TSTP Solution File: SET595+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET595+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 : n020.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 18:21:32 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   60 (   9 unt;   0 def)
%            Number of atoms       :  175 (  18 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  186 (  71   ~;  70   |;  32   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  104 (  97   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f192,plain,
    $false,
    inference(subsumption_resolution,[],[f191,f163]) ).

fof(f163,plain,
    ~ subset(sK4,sF6),
    inference(subsumption_resolution,[],[f162,f68]) ).

fof(f68,plain,
    sF6 != sK4,
    inference(definition_folding,[],[f60,f67,f66]) ).

fof(f66,plain,
    sF5 = difference(sK4,sK3),
    introduced(function_definition,[]) ).

fof(f67,plain,
    union(sK3,sF5) = sF6,
    introduced(function_definition,[]) ).

fof(f60,plain,
    sK4 != union(sK3,difference(sK4,sK3)),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ( subset(sK3,sK4)
    & sK4 != union(sK3,difference(sK4,sK3)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f16,f38]) ).

fof(f38,plain,
    ( ? [X0,X1] :
        ( subset(X0,X1)
        & union(X0,difference(X1,X0)) != X1 )
   => ( subset(sK3,sK4)
      & sK4 != union(sK3,difference(sK4,sK3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1] :
      ( subset(X0,X1)
      & union(X0,difference(X1,X0)) != X1 ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => union(X0,difference(X1,X0)) = X1 ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => union(X0,difference(X1,X0)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th54) ).

fof(f162,plain,
    ( ~ subset(sK4,sF6)
    | sF6 = sK4 ),
    inference(resolution,[],[f160,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( X0 = X1
    <=> ( subset(X0,X1)
        & subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

fof(f160,plain,
    subset(sF6,sK4),
    inference(duplicate_literal_removal,[],[f157]) ).

fof(f157,plain,
    ( subset(sF6,sK4)
    | subset(sF6,sK4) ),
    inference(resolution,[],[f156,f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( member(sK2(X0,X1),X1)
          & ~ member(sK2(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f35,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & ~ member(X3,X0) )
     => ( member(sK2(X0,X1),X1)
        & ~ member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0] :
      ( ( ! [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,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

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

fof(f156,plain,
    ! [X2] :
      ( ~ member(sK2(sK4,X2),sF6)
      | subset(X2,sK4) ),
    inference(subsumption_resolution,[],[f154,f139]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(sK2(sK4,X0),sK3)
      | subset(X0,sK4) ),
    inference(resolution,[],[f134,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f134,plain,
    ! [X0] :
      ( member(X0,sK4)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f59,f61]) ).

fof(f61,plain,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f39]) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | member(X2,X0)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f154,plain,
    ! [X2] :
      ( ~ member(sK2(sK4,X2),sF6)
      | subset(X2,sK4)
      | member(sK2(sK4,X2),sK3) ),
    inference(resolution,[],[f145,f81]) ).

fof(f81,plain,
    ! [X8] :
      ( ~ member(sK2(sK4,X8),sF5)
      | subset(X8,sK4) ),
    inference(resolution,[],[f57,f76]) ).

fof(f76,plain,
    ! [X0] :
      ( member(X0,sK4)
      | ~ member(X0,sF5) ),
    inference(superposition,[],[f54,f66]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X2,X0)
          & ~ member(X2,X1) )
        | ~ member(X2,difference(X0,X1)) )
      & ( member(X2,difference(X0,X1))
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X0,X2,X1] :
      ( ( ( member(X1,X0)
          & ~ member(X1,X2) )
        | ~ member(X1,difference(X0,X2)) )
      & ( member(X1,difference(X0,X2))
        | ~ member(X1,X0)
        | member(X1,X2) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X2,X1] :
      ( ( ( member(X1,X0)
          & ~ member(X1,X2) )
        | ~ member(X1,difference(X0,X2)) )
      & ( member(X1,difference(X0,X2))
        | ~ member(X1,X0)
        | member(X1,X2) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X2,X1] :
      ( ( member(X1,X0)
        & ~ member(X1,X2) )
    <=> member(X1,difference(X0,X2)) ),
    inference(rectify,[],[f3]) ).

