TSTP Solution File: SET893+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET893+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 18:22:41 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   57 (   2 unt;   0 def)
%            Number of atoms       :  210 (  75 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  251 (  98   ~; 103   |;  35   &)
%                                         (  12 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   95 (  72   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f85,plain,
    $false,
    inference(avatar_sat_refutation,[],[f51,f56,f57,f64,f75,f84]) ).

fof(f84,plain,
    ( ~ spl5_1
    | spl5_2
    | ~ spl5_3 ),
    inference(avatar_contradiction_clause,[],[f83]) ).

fof(f83,plain,
    ( $false
    | ~ spl5_1
    | spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f82,f41]) ).

fof(f41,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f40]) ).

fof(f40,plain,
    ! [X2,X1] :
      ( in(X2,X1)
      | singleton(X2) != X1 ),
    inference(equality_resolution,[],[f35]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( in(X2,X1)
      | X0 != X2
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ( ( sK4(X0,X1) != X0
            | ~ in(sK4(X0,X1),X1) )
          & ( sK4(X0,X1) = X0
            | in(sK4(X0,X1),X1) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( X0 != X3
            | ~ in(X3,X1) )
          & ( X0 = X3
            | in(X3,X1) ) )
     => ( ( sK4(X0,X1) != X0
          | ~ in(sK4(X0,X1),X1) )
        & ( sK4(X0,X1) = X0
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X3] :
            ( ( X0 != X3
              | ~ in(X3,X1) )
            & ( X0 = X3
              | in(X3,X1) ) ) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( in(X2,X0)
              | X1 != X2 )
            & ( X1 = X2
              | ~ in(X2,X0) ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X2] :
            ( ( X1 != X2
              | ~ in(X2,X0) )
            & ( X1 = X2
              | in(X2,X0) ) ) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> X1 = X2 )
    <=> singleton(X1) = X0 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f82,plain,
    ( ~ in(sK0,singleton(sK0))
    | ~ spl5_1
    | spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f80,f41]) ).

fof(f80,plain,
    ( ~ in(sK1,singleton(sK1))
    | ~ in(sK0,singleton(sK0))
    | ~ spl5_1
    | spl5_2
    | ~ spl5_3 ),
    inference(resolution,[],[f38,f77]) ).

fof(f77,plain,
    ( ~ in(ordered_pair(sK1,sK0),cartesian_product2(singleton(sK1),singleton(sK0)))
    | ~ spl5_1
    | spl5_2
    | ~ spl5_3 ),
    inference(forward_demodulation,[],[f76,f54]) ).

fof(f54,plain,
    ( sK1 = sK2
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f53,plain,
    ( spl5_3
  <=> sK1 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f76,plain,
    ( ~ in(ordered_pair(sK2,sK0),cartesian_product2(singleton(sK1),singleton(sK0)))
    | ~ spl5_1
    | spl5_2 ),
    inference(forward_demodulation,[],[f49,f46]) ).

fof(f46,plain,
    ( sK3 = sK0
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f44]) ).

fof(f44,plain,
    ( spl5_1
  <=> sK3 = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f49,plain,
    ( ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
    | spl5_2 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f48,plain,
    ( spl5_2
  <=> in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f38,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X0))
      | ~ in(X1,X3)
      | ~ in(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

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

fof(f26,plain,
    ! [X2,X1,X3,X0] :
      ( ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
        | ~ in(X1,X0)
        | ~ in(X3,X2) )
      & ( ( in(X1,X0)
          & in(X3,X2) )
        | ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2)) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X2,X1,X3,X0] :
      ( ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
        | ~ in(X1,X0)
        | ~ in(X3,X2) )
      & ( ( in(X1,X0)
          & in(X3,X2) )
        | ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2)) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X2,X1,X3,X0] :
      ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
    <=> ( in(X1,X0)
        & in(X3,X2) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X0,X3,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X0,X2)
        & in(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f75,plain,
    ( ~ spl5_1
    | ~ spl5_2
    | spl5_3 ),
    inference(avatar_contradiction_clause,[],[f74]) ).

fof(f74,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2
    | spl5_3 ),
    inference(subsumption_resolution,[],[f72,f55]) ).

fof(f55,plain,
    ( sK1 != sK2
    | spl5_3 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f72,plain,
    ( sK1 = sK2
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(resolution,[],[f71,f42]) ).

