TSTP Solution File: SET700+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET700+4 : 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 : 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 18:21:55 EDT 2022

% Result   : Theorem 1.19s 0.53s
% Output   : Refutation 1.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   60 (   2 unt;   0 def)
%            Number of atoms       :  205 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  224 (  79   ~;  80   |;  46   &)
%                                         (  11 <=>;   6  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   96 (  78   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f355,plain,
    $false,
    inference(avatar_sat_refutation,[],[f55,f56,f308,f354]) ).

fof(f354,plain,
    ( ~ spl4_1
    | spl4_2 ),
    inference(avatar_contradiction_clause,[],[f353]) ).

fof(f353,plain,
    ( $false
    | ~ spl4_1
    | spl4_2 ),
    inference(subsumption_resolution,[],[f339,f329]) ).

fof(f329,plain,
    ( ~ member(sK0(intersection(sK2,difference(sK1,sK3)),sK3),sK2)
    | ~ spl4_1
    | spl4_2 ),
    inference(unit_resulting_resolution,[],[f50,f320,f42]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( member(sK0(X0,X1),X0)
          & ~ member(sK0(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X0)
          & ~ member(X3,X1) )
     => ( member(sK0(X0,X1),X0)
        & ~ member(sK0(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( member(X3,X0)
            & ~ member(X3,X1) ) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f320,plain,
    ( ~ member(sK0(intersection(sK2,difference(sK1,sK3)),sK3),sK3)
    | spl4_2 ),
    inference(resolution,[],[f53,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f53,plain,
    ( ~ subset(intersection(sK2,difference(sK1,sK3)),sK3)
    | spl4_2 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f52,plain,
    ( spl4_2
  <=> subset(intersection(sK2,difference(sK1,sK3)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f50,plain,
    ( subset(sK2,sK3)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f48,plain,
    ( spl4_1
  <=> subset(sK2,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f339,plain,
    ( member(sK0(intersection(sK2,difference(sK1,sK3)),sK3),sK2)
    | spl4_2 ),
    inference(unit_resulting_resolution,[],[f319,f36]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X2,X0)
          & member(X2,X1) )
        | ~ member(X2,intersection(X0,X1)) )
      & ( member(X2,intersection(X0,X1))
        | ~ member(X2,X0)
        | ~ member(X2,X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X2,X0] :
      ( ( ( member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,intersection(X1,X2)) )
      & ( member(X0,intersection(X1,X2))
        | ~ member(X0,X1)
        | ~ member(X0,X2) ) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X1,X2,X0] :
      ( ( ( member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,intersection(X1,X2)) )
      & ( member(X0,intersection(X1,X2))
        | ~ member(X0,X1)
        | ~ member(X0,X2) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X2,X0] :
      ( ( member(X0,X1)
        & member(X0,X2) )
    <=> member(X0,intersection(X1,X2)) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X0)
        & member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).

fof(f319,plain,
    ( member(sK0(intersection(sK2,difference(sK1,sK3)),sK3),intersection(sK2,difference(sK1,sK3)))
    | spl4_2 ),
    inference(resolution,[],[f53,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f308,plain,
    ( spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f307]) ).

fof(f307,plain,
    ( $false
    | spl4_1
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f299,f90]) ).

fof(f90,plain,
    ( member(sK0(sK2,sK3),difference(sK1,sK3))
    | spl4_1 ),
    inference(unit_resulting_resolution,[],[f62,f66,f37]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( member(X1,X2)
      | ~ member(X1,X0)
      | member(X1,difference(X0,X2)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,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,[],[f24]) ).

fof(f24,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,[],[f23]) ).

fof(f23,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,[],[f16]) ).

fof(f16,plain,
    ! [X2,X0,X1] :
      ( ( member(X0,X2)
        & ~ member(X0,X1) )
    <=> member(X0,difference(X2,X1)) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( member(X1,X3)
        & ~ member(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).

fof(f66,plain,
    ( member(sK0(sK2,sK3),sK1)
    | spl4_1 ),
    inference(unit_resulting_resolution,[],[f44,f61,f42]) ).

fof(f61,plain,
    ( member(sK0(sK2,sK3),sK2)
    | spl4_1 ),
    inference(resolution,[],[f49,f41]) ).

fof(f49,plain,
    ( ~ subset(sK2,sK3)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f44,plain,
    subset(sK2,sK1),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ( ( ~ subset(sK2,sK3)
      | ~ subset(intersection(sK2,difference(sK1,sK3)),sK3) )
    & ( subset(sK2,sK3)
      | subset(intersection(sK2,difference(sK1,sK3)),sK3) )
    & subset(sK2,sK1)
    & subset(sK3,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f31,f32]) ).

