%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET954+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 : 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 18:22:51 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   34 (  12 unt;   0 def)
%            Number of atoms       :   74 (   3 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   70 (  30   ~;  19   |;  13   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   74 (  62   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f64,plain,
    $false,
    inference(avatar_sat_refutation,[],[f61,f62,f63]) ).

fof(f63,plain,
    spl6_2,
    inference(avatar_split_clause,[],[f48,f58]) ).

fof(f58,plain,
    ( spl6_2
  <=> in(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f48,plain,
    in(sK2,sK1),
    inference(resolution,[],[f45,f41]) ).

fof(f41,plain,
    in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK1,sK4)),
    inference(definition_unfolding,[],[f33,f30]) ).

fof(f30,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(f33,plain,
    in(ordered_pair(sK2,sK3),cartesian_product2(sK1,sK4)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK4,sK1))
    & in(ordered_pair(sK2,sK3),cartesian_product2(sK1,sK4)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f20,f21]) ).

fof(f21,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ in(ordered_pair(X2,X1),cartesian_product2(X3,X0))
        & in(ordered_pair(X1,X2),cartesian_product2(X0,X3)) )
   => ( ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK4,sK1))
      & in(ordered_pair(sK2,sK3),cartesian_product2(sK1,sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X2,X1),cartesian_product2(X3,X0))
      & in(ordered_pair(X1,X2),cartesian_product2(X0,X3)) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ? [X0,X2,X3,X1] :
      ( ~ in(ordered_pair(X3,X2),cartesian_product2(X1,X0))
      & in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ~ ! [X3,X0,X2,X1] :
        ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
       => in(ordered_pair(X3,X2),cartesian_product2(X1,X0)) ),
    inference(rectify,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X2,X3,X0,X1] :
        ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
       => in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
     => in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).

fof(f45,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3))
      | in(X0,X1) ),
    inference(definition_unfolding,[],[f37,f30]) ).

fof(f37,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,X1)
      | ~ in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X2),cartesian_product2(X1,X3))
        | ~ in(X2,X3)
        | ~ in(X0,X1) )
      & ( ( in(X2,X3)
          & in(X0,X1) )
        | ~ in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X3,X2,X0,X1] :
      ( ( in(ordered_pair(X3,X0),cartesian_product2(X2,X1))
        | ~ in(X0,X1)
        | ~ in(X3,X2) )
      & ( ( in(X0,X1)
          & in(X3,X2) )
        | ~ in(ordered_pair(X3,X0),cartesian_product2(X2,X1)) ) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X3,X2,X0,X1] :
      ( ( in(ordered_pair(X3,X0),cartesian_product2(X2,X1))
        | ~ in(X0,X1)
        | ~ in(X3,X2) )
      & ( ( in(X0,X1)
          & in(X3,X2) )
        | ~ in(ordered_pair(X3,X0),cartesian_product2(X2,X1)) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X3,X2,X0,X1] :
      ( in(ordered_pair(X3,X0),cartesian_product2(X2,X1))
    <=> ( in(X0,X1)
        & in(X3,X2) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X3,X2,X0] :
      ( ( in(X0,X2)
        & in(X1,X3) )
    <=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f62,plain,
    spl6_1,
    inference(avatar_split_clause,[],[f47,f54]) ).

fof(f54,plain,
    ( spl6_1
  <=> in(sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f47,plain,
    in(sK3,sK4),
    inference(resolution,[],[f44,f41]) ).

fof(f44,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3))
      | in(X2,X3) ),
    inference(definition_unfolding,[],[f38,f30]) ).

fof(f38,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X3)
      | ~ in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f61,plain,
    ( ~ spl6_1
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f49,f58,f54]) ).

fof(f49,plain,
    ( ~ in(sK2,sK1)
    | ~ in(sK3,sK4) ),
    inference(resolution,[],[f43,f40]) ).

fof(f40,plain,
    ~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK4,sK1)),
    inference(definition_unfolding,[],[f34,f30]) ).

fof(f34,plain,
    ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK4,sK1)),
    inference(cnf_transformation,[],[f22]) ).

fof(f43,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3))
      | ~ in(X0,X1)
      | ~ in(X2,X3) ),
    inference(definition_unfolding,[],[f39,f30]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X2),cartesian_product2(X1,X3))
      | ~ in(X2,X3)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % 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 : n017.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 13:56:05 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (25483)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.50  % (25498)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  % (25498)First to succeed.
% 0.19/0.50  % (25496)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.50  % (25498)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  % (25498)------------------------------
% 0.19/0.50  % (25498)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (25498)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (25498)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (25498)Memory used [KB]: 5884
% 0.19/0.50  % (25498)Time elapsed: 0.055 s
% 0.19/0.50  % (25498)Instructions burned: 1 (million)
% 0.19/0.50  % (25498)------------------------------
% 0.19/0.50  % (25498)------------------------------
% 0.19/0.50  % (25474)Success in time 0.154 s
%------------------------------------------------------------------------------