TSTP Solution File: SEU173+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU173+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 : Tue Apr 30 15:23:14 EDT 2024

% Result   : Theorem 0.16s 0.34s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   35 (   8 unt;   0 def)
%            Number of atoms       :  135 (   8 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  161 (  61   ~;  54   |;  28   &)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   71 (  61   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f193,plain,
    $false,
    inference(resolution,[],[f191,f145]) ).

fof(f145,plain,
    ~ subset(sK0,sK1),
    inference(resolution,[],[f142,f54]) ).

fof(f54,plain,
    ! [X0] : ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] : ~ empty(powerset(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(f142,plain,
    ( empty(powerset(sK1))
    | ~ subset(sK0,sK1) ),
    inference(resolution,[],[f134,f78]) ).

fof(f78,plain,
    ! [X3,X0] :
      ( in(X3,powerset(X0))
      | ~ subset(X3,X0) ),
    inference(equality_resolution,[],[f71]) ).

fof(f71,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ subset(X3,X0)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK6(X0,X1),X0)
            | ~ in(sK6(X0,X1),X1) )
          & ( subset(sK6(X0,X1),X0)
            | in(sK6(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f44,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK6(X0,X1),X0)
          | ~ in(sK6(X0,X1),X1) )
        & ( subset(sK6(X0,X1),X0)
          | in(sK6(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f43,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f134,plain,
    ( ~ in(sK0,powerset(sK1))
    | empty(powerset(sK1)) ),
    inference(resolution,[],[f63,f52]) ).

fof(f52,plain,
    ~ element(sK0,powerset(sK1)),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( ~ element(sK0,powerset(sK1))
    & ! [X2] :
        ( in(X2,sK1)
        | ~ in(X2,sK0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f30]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( ~ element(X0,powerset(X1))
        & ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) ) )
   => ( ~ element(sK0,powerset(sK1))
      & ! [X2] :
          ( in(X2,sK1)
          | ~ in(X2,sK0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ? [X0,X1] :
      ( ~ element(X0,powerset(X1))
      & ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1] :
        ( ! [X2] :
            ( in(X2,X0)
           => in(X2,X1) )
       => element(X0,powerset(X1)) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
     => element(X0,powerset(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).

fof(f63,plain,
    ! [X0,X1] :
      ( element(X1,X0)
      | ~ in(X1,X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( ( ( element(X1,X0)
            | ~ empty(X1) )
          & ( empty(X1)
            | ~ element(X1,X0) ) )
        | ~ empty(X0) )
      & ( ( ( element(X1,X0)
            | ~ in(X1,X0) )
          & ( in(X1,X0)
            | ~ element(X1,X0) ) )
        | empty(X0) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( ( element(X1,X0)
        <=> empty(X1) )
        | ~ empty(X0) )
      & ( ( element(X1,X0)
        <=> in(X1,X0) )
        | empty(X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ( 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(f191,plain,
    subset(sK0,sK1),
    inference(resolution,[],[f189,f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( in(sK5(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK5(X0,X1),X1)
          & in(sK5(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f40,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK5(X0,X1),X1)
        & in(sK5(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f189,plain,
    ~ in(sK5(sK0,sK1),sK0),
    inference(resolution,[],[f188,f51]) ).

fof(f51,plain,
    ! [X2] :
      ( in(X2,sK1)
      | ~ in(X2,sK0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f188,plain,
    ~ in(sK5(sK0,sK1),sK1),
    inference(resolution,[],[f69,f145]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK5(X0,X1),X1) ),
    inference(cnf_transformation,[],[f42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SEU173+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31  % Computer : n011.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon Apr 29 20:42:31 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.32  % (24329)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (24330)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33  % (24331)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33  % (24335)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.33  % (24333)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33  % (24336)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.33  % (24332)WARNING: value z3 for option sas not known
% 0.16/0.33  % (24334)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.33  TRYING [1]
% 0.16/0.33  TRYING [2]
% 0.16/0.33  % (24332)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.33  TRYING [3]
% 0.16/0.34  TRYING [1]
% 0.16/0.34  TRYING [4]
% 0.16/0.34  % (24335)First to succeed.
% 0.16/0.34  TRYING [2]
% 0.16/0.34  TRYING [1]
% 0.16/0.34  TRYING [2]
% 0.16/0.34  TRYING [3]
% 0.16/0.34  % (24335)Refutation found. Thanks to Tanya!
% 0.16/0.34  % SZS status Theorem for theBenchmark
% 0.16/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.34  % (24335)------------------------------
% 0.16/0.34  % (24335)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.34  % (24335)Termination reason: Refutation
% 0.16/0.34  
% 0.16/0.34  % (24335)Memory used [KB]: 847
% 0.16/0.34  % (24335)Time elapsed: 0.006 s
% 0.16/0.34  % (24335)Instructions burned: 8 (million)
% 0.16/0.34  % (24335)------------------------------
% 0.16/0.34  % (24335)------------------------------
% 0.16/0.34  % (24329)Success in time 0.014 s
%------------------------------------------------------------------------------