TSTP Solution File: SEU171+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n012.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 18:27:05 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   44 (  13 unt;   0 def)
%            Number of atoms       :  198 (  29 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  247 (  93   ~;  60   |;  66   &)
%                                         (  10 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   87 (  68   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f114,plain,
    $false,
    inference(subsumption_resolution,[],[f112,f103]) ).

fof(f103,plain,
    in(sK3,sK1),
    inference(unit_resulting_resolution,[],[f95,f78,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( ( ( empty(X0)
            | ~ element(X0,X1) )
          & ( element(X0,X1)
            | ~ empty(X0) ) )
        | ~ empty(X1) )
      & ( ( ( element(X0,X1)
            | ~ in(X0,X1) )
          & ( in(X0,X1)
            | ~ element(X0,X1) ) )
        | empty(X1) ) ),
    inference(nnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( ( empty(X0)
        <=> element(X0,X1) )
        | ~ empty(X1) )
      & ( ( element(X0,X1)
        <=> in(X0,X1) )
        | empty(X1) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0] :
      ( ( empty(X1)
       => ( empty(X0)
        <=> element(X0,X1) ) )
      & ( ~ empty(X1)
       => ( element(X0,X1)
        <=> in(X0,X1) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ( empty(X0)
       => ( element(X1,X0)
        <=> empty(X1) ) )
      & ( ~ empty(X0)
       => ( element(X1,X0)
        <=> in(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).

fof(f78,plain,
    element(sK3,sK1),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ( ~ in(sK3,subset_complement(sK1,sK2))
    & element(sK3,sK1)
    & ~ in(sK3,sK2)
    & element(sK2,powerset(sK1))
    & empty_set != sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f32,f50,f49,f48]) ).

fof(f48,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ in(X2,subset_complement(X0,X1))
                & element(X2,X0)
                & ~ in(X2,X1) )
            & element(X1,powerset(X0)) )
        & empty_set != X0 )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,subset_complement(sK1,X1))
              & element(X2,sK1)
              & ~ in(X2,X1) )
          & element(X1,powerset(sK1)) )
      & empty_set != sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ in(X2,subset_complement(sK1,X1))
            & element(X2,sK1)
            & ~ in(X2,X1) )
        & element(X1,powerset(sK1)) )
   => ( ? [X2] :
          ( ~ in(X2,subset_complement(sK1,sK2))
          & element(X2,sK1)
          & ~ in(X2,sK2) )
      & element(sK2,powerset(sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ( ? [X2] :
        ( ~ in(X2,subset_complement(sK1,sK2))
        & element(X2,sK1)
        & ~ in(X2,sK2) )
   => ( ~ in(sK3,subset_complement(sK1,sK2))
      & element(sK3,sK1)
      & ~ in(sK3,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,subset_complement(X0,X1))
              & element(X2,X0)
              & ~ in(X2,X1) )
          & element(X1,powerset(X0)) )
      & empty_set != X0 ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,subset_complement(X0,X1))
              & ~ in(X2,X1)
              & element(X2,X0) )
          & element(X1,powerset(X0)) )
      & empty_set != X0 ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( empty_set != X0
       => ! [X1] :
            ( element(X1,powerset(X0))
           => ! [X2] :
                ( element(X2,X0)
               => ( ~ in(X2,X1)
                 => in(X2,subset_complement(X0,X1)) ) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X0] :
      ( empty_set != X0
     => ! [X1] :
          ( element(X1,powerset(X0))
         => ! [X2] :
              ( element(X2,X0)
             => ( ~ in(X2,X1)
               => in(X2,subset_complement(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).

fof(f95,plain,
    ~ empty(sK1),
    inference(unit_resulting_resolution,[],[f86,f75,f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ empty(X0)
      | X0 = X1
      | ~ empty(X1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ~ ( X0 != X1
        & empty(X1)
        & empty(X0) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X1,X0] :
      ~ ( X0 != X1
        & empty(X0)
        & empty(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

fof(f75,plain,
    empty_set != sK1,
    inference(cnf_transformation,[],[f51]) ).

fof(f86,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f112,plain,
    ~ in(sK3,sK1),
    inference(unit_resulting_resolution,[],[f77,f110,f93]) ).

fof(f93,plain,
    ! [X3,X0,X1] :
      ( in(X3,set_difference(X0,X1))
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(equality_resolution,[],[f71]) ).