fof(f32,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ subset(X1,X2)
          | ~ subset(intersection(X1,difference(X0,X2)),X2) )
        & ( subset(X1,X2)
          | subset(intersection(X1,difference(X0,X2)),X2) )
        & subset(X1,X0)
        & subset(X2,X0) )
   => ( ( ~ subset(sK2,sK3)
        | ~ subset(intersection(sK2,difference(sK1,sK3)),sK3) )
      & ( subset(sK2,sK3)
        | subset(intersection(sK2,difference(sK1,sK3)),sK3) )
      & subset(sK2,sK1)
      & subset(sK3,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(X1,X2)
        | ~ subset(intersection(X1,difference(X0,X2)),X2) )
      & ( subset(X1,X2)
        | subset(intersection(X1,difference(X0,X2)),X2) )
      & subset(X1,X0)
      & subset(X2,X0) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(X1,X2)
        | ~ subset(intersection(X1,difference(X0,X2)),X2) )
      & ( subset(X1,X2)
        | subset(intersection(X1,difference(X0,X2)),X2) )
      & subset(X1,X0)
      & subset(X2,X0) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ? [X0,X1,X2] :
      ( ( subset(intersection(X1,difference(X0,X2)),X2)
      <~> subset(X1,X2) )
      & subset(X1,X0)
      & subset(X2,X0) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ? [X1,X0,X2] :
      ( ( subset(intersection(X1,difference(X0,X2)),X2)
      <~> subset(X1,X2) )
      & subset(X2,X0)
      & subset(X1,X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X1,X0,X2] :
        ( ( subset(X2,X0)
          & subset(X1,X0) )
       => ( subset(X1,X2)
        <=> subset(intersection(X1,difference(X0,X2)),X2) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X3,X0,X1] :
        ( ( subset(X0,X3)
          & subset(X1,X3) )
       => ( subset(X0,X1)
        <=> subset(intersection(X0,difference(X3,X1)),X1) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X3,X0,X1] :
      ( ( subset(X0,X3)
        & subset(X1,X3) )
     => ( subset(X0,X1)
      <=> subset(intersection(X0,difference(X3,X1)),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI34) ).

fof(f62,plain,
    ( ~ member(sK0(sK2,sK3),sK3)
    | spl4_1 ),
    inference(resolution,[],[f49,f40]) ).

fof(f299,plain,
    ( ~ member(sK0(sK2,sK3),difference(sK1,sK3))
    | spl4_1
    | ~ spl4_2 ),
    inference(unit_resulting_resolution,[],[f61,f121]) ).

fof(f121,plain,
    ( ! [X0] :
        ( ~ member(X0,difference(sK1,sK3))
        | ~ member(X0,sK2) )
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f114,f38]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,X2)
      | ~ member(X1,difference(X0,X2)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f114,plain,
    ( ! [X0] :
        ( member(X0,sK3)
        | ~ member(X0,difference(sK1,sK3))
        | ~ member(X0,sK2) )
    | ~ spl4_2 ),
    inference(resolution,[],[f72,f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f72,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(sK2,difference(sK1,sK3)))
        | member(X0,sK3) )
    | ~ spl4_2 ),
    inference(resolution,[],[f54,f42]) ).

fof(f54,plain,
    ( subset(intersection(sK2,difference(sK1,sK3)),sK3)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f56,plain,
    ( ~ spl4_2
    | ~ spl4_1 ),
    inference(avatar_split_clause,[],[f46,f48,f52]) ).

fof(f46,plain,
    ( ~ subset(sK2,sK3)
    | ~ subset(intersection(sK2,difference(sK1,sK3)),sK3) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f55,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f45,f52,f48]) ).

fof(f45,plain,
    ( subset(intersection(sK2,difference(sK1,sK3)),sK3)
    | subset(sK2,sK3) ),
    inference(cnf_transformation,[],[f33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET700+4 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.14/0.35  % Computer : n019.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:28:20 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  % (26752)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)
% 0.21/0.51  % (26768)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.21/0.51  % (26760)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)
% 0.21/0.51  % (26754)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)
% 1.19/0.51  % (26763)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.19/0.52  % (26763)Refutation not found, incomplete strategy% (26763)------------------------------
% 1.19/0.52  % (26763)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.19/0.52  % (26755)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.19/0.52  % (26769)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 1.19/0.52  % (26763)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.19/0.52  % (26763)Termination reason: Refutation not found, incomplete strategy
% 1.19/0.52  
% 1.19/0.52  % (26763)Memory used [KB]: 1407
% 1.19/0.52  % (26763)Time elapsed: 0.066 s
% 1.19/0.52  % (26763)Instructions burned: 1 (million)
% 1.19/0.52  % (26763)------------------------------
% 1.19/0.52  % (26763)------------------------------
% 1.19/0.52  % (26747)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)
% 1.19/0.52  % (26746)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)
% 1.19/0.52  % (26754)Instruction limit reached!
% 1.19/0.52  % (26754)------------------------------
% 1.19/0.52  % (26754)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.19/0.52  % (26765)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)
% 1.19/0.53  % (26755)Instruction limit reached!
% 1.19/0.53  % (26755)------------------------------
% 1.19/0.53  % (26755)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.19/0.53  % (26755)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.19/0.53  % (26755)Termination reason: Unknown
% 1.19/0.53  % (26755)Termination phase: Saturation
% 1.19/0.53  
% 1.19/0.53  % (26755)Memory used [KB]: 6012
% 1.19/0.53  % (26755)Time elapsed: 0.072 s
% 1.19/0.53  % (26755)Instructions burned: 8 (million)
% 1.19/0.53  % (26755)------------------------------
% 1.19/0.53  % (26755)------------------------------
% 1.19/0.53  % (26747)First to succeed.
% 1.19/0.53  % (26744)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)
% 1.19/0.53  % (26747)Refutation found. Thanks to Tanya!
% 1.19/0.53  % SZS status Theorem for theBenchmark
% 1.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.19/0.53  % (26747)------------------------------
% 1.19/0.53  % (26747)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.19/0.53  % (26747)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.19/0.53  % (26747)Termination reason: Refutation
% 1.19/0.53  
% 1.19/0.53  % (26747)Memory used [KB]: 6012
% 1.19/0.53  % (26747)Time elapsed: 0.080 s
% 1.19/0.53  % (26747)Instructions burned: 9 (million)
% 1.19/0.53  % (26747)------------------------------
% 1.19/0.53  % (26747)------------------------------
% 1.19/0.53  % (26739)Success in time 0.167 s
%------------------------------------------------------------------------------