%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET923+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 : 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 18:22:45 EDT 2022

% Result   : Theorem 1.26s 0.52s
% Output   : Refutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (   6 unt;   0 def)
%            Number of atoms       :   57 (  44 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   68 (  32   ~;  14   |;  19   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   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   :   24 (  20   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f44,plain,
    $false,
    inference(subsumption_resolution,[],[f43,f22]) ).

fof(f22,plain,
    singleton(sK1) != sK2,
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( empty_set = set_difference(sK2,singleton(sK1))
    & empty_set != sK2
    & singleton(sK1) != sK2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f14]) ).

fof(f14,plain,
    ( ? [X0,X1] :
        ( empty_set = set_difference(X1,singleton(X0))
        & empty_set != X1
        & singleton(X0) != X1 )
   => ( empty_set = set_difference(sK2,singleton(sK1))
      & empty_set != sK2
      & singleton(sK1) != sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0,X1] :
      ( empty_set = set_difference(X1,singleton(X0))
      & empty_set != X1
      & singleton(X0) != X1 ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,plain,
    ~ ! [X1,X0] :
        ~ ( empty_set = set_difference(X1,singleton(X0))
          & empty_set != X1
          & singleton(X0) != X1 ),
    inference(rectify,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X1,X0] :
        ~ ( empty_set != X0
          & empty_set = set_difference(X0,singleton(X1))
          & singleton(X1) != X0 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X1,X0] :
      ~ ( empty_set != X0
        & empty_set = set_difference(X0,singleton(X1))
        & singleton(X1) != X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).

fof(f43,plain,
    singleton(sK1) = sK2,
    inference(subsumption_resolution,[],[f42,f23]) ).

fof(f23,plain,
    empty_set != sK2,
    inference(cnf_transformation,[],[f15]) ).

fof(f42,plain,
    ( empty_set = sK2
    | singleton(sK1) = sK2 ),
    inference(resolution,[],[f30,f38]) ).

fof(f38,plain,
    subset(sK2,singleton(sK1)),
    inference(trivial_inequality_removal,[],[f37]) ).

fof(f37,plain,
    ( empty_set != empty_set
    | subset(sK2,singleton(sK1)) ),
    inference(superposition,[],[f26,f24]) ).

fof(f24,plain,
    empty_set = set_difference(sK2,singleton(sK1)),
    inference(cnf_transformation,[],[f15]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( empty_set != set_difference(X0,X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | empty_set != set_difference(X0,X1) )
      & ( empty_set = set_difference(X0,X1)
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> empty_set = set_difference(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ subset(X0,singleton(X1))
      | empty_set = X0
      | singleton(X1) = X0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,singleton(X1))
        | ( empty_set != X0
          & singleton(X1) != X0 ) )
      & ( empty_set = X0
        | singleton(X1) = X0
        | ~ subset(X0,singleton(X1)) ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( subset(X0,singleton(X1))
        | ( empty_set != X0
          & singleton(X1) != X0 ) )
      & ( empty_set = X0
        | singleton(X1) = X0
        | ~ subset(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
    <=> ( empty_set = X0
        | singleton(X1) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET923+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:33:20 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.51  % (8565)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)
% 0.20/0.51  % (8557)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)
% 0.20/0.51  % (8555)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 1.26/0.52  % (8557)First to succeed.
% 1.26/0.52  % (8565)Also succeeded, but the first one will report.
% 1.26/0.52  % (8557)Refutation found. Thanks to Tanya!
% 1.26/0.52  % SZS status Theorem for theBenchmark
% 1.26/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.26/0.52  % (8557)------------------------------
% 1.26/0.52  % (8557)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.26/0.52  % (8557)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.26/0.52  % (8557)Termination reason: Refutation
% 1.26/0.52  
% 1.26/0.52  % (8557)Memory used [KB]: 5884
% 1.26/0.52  % (8557)Time elapsed: 0.062 s
% 1.26/0.52  % (8557)Instructions burned: 1 (million)
% 1.26/0.52  % (8557)------------------------------
% 1.26/0.52  % (8557)------------------------------
% 1.26/0.52  % (8542)Success in time 0.166 s
%------------------------------------------------------------------------------