TSTP Solution File: SET901+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET901+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 : n025.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 18:22:42 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   59 (   8 unt;   0 def)
%            Number of atoms       :  218 ( 123 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  265 ( 106   ~;  99   |;  48   &)
%                                         (  10 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   64 (  49   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f89,plain,
    $false,
    inference(avatar_sat_refutation,[],[f48,f53,f58,f63,f65,f71,f74,f82,f87]) ).

fof(f87,plain,
    ( spl3_2
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f86]) ).

fof(f86,plain,
    ( $false
    | spl3_2
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f83,f37]) ).

fof(f37,plain,
    ! [X0,X1] : subset(empty_set,unordered_pair(X0,X1)),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( subset(X2,unordered_pair(X0,X1))
      | empty_set != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( singleton(X0) = X2
        | empty_set = X2
        | singleton(X1) = X2
        | unordered_pair(X0,X1) = X2
        | ~ subset(X2,unordered_pair(X0,X1)) )
      & ( subset(X2,unordered_pair(X0,X1))
        | ( singleton(X0) != X2
          & empty_set != X2
          & singleton(X1) != X2
          & unordered_pair(X0,X1) != X2 ) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X1,X2,X0] :
      ( ( singleton(X1) = X0
        | empty_set = X0
        | singleton(X2) = X0
        | unordered_pair(X1,X2) = X0
        | ~ subset(X0,unordered_pair(X1,X2)) )
      & ( subset(X0,unordered_pair(X1,X2))
        | ( singleton(X1) != X0
          & empty_set != X0
          & singleton(X2) != X0
          & unordered_pair(X1,X2) != X0 ) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X1,X2,X0] :
      ( ( singleton(X1) = X0
        | empty_set = X0
        | singleton(X2) = X0
        | unordered_pair(X1,X2) = X0
        | ~ subset(X0,unordered_pair(X1,X2)) )
      & ( subset(X0,unordered_pair(X1,X2))
        | ( singleton(X1) != X0
          & empty_set != X0
          & singleton(X2) != X0
          & unordered_pair(X1,X2) != X0 ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X2,X0] :
      ( ( singleton(X1) = X0
        | empty_set = X0
        | singleton(X2) = X0
        | unordered_pair(X1,X2) = X0 )
    <=> subset(X0,unordered_pair(X1,X2)) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X2,X1,X0] :
      ( subset(X0,unordered_pair(X1,X2))
    <=> ~ ( singleton(X2) != X0
          & empty_set != X0
          & unordered_pair(X1,X2) != X0
          & singleton(X1) != X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).

fof(f83,plain,
    ( ~ subset(empty_set,unordered_pair(sK1,sK2))
    | spl3_2
    | ~ spl3_5 ),
    inference(backward_demodulation,[],[f47,f61]) ).

fof(f61,plain,
    ( empty_set = sK0
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl3_5
  <=> empty_set = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f47,plain,
    ( ~ subset(sK0,unordered_pair(sK1,sK2))
    | spl3_2 ),
    inference(avatar_component_clause,[],[f45]) ).

fof(f45,plain,
    ( spl3_2
  <=> subset(sK0,unordered_pair(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f82,plain,
    ( ~ spl3_1
    | spl3_2 ),
    inference(avatar_contradiction_clause,[],[f79]) ).

fof(f79,plain,
    ( $false
    | ~ spl3_1
    | spl3_2 ),
    inference(unit_resulting_resolution,[],[f47,f76]) ).

fof(f76,plain,
    ( ! [X1] : subset(sK0,unordered_pair(X1,sK2))
    | ~ spl3_1 ),
    inference(superposition,[],[f38,f42]) ).

fof(f42,plain,
    ( singleton(sK2) = sK0
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f41]) ).

