668)Instruction limit reached!
% 0.19/0.51  % (3668)------------------------------
% 0.19/0.51  % (3668)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (3668)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (3668)Termination reason: Unknown
% 0.19/0.51  % (3668)Termination phase: Preprocessing 3
% 0.19/0.51  
% 0.19/0.51  % (3668)Memory used [KB]: 1535
% 0.19/0.51  % (3668)Time elapsed: 0.004 s
% 0.19/0.51  % (3668)Instructions burned: 3 (million)
% 0.19/0.51  % (3668)------------------------------
% 0.19/0.51  % (3668)------------------------------
% 0.19/0.51  % (3662)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  % (3676)First to succeed.
% 0.19/0.51  % (3660)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (3660)Also succeeded, but the first one will report.
% 0.19/0.51  % (3676)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  % (3676)------------------------------
% 0.19/0.51  % (3676)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (3676)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (3676)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (3676)Memory used [KB]: 6012
% 0.19/0.51  % (3676)Time elapsed: 0.057 s
% 0.19/0.51  % (3676)Instructions burned: 6 (million)
% 0.19/0.51  % (3676)------------------------------
% 0.19/0.51  % (3676)------------------------------
% 0.19/0.51  % (3653)Success in time 0.163 s
%------------------------------------------------------------------------------