fof(f42,plain,
    ! [X2,X0] :
      ( ~ in(X2,singleton(X0))
      | X0 = X2 ),
    inference(equality_resolution,[],[f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | ~ in(X2,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f71,plain,
    ( in(sK2,singleton(sK1))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(resolution,[],[f37,f68]) ).

fof(f68,plain,
    ( in(ordered_pair(sK2,sK0),cartesian_product2(singleton(sK1),singleton(sK0)))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(backward_demodulation,[],[f50,f46]) ).

fof(f50,plain,
    ( in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f37,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X0))
      | in(X1,X3) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f64,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f62,f48,f44]) ).

fof(f62,plain,
    ( sK3 = sK0
    | ~ spl5_2 ),
    inference(resolution,[],[f61,f42]) ).

fof(f61,plain,
    ( in(sK3,singleton(sK0))
    | ~ spl5_2 ),
    inference(resolution,[],[f36,f50]) ).

fof(f36,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X0))
      | in(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f57,plain,
    ( spl5_3
    | spl5_2 ),
    inference(avatar_split_clause,[],[f30,f48,f53]) ).

fof(f30,plain,
    ( in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
    | sK1 = sK2 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( ( sK1 != sK2
      | sK3 != sK0
      | ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) )
    & ( ( sK1 = sK2
        & sK3 = sK0 )
      | in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( X1 != X2
          | X0 != X3
          | ~ in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) )
        & ( ( X1 = X2
            & X0 = X3 )
          | in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) ) )
   => ( ( sK1 != sK2
        | sK3 != sK0
        | ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) )
      & ( ( sK1 = sK2
          & sK3 = sK0 )
        | in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1,X2,X3] :
      ( ( X1 != X2
        | X0 != X3
        | ~ in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) )
      & ( ( X1 = X2
          & X0 = X3 )
        | in(ordered_pair(X2,X3),cartesian_product2(singleton(X1),singleton(X0))) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X0,X2,X1,X3] :
      ( ( X1 != X2
        | X0 != X3
        | ~ in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) )
      & ( ( X1 = X2
          & X0 = X3 )
        | in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X0,X2,X1,X3] :
      ( ( X1 != X2
        | X0 != X3
        | ~ in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) )
      & ( ( X1 = X2
          & X0 = X3 )
        | in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ? [X0,X2,X1,X3] :
      ( in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0)))
    <~> ( X1 = X2
        & X0 = X3 ) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X2,X1,X0,X3] :
        ( ( X1 = X2
          & X0 = X3 )
      <=> in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),singleton(X0))) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X3,X0,X2,X1] :
        ( ( X1 = X3
          & X0 = X2 )
      <=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X3,X0,X2,X1] :
      ( ( X1 = X3
        & X0 = X2 )
    <=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).

fof(f56,plain,
    ( ~ spl5_2
    | ~ spl5_3
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f31,f44,f53,f48]) ).

fof(f31,plain,
    ( sK3 != sK0
    | sK1 != sK2
    | ~ in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0))) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f51,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f29,f48,f44]) ).

fof(f29,plain,
    ( in(ordered_pair(sK2,sK3),cartesian_product2(singleton(sK1),singleton(sK0)))
    | sK3 = sK0 ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 14:29:56 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.50  % (11053)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.50  % (11045)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.50  % (11063)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.50  % (11054)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.50  % (11054)Refutation not found, incomplete strategy% (11054)------------------------------
% 0.20/0.50  % (11054)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (11054)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (11054)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50  
% 0.20/0.50  % (11054)Memory used [KB]: 5884
% 0.20/0.50  % (11054)Time elapsed: 0.106 s
% 0.20/0.50  % (11054)Instructions burned: 2 (million)
% 0.20/0.50  % (11054)------------------------------
% 0.20/0.50  % (11054)------------------------------
% 0.20/0.51  % (11049)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.51  % (11058)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  % (11056)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)
% 0.20/0.51  % (11048)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)
% 0.20/0.51  % (11048)First to succeed.
% 0.20/0.51  % (11048)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (11048)------------------------------
% 0.20/0.52  % (11048)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (11048)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (11048)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (11048)Memory used [KB]: 6012
% 0.20/0.52  % (11048)Time elapsed: 0.119 s
% 0.20/0.52  % (11048)Instructions burned: 2 (million)
% 0.20/0.52  % (11048)------------------------------
% 0.20/0.52  % (11048)------------------------------
% 0.20/0.52  % (11043)Success in time 0.167 s
%------------------------------------------------------------------------------