fof(f41,plain,
    ( spl3_1
  <=> singleton(sK2) = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f38,plain,
    ! [X0,X1] : subset(singleton(X1),unordered_pair(X0,X1)),
    inference(equality_resolution,[],[f32]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( subset(X2,unordered_pair(X0,X1))
      | singleton(X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f74,plain,
    ( spl3_2
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f73]) ).

fof(f73,plain,
    ( $false
    | spl3_2
    | ~ spl3_4 ),
    inference(subsumption_resolution,[],[f72,f24]) ).

fof(f24,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ! [X1] : subset(X1,X1),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f72,plain,
    ( ~ subset(sK0,sK0)
    | spl3_2
    | ~ spl3_4 ),
    inference(backward_demodulation,[],[f47,f56]) ).

fof(f56,plain,
    ( unordered_pair(sK1,sK2) = sK0
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f55,plain,
    ( spl3_4
  <=> unordered_pair(sK1,sK2) = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f71,plain,
    ( spl3_2
    | ~ spl3_3 ),
    inference(avatar_contradiction_clause,[],[f68]) ).

fof(f68,plain,
    ( $false
    | spl3_2
    | ~ spl3_3 ),
    inference(unit_resulting_resolution,[],[f47,f66]) ).

fof(f66,plain,
    ( ! [X0] : subset(sK0,unordered_pair(sK1,X0))
    | ~ spl3_3 ),
    inference(superposition,[],[f36,f51]) ).

fof(f51,plain,
    ( singleton(sK1) = sK0
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f50,plain,
    ( spl3_3
  <=> singleton(sK1) = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f36,plain,
    ! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
    inference(equality_resolution,[],[f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( subset(X2,unordered_pair(X0,X1))
      | singleton(X0) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f65,plain,
    ( spl3_3
    | spl3_5
    | spl3_1
    | spl3_4 ),
    inference(avatar_split_clause,[],[f64,f55,f41,f60,f50]) ).

