TSTP Solution File: SET009+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n003.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 18:18:18 EDT 2022

% Result   : Theorem 0.20s 0.47s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   41 (   9 unt;   0 def)
%            Number of atoms       :  108 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  114 (  47   ~;  33   |;  21   &)
%                                         (   7 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   72 (  60   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f78,plain,
    $false,
    inference(avatar_sat_refutation,[],[f52,f66,f77]) ).

fof(f77,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f76]) ).

fof(f76,plain,
    ( $false
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f67,f47]) ).

fof(f47,plain,
    ( member(sK0(difference(sK2,sK1),difference(sK2,sK3)),sK3)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f45]) ).

fof(f45,plain,
    ( spl4_1
  <=> member(sK0(difference(sK2,sK1),difference(sK2,sK3)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f67,plain,
    ~ member(sK0(difference(sK2,sK1),difference(sK2,sK3)),sK3),
    inference(unit_resulting_resolution,[],[f32,f36]) ).

fof(f36,plain,
    ! [X4,X5] :
      ( ~ member(X4,difference(X5,sK1))
      | ~ member(X4,sK3) ),
    inference(resolution,[],[f29,f27]) ).

fof(f27,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,difference(X0,X2))
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X1,X0)
          & ~ member(X1,X2) )
        | ~ member(X1,difference(X0,X2)) )
      & ( member(X1,difference(X0,X2))
        | ~ member(X1,X0)
        | member(X1,X2) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X2,X0,X1] :
      ( ( ( member(X0,X2)
          & ~ member(X0,X1) )
        | ~ member(X0,difference(X2,X1)) )
      & ( member(X0,difference(X2,X1))
        | ~ member(X0,X2)
        | member(X0,X1) ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X2,X0,X1] :
      ( ( ( member(X0,X2)
          & ~ member(X0,X1) )
        | ~ member(X0,difference(X2,X1)) )
      & ( member(X0,difference(X2,X1))
        | ~ member(X0,X2)
        | member(X0,X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,plain,
    ! [X2,X0,X1] :
      ( ( member(X0,X2)
        & ~ member(X0,X1) )
    <=> member(X0,difference(X2,X1)) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X2,X1,X0] :
      ( member(X2,difference(X0,X1))
    <=> ( member(X2,X0)
        & ~ member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(f29,plain,
    ! [X0] :
      ( member(X0,sK1)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f24,f20]) ).

fof(f20,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ subset(X0,X1)
      | ~ member(X3,X0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) )
      & ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f24,plain,
    subset(sK3,sK1),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ~ subset(difference(sK2,sK1),difference(sK2,sK3))
    & subset(sK3,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f14,f15]) ).

fof(f15,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(difference(X1,X0),difference(X1,X2))
        & subset(X2,X0) )
   => ( ~ subset(difference(sK2,sK1),difference(sK2,sK3))
      & subset(sK3,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( ~ subset(difference(X1,X0),difference(X1,X2))
      & subset(X2,X0) ),
    inference(rectify,[],[f8]) ).

fof(f8,plain,
    ? [X1,X2,X0] :
      ( ~ subset(difference(X2,X1),difference(X2,X0))
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ! [X1,X0,X2] :
        ( subset(X0,X1)
       => subset(difference(X2,X1),difference(X2,X0)) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ! [X1,X0,X2] :
      ( subset(X0,X1)
     => subset(difference(X2,X1),difference(X2,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_difference) ).

fof(f32,plain,
    member(sK0(difference(sK2,sK1),difference(sK2,sK3)),difference(sK2,sK1)),
    inference(resolution,[],[f25,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f25,plain,
    ~ subset(difference(sK2,sK1),difference(sK2,sK3)),
    inference(cnf_transformation,[],[f16]) ).

fof(f66,plain,
    spl4_2,
    inference(avatar_split_clause,[],[f54,f49]) ).

fof(f49,plain,
    ( spl4_2
  <=> member(sK0(difference(sK2,sK1),difference(sK2,sK3)),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f54,plain,
    member(sK0(difference(sK2,sK1),difference(sK2,sK3)),sK2),
    inference(unit_resulting_resolution,[],[f32,f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( member(X1,X0)
      | ~ member(X1,difference(X0,X2)) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f52,plain,
    ( spl4_1
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f40,f49,f45]) ).

fof(f40,plain,
    ( ~ member(sK0(difference(sK2,sK1),difference(sK2,sK3)),sK2)
    | member(sK0(difference(sK2,sK1),difference(sK2,sK3)),sK3) ),
    inference(resolution,[],[f31,f26]) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,X0)
      | member(X1,difference(X0,X2))
      | member(X1,X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f31,plain,
    ~ member(sK0(difference(sK2,sK1),difference(sK2,sK3)),difference(sK2,sK3)),
    inference(unit_resulting_resolution,[],[f25,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.13/0.34  % Computer : n003.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 12:51:37 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.46  % (21964)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)
% 0.20/0.46  % (21964)Instruction limit reached!
% 0.20/0.46  % (21964)------------------------------
% 0.20/0.46  % (21964)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.46  % (21964)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.46  % (21964)Termination reason: Unknown
% 0.20/0.46  % (21964)Termination phase: Saturation
% 0.20/0.46  
% 0.20/0.46  % (21964)Memory used [KB]: 5884
% 0.20/0.46  % (21964)Time elapsed: 0.074 s
% 0.20/0.46  % (21964)Instructions burned: 3 (million)
% 0.20/0.46  % (21964)------------------------------
% 0.20/0.46  % (21964)------------------------------
% 0.20/0.46  % (21956)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)
% 0.20/0.47  % (21957)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)
% 0.20/0.47  % (21957)First to succeed.
% 0.20/0.47  % (21957)Refutation found. Thanks to Tanya!
% 0.20/0.47  % SZS status Theorem for theBenchmark
% 0.20/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47  % (21957)------------------------------
% 0.20/0.47  % (21957)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.47  % (21957)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.47  % (21957)Termination reason: Refutation
% 0.20/0.47  
% 0.20/0.47  % (21957)Memory used [KB]: 6012
% 0.20/0.47  % (21957)Time elapsed: 0.075 s
% 0.20/0.47  % (21957)Instructions burned: 2 (million)
% 0.20/0.47  % (21957)------------------------------
% 0.20/0.47  % (21957)------------------------------
% 0.20/0.47  % (21949)Success in time 0.125 s
%------------------------------------------------------------------------------