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

fof(f145,plain,
    ! [X0] :
      ( member(X0,sF5)
      | ~ member(X0,sF6)
      | member(X0,sK3) ),
    inference(superposition,[],[f48,f67]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X1,X0))
      | member(X2,X1)
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X1,X0))
        | ( ~ member(X2,X0)
          & ~ member(X2,X1) ) )
      & ( member(X2,X0)
        | member(X2,X1)
        | ~ member(X2,union(X1,X0)) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,union(X0,X2))
        | ( ~ member(X1,X2)
          & ~ member(X1,X0) ) )
      & ( member(X1,X2)
        | member(X1,X0)
        | ~ member(X1,union(X0,X2)) ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,union(X0,X2))
        | ( ~ member(X1,X2)
          & ~ member(X1,X0) ) )
      & ( member(X1,X2)
        | member(X1,X0)
        | ~ member(X1,union(X0,X2)) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X2,X0,X1] :
      ( member(X1,union(X0,X2))
    <=> ( member(X1,X2)
        | member(X1,X0) ) ),
    inference(rectify,[],[f2]) ).

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

fof(f191,plain,
    subset(sK4,sF6),
    inference(duplicate_literal_removal,[],[f187]) ).

fof(f187,plain,
    ( subset(sK4,sF6)
    | subset(sK4,sF6) ),
    inference(resolution,[],[f186,f58]) ).

fof(f186,plain,
    ! [X1] :
      ( ~ member(sK2(sF6,X1),sK4)
      | subset(X1,sF6) ),
    inference(subsumption_resolution,[],[f182,f80]) ).

fof(f80,plain,
    ! [X7] :
      ( ~ member(sK2(sF6,X7),sK3)
      | subset(X7,sF6) ),
    inference(resolution,[],[f57,f69]) ).

fof(f69,plain,
    ! [X0] :
      ( member(X0,sF6)
      | ~ member(X0,sK3) ),
    inference(superposition,[],[f49,f67]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X1,X0))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f182,plain,
    ! [X1] :
      ( ~ member(sK2(sF6,X1),sK4)
      | member(sK2(sF6,X1),sK3)
      | subset(X1,sF6) ),
    inference(resolution,[],[f151,f79]) ).

fof(f79,plain,
    ! [X6] :
      ( ~ member(sK2(sF6,X6),sF5)
      | subset(X6,sF6) ),
    inference(resolution,[],[f57,f72]) ).

fof(f72,plain,
    ! [X0] :
      ( member(X0,sF6)
      | ~ member(X0,sF5) ),
    inference(superposition,[],[f50,f67]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X1,X0))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f151,plain,
    ! [X0] :
      ( member(X0,sF5)
      | member(X0,sK3)
      | ~ member(X0,sK4) ),
    inference(superposition,[],[f52,f66]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SET595+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14  % 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 : n020.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 14:03:30 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  % (16531)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)
% 0.21/0.50  % (16523)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)
% 0.21/0.50  % (16523)Refutation not found, incomplete strategy% (16523)------------------------------
% 0.21/0.50  % (16523)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50  % (16523)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50  % (16523)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50  
% 0.21/0.50  % (16523)Memory used [KB]: 6012
% 0.21/0.50  % (16523)Time elapsed: 0.087 s
% 0.21/0.50  % (16523)Instructions burned: 2 (million)
% 0.21/0.50  % (16523)------------------------------
% 0.21/0.50  % (16523)------------------------------
% 0.21/0.50  % (16531)Refutation not found, incomplete strategy% (16531)------------------------------
% 0.21/0.50  % (16531)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50  % (16544)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)
% 0.21/0.50  % (16531)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50  % (16531)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50  
% 0.21/0.50  % (16531)Memory used [KB]: 6012
% 0.21/0.50  % (16531)Time elapsed: 0.103 s
% 0.21/0.50  % (16531)Instructions burned: 3 (million)
% 0.21/0.50  % (16531)------------------------------
% 0.21/0.50  % (16531)------------------------------
% 0.21/0.51  % (16521)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)
% 0.21/0.51  % (16520)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.52  % (16520)First to succeed.
% 0.21/0.52  % (16520)Refutation found. Thanks to Tanya!
% 0.21/0.52  % SZS status Theorem for theBenchmark
% 0.21/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (16520)------------------------------
% 0.21/0.52  % (16520)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (16520)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (16520)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (16520)Memory used [KB]: 6012
% 0.21/0.52  % (16520)Time elapsed: 0.116 s
% 0.21/0.52  % (16520)Instructions burned: 4 (million)
% 0.21/0.52  % (16520)------------------------------
% 0.21/0.52  % (16520)------------------------------
% 0.21/0.52  % (16512)Success in time 0.156 s
%------------------------------------------------------------------------------