fof(f64,plain,
    ( unordered_pair(sK1,sK2) = sK0
    | singleton(sK2) = sK0
    | empty_set = sK0
    | singleton(sK1) = sK0 ),
    inference(subsumption_resolution,[],[f26,f35]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X2,unordered_pair(X0,X1))
      | unordered_pair(X0,X1) = X2
      | empty_set = X2
      | singleton(X1) = X2
      | singleton(X0) = X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f26,plain,
    ( singleton(sK2) = sK0
    | subset(sK0,unordered_pair(sK1,sK2))
    | empty_set = sK0
    | singleton(sK1) = sK0
    | unordered_pair(sK1,sK2) = sK0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( ( ~ subset(sK0,unordered_pair(sK1,sK2))
      | ( singleton(sK1) != sK0
        & unordered_pair(sK1,sK2) != sK0
        & empty_set != sK0
        & singleton(sK2) != sK0 ) )
    & ( subset(sK0,unordered_pair(sK1,sK2))
      | singleton(sK1) = sK0
      | unordered_pair(sK1,sK2) = sK0
      | empty_set = sK0
      | singleton(sK2) = sK0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ subset(X0,unordered_pair(X1,X2))
          | ( singleton(X1) != X0
            & unordered_pair(X1,X2) != X0
            & empty_set != X0
            & singleton(X2) != X0 ) )
        & ( subset(X0,unordered_pair(X1,X2))
          | singleton(X1) = X0
          | unordered_pair(X1,X2) = X0
          | empty_set = X0
          | singleton(X2) = X0 ) )
   => ( ( ~ subset(sK0,unordered_pair(sK1,sK2))
        | ( singleton(sK1) != sK0
          & unordered_pair(sK1,sK2) != sK0
          & empty_set != sK0
          & singleton(sK2) != sK0 ) )
      & ( subset(sK0,unordered_pair(sK1,sK2))
        | singleton(sK1) = sK0
        | unordered_pair(sK1,sK2) = sK0
        | empty_set = sK0
        | singleton(sK2) = sK0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(X0,unordered_pair(X1,X2))
        | ( singleton(X1) != X0
          & unordered_pair(X1,X2) != X0
          & empty_set != X0
          & singleton(X2) != X0 ) )
      & ( subset(X0,unordered_pair(X1,X2))
        | singleton(X1) = X0
        | unordered_pair(X1,X2) = X0
        | empty_set = X0
        | singleton(X2) = X0 ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X0,X2,X1] :
      ( ( ~ subset(X0,unordered_pair(X2,X1))
        | ( singleton(X2) != X0
          & unordered_pair(X2,X1) != X0
          & empty_set != X0
          & singleton(X1) != X0 ) )
      & ( subset(X0,unordered_pair(X2,X1))
        | singleton(X2) = X0
        | unordered_pair(X2,X1) = X0
        | empty_set = X0
        | singleton(X1) = X0 ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X0,X2,X1] :
      ( ( ~ subset(X0,unordered_pair(X2,X1))
        | ( singleton(X2) != X0
          & unordered_pair(X2,X1) != X0
          & empty_set != X0
          & singleton(X1) != X0 ) )
      & ( subset(X0,unordered_pair(X2,X1))
        | singleton(X2) = X0
        | unordered_pair(X2,X1) = X0
        | empty_set = X0
        | singleton(X1) = X0 ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ? [X0,X2,X1] :
      ( ( singleton(X2) = X0
        | unordered_pair(X2,X1) = X0
        | empty_set = X0
        | singleton(X1) = X0 )
    <~> subset(X0,unordered_pair(X2,X1)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ! [X2,X0,X1] :
        ( ~ ( singleton(X2) != X0
            & singleton(X1) != X0
            & empty_set != X0
            & unordered_pair(X2,X1) != X0 )
      <=> subset(X0,unordered_pair(X2,X1)) ),
    inference(rectify,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( subset(X0,unordered_pair(X1,X2))
      <=> ~ ( singleton(X1) != X0
            & unordered_pair(X1,X2) != X0
            & singleton(X2) != X0
            & empty_set != X0 ) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X0,X2,X1] :
      ( subset(X0,unordered_pair(X1,X2))
    <=> ~ ( singleton(X1) != X0
          & unordered_pair(X1,X2) != X0
          & singleton(X2) != X0
          & empty_set != X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).

fof(f63,plain,
    ( ~ spl3_5
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f28,f45,f60]) ).

fof(f28,plain,
    ( ~ subset(sK0,unordered_pair(sK1,sK2))
    | empty_set != sK0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f58,plain,
    ( ~ spl3_2
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f29,f55,f45]) ).

fof(f29,plain,
    ( unordered_pair(sK1,sK2) != sK0
    | ~ subset(sK0,unordered_pair(sK1,sK2)) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f53,plain,
    ( ~ spl3_3
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f30,f45,f50]) ).

fof(f30,plain,
    ( ~ subset(sK0,unordered_pair(sK1,sK2))
    | singleton(sK1) != sK0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f48,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f27,f45,f41]) ).

fof(f27,plain,
    ( ~ subset(sK0,unordered_pair(sK1,sK2))
    | singleton(sK2) != sK0 ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET901+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 : n025.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 14:37:45 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (18007)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)
% 0.20/0.50  % (18012)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50  % (18027)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.50  % (18004)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (18004)First to succeed.
% 0.20/0.50  % (18010)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  % (18012)Also succeeded, but the first one will report.
% 0.20/0.51  % (18004)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
% 0.20/0.51  % (18004)------------------------------
% 0.20/0.51  % (18004)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (18004)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (18004)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (18004)Memory used [KB]: 6012
% 0.20/0.51  % (18004)Time elapsed: 0.102 s
% 0.20/0.51  % (18004)Instructions burned: 3 (million)
% 0.20/0.51  % (18004)------------------------------
% 0.20/0.51  % (18004)------------------------------
% 0.20/0.51  % (17996)Success in time 0.154 s
%------------------------------------------------------------------------------