TSTP Solution File: SET183+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET183+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 18:19:41 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   53 (  14 unt;   0 def)
%            Number of atoms       :  143 (  27 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  147 (  57   ~;  49   |;  29   &)
%                                         (   7 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   92 (  83   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1411,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1224,f1397]) ).

fof(f1397,plain,
    ~ spl4_4,
    inference(avatar_contradiction_clause,[],[f1396]) ).

fof(f1396,plain,
    ( $false
    | ~ spl4_4 ),
    inference(trivial_inequality_removal,[],[f1288]) ).

fof(f1288,plain,
    ( sK3 != sK3
    | ~ spl4_4 ),
    inference(superposition,[],[f58,f1215]) ).

fof(f1215,plain,
    ( intersection(sK2,sK3) = sK3
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f1213]) ).

fof(f1213,plain,
    ( spl4_4
  <=> intersection(sK2,sK3) = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f58,plain,
    intersection(sK2,sK3) != sK3,
    inference(superposition,[],[f50,f49]) ).

fof(f49,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f50,plain,
    sK3 != intersection(sK3,sK2),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ( subset(sK3,sK2)
    & sK3 != intersection(sK3,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f31,f32]) ).

fof(f32,plain,
    ( ? [X0,X1] :
        ( subset(X1,X0)
        & intersection(X1,X0) != X1 )
   => ( subset(sK3,sK2)
      & sK3 != intersection(sK3,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ? [X0,X1] :
      ( subset(X1,X0)
      & intersection(X1,X0) != X1 ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ? [X1,X0] :
      ( subset(X0,X1)
      & intersection(X0,X1) != X0 ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X1,X0] :
        ( subset(X0,X1)
       => intersection(X0,X1) = X0 ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X1,X0] :
      ( subset(X0,X1)
     => intersection(X0,X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_intersection) ).

fof(f1224,plain,
    spl4_4,
    inference(avatar_split_clause,[],[f1207,f1213]) ).

fof(f1207,plain,
    intersection(sK2,sK3) = sK3,
    inference(resolution,[],[f1169,f150]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ~ subset(X0,intersection(X1,X0))
      | intersection(X1,X0) = X0 ),
    inference(superposition,[],[f94,f49]) ).

fof(f94,plain,
    ! [X8,X7] :
      ( ~ subset(X7,intersection(X7,X8))
      | intersection(X7,X8) = X7 ),
    inference(resolution,[],[f47,f37]) ).

fof(f37,plain,
    ! [X0,X1] : subset(intersection(X1,X0),X1),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] : subset(intersection(X1,X0),X1),
    inference(rectify,[],[f2]) ).

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

fof(f47,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) )
      & ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) )
      & ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( X0 = X1
    <=> ( subset(X0,X1)
        & subset(X1,X0) ) ),
    inference(rectify,[],[f4]) ).

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

fof(f1169,plain,
    subset(sK3,intersection(sK2,sK3)),
    inference(duplicate_literal_removal,[],[f1143]) ).

fof(f1143,plain,
    ( subset(sK3,intersection(sK2,sK3))
    | subset(sK3,intersection(sK2,sK3)) ),
    inference(resolution,[],[f233,f85]) ).

fof(f85,plain,
    ! [X0] :
      ( member(sK0(sK3,X0),sK2)
      | subset(sK3,X0) ),
    inference(resolution,[],[f76,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,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])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,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,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f76,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | member(X0,sK2) ),
    inference(resolution,[],[f38,f51]) ).

fof(f51,plain,
    subset(sK3,sK2),
    inference(cnf_transformation,[],[f33]) ).

fof(f38,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | member(X3,X1)
      | ~ member(X3,X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,intersection(X1,X0)),X1)
      | subset(X0,intersection(X1,X0)) ),
    inference(duplicate_literal_removal,[],[f220]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( subset(X0,intersection(X1,X0))
      | subset(X0,intersection(X1,X0))
      | ~ member(sK0(X0,intersection(X1,X0)),X1) ),
    inference(resolution,[],[f108,f39]) ).

fof(f108,plain,
    ! [X8,X6,X7] :
      ( ~ member(sK0(X6,intersection(X7,X8)),X8)
      | subset(X6,intersection(X7,X8))
      | ~ member(sK0(X6,intersection(X7,X8)),X7) ),
    inference(resolution,[],[f34,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X1,intersection(X0,X2))
      | ~ member(X1,X2)
      | ~ member(X1,X0) ),
    inference(cnf_transformation,[],[f19]) ).

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

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

fof(f17,plain,
    ! [X2,X1,X0] :
      ( ( ( member(X1,X2)
          & member(X1,X0) )
        | ~ member(X1,intersection(X2,X0)) )
      & ( member(X1,intersection(X2,X0))
        | ~ member(X1,X2)
        | ~ member(X1,X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X2,X1,X0] :
      ( ( member(X1,X2)
        & member(X1,X0) )
    <=> member(X1,intersection(X2,X0)) ),
    inference(rectify,[],[f1]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET183+3 : 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
% 0.14/0.33  % Computer : n003.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue Aug 30 13:25:37 EDT 2022
% 0.14/0.33  % CPUTime    : 
% 0.20/0.45  % (14577)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)
% 0.20/0.46  % (14577)Refutation not found, incomplete strategy% (14577)------------------------------
% 0.20/0.46  % (14577)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.46  % (14593)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)
% 0.20/0.46  % (14577)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.46  % (14577)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.46  
% 0.20/0.46  % (14577)Memory used [KB]: 5884
% 0.20/0.46  % (14577)Time elapsed: 0.063 s
% 0.20/0.46  % (14577)Instructions burned: 2 (million)
% 0.20/0.46  % (14577)------------------------------
% 0.20/0.46  % (14577)------------------------------
% 0.20/0.49  % (14572)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  % (14593)First to succeed.
% 0.20/0.50  % (14582)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  % (14571)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.50  % (14593)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (14593)------------------------------
% 0.20/0.50  % (14593)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (14593)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (14593)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (14593)Memory used [KB]: 6396
% 0.20/0.50  % (14593)Time elapsed: 0.100 s
% 0.20/0.50  % (14593)Instructions burned: 37 (million)
% 0.20/0.50  % (14593)------------------------------
% 0.20/0.50  % (14593)------------------------------
% 0.20/0.50  % (14570)Success in time 0.162 s
%------------------------------------------------------------------------------