fof(f71,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | ~ in(X3,X0)
      | in(X3,X1)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X0)
                & ~ in(X3,X1) )
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ~ in(X3,X0)
              | in(X3,X1) ) )
        | set_difference(X0,X1) != X2 )
      & ( set_difference(X0,X1) = X2
        | ( ( ~ in(sK0(X0,X1,X2),X2)
            | ~ in(sK0(X0,X1,X2),X0)
            | in(sK0(X0,X1,X2),X1) )
          & ( in(sK0(X0,X1,X2),X2)
            | ( in(sK0(X0,X1,X2),X0)
              & ~ in(sK0(X0,X1,X2),X1) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f45,f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X2)
            | ~ in(X4,X0)
            | in(X4,X1) )
          & ( in(X4,X2)
            | ( in(X4,X0)
              & ~ in(X4,X1) ) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X2)
          | ~ in(sK0(X0,X1,X2),X0)
          | in(sK0(X0,X1,X2),X1) )
        & ( in(sK0(X0,X1,X2),X2)
          | ( in(sK0(X0,X1,X2),X0)
            & ~ in(sK0(X0,X1,X2),X1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X0)
                & ~ in(X3,X1) )
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ~ in(X3,X0)
              | in(X3,X1) ) )
        | set_difference(X0,X1) != X2 )
      & ( set_difference(X0,X1) = X2
        | ? [X4] :
            ( ( ~ in(X4,X2)
              | ~ in(X4,X0)
              | in(X4,X1) )
            & ( in(X4,X2)
              | ( in(X4,X0)
                & ~ in(X4,X1) ) ) ) ) ),
    inference(rectify,[],[f44]) ).

fof(f44,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( ( in(X3,X0)
                & ~ in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) ) )
        | set_difference(X0,X2) != X1 )
      & ( set_difference(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) )
            & ( in(X3,X1)
              | ( in(X3,X0)
                & ~ in(X3,X2) ) ) ) ) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( ( in(X3,X0)
                & ~ in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) ) )
        | set_difference(X0,X2) != X1 )
      & ( set_difference(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) )
            & ( in(X3,X1)
              | ( in(X3,X0)
                & ~ in(X3,X2) ) ) ) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ( in(X3,X0)
            & ~ in(X3,X2) )
        <=> in(X3,X1) )
    <=> set_difference(X0,X2) = X1 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X2,X1] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( ( ~ in(X3,X1)
            & in(X3,X0) )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f110,plain,
    ~ in(sK3,set_difference(sK1,sK2)),
    inference(backward_demodulation,[],[f79,f104]) ).

fof(f104,plain,
    set_difference(sK1,sK2) = subset_complement(sK1,sK2),
    inference(unit_resulting_resolution,[],[f76,f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | set_difference(X0,X1) = subset_complement(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | set_difference(X0,X1) = subset_complement(X0,X1) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X1,X0] :
      ( ~ element(X0,powerset(X1))
      | subset_complement(X1,X0) = set_difference(X1,X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
     => subset_complement(X1,X0) = set_difference(X1,X0) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( element(X1,powerset(X0))
     => set_difference(X0,X1) = subset_complement(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).

fof(f76,plain,
    element(sK2,powerset(sK1)),
    inference(cnf_transformation,[],[f51]) ).

fof(f79,plain,
    ~ in(sK3,subset_complement(sK1,sK2)),
    inference(cnf_transformation,[],[f51]) ).

fof(f77,plain,
    ~ in(sK3,sK2),
    inference(cnf_transformation,[],[f51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:44:50 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.52  % (22864)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)
% 0.20/0.52  % (22856)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)
% 0.20/0.52  % (22863)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)
% 0.20/0.52  % (22858)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)
% 0.20/0.52  % (22854)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)
% 0.20/0.52  % (22854)First to succeed.
% 0.20/0.52  % (22877)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53  % (22857)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.53  % (22854)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (22854)------------------------------
% 0.20/0.53  % (22854)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (22854)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (22854)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (22854)Memory used [KB]: 6012
% 0.20/0.53  % (22854)Time elapsed: 0.128 s
% 0.20/0.53  % (22854)Instructions burned: 3 (million)
% 0.20/0.53  % (22854)------------------------------
% 0.20/0.53  % (22854)------------------------------
% 0.20/0.53  % (22848)Success in time 0.175 s
%------------------------------------------------------------------------------