%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n019.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 18:23:37 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 (  35 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   :   27 (  15   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f297,plain,
    $false,
    inference(trivial_inequality_removal,[],[f296]) ).

fof(f296,plain,
    unordered_pair(sK4,sK4) != unordered_pair(sK4,sK4),
    inference(resolution,[],[f295,f292]) ).

fof(f292,plain,
    member(sK4,universal_class),
    inference(equality_resolution,[],[f209]) ).

fof(f209,plain,
    ! [X1] :
      ( sK3 != X1
      | member(sK4,universal_class) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ! [X1] :
      ( ( ~ member(X1,universal_class)
        | singleton(X1) != sK3 )
      & ( sK3 != X1
        | ( singleton(sK4) = sK3
          & member(sK4,universal_class) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f76,f132,f131]) ).

fof(f131,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( ~ member(X1,universal_class)
          | singleton(X1) != X0 )
        & ( X0 != X1
          | ? [X2] :
              ( singleton(X2) = X0
              & member(X2,universal_class) ) ) )
   => ! [X1] :
        ( ( ~ member(X1,universal_class)
          | singleton(X1) != sK3 )
        & ( sK3 != X1
          | ? [X2] :
              ( singleton(X2) = sK3
              & member(X2,universal_class) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X2] :
        ( singleton(X2) = sK3
        & member(X2,universal_class) )
   => ( singleton(sK4) = sK3
      & member(sK4,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ? [X0] :
    ! [X1] :
      ( ( ~ member(X1,universal_class)
        | singleton(X1) != X0 )
      & ( X0 != X1
        | ? [X2] :
            ( singleton(X2) = X0
            & member(X2,universal_class) ) ) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ~ ! [X0] :
      ? [X1] :
        ( ( singleton(X1) = X0
          & member(X1,universal_class) )
        | ( ~ ? [X2] :
                ( singleton(X2) = X0
                & member(X2,universal_class) )
          & X0 = X1 ) ),
    inference(rectify,[],[f45]) ).

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

fof(f44,conjecture,
    ! [X0] :
    ? [X2] :
      ( ( X0 = X2
        & ~ ? [X1] :
              ( singleton(X1) = X0
              & member(X1,universal_class) ) )
      | ( singleton(X2) = X0
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_substitution) ).

fof(f295,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | unordered_pair(X1,X1) != unordered_pair(sK4,sK4) ),
    inference(forward_demodulation,[],[f274,f291]) ).

fof(f291,plain,
    sK3 = unordered_pair(sK4,sK4),
    inference(equality_resolution,[],[f275]) ).

fof(f275,plain,
    ! [X1] :
      ( sK3 != X1
      | sK3 = unordered_pair(sK4,sK4) ),
    inference(definition_unfolding,[],[f210,f208]) ).

fof(f208,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(f210,plain,
    ! [X1] :
      ( sK3 != X1
      | singleton(sK4) = sK3 ),
    inference(cnf_transformation,[],[f133]) ).

fof(f274,plain,
    ! [X1] :
      ( unordered_pair(X1,X1) != sK3
      | ~ member(X1,universal_class) ),
    inference(definition_unfolding,[],[f211,f208]) ).

fof(f211,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | singleton(X1) != sK3 ),
    inference(cnf_transformation,[],[f133]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n019.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 13:15:50 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (10934)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.50  % (10926)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.50  % (10918)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (10935)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.50  % (10934)First to succeed.
% 0.19/0.51  % (10934)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  % (10934)------------------------------
% 0.19/0.51  % (10934)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (10934)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (10934)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (10934)Memory used [KB]: 1023
% 0.19/0.51  % (10934)Time elapsed: 0.055 s
% 0.19/0.51  % (10934)Instructions burned: 6 (million)
% 0.19/0.51  % (10934)------------------------------
% 0.19/0.51  % (10934)------------------------------
% 0.19/0.51  % (10911)Success in time 0.156 s
%------------------------------------------------------------------------------