TSTP Solution File: SEU148+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% 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 : n008.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 18:26:54 EDT 2022

% Result   : Theorem 0.18s 0.50s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   31 (   9 unt;   0 def)
%            Number of atoms       :  103 (  60 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  119 (  47   ~;  40   |;  22   &)
%                                         (   5 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   55 (  46   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f57,plain,
    $false,
    inference(subsumption_resolution,[],[f55,f44]) ).

fof(f44,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f43]) ).

fof(f43,plain,
    ! [X2,X1] :
      ( in(X2,X1)
      | singleton(X2) != X1 ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( in(X2,X1)
      | X0 != X2
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ( ( ~ in(sK0(X0,X1),X1)
            | sK0(X0,X1) != X0 )
          & ( in(sK0(X0,X1),X1)
            | sK0(X0,X1) = X0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | X0 != X3 )
          & ( in(X3,X1)
            | X0 = X3 ) )
     => ( ( ~ in(sK0(X0,X1),X1)
          | sK0(X0,X1) != X0 )
        & ( in(sK0(X0,X1),X1)
          | sK0(X0,X1) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | X0 != X3 )
            & ( in(X3,X1)
              | X0 = X3 ) ) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | X1 != X2 )
            & ( in(X2,X0)
              | X1 = X2 ) ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( X1 = X2
        <=> in(X2,X0) )
    <=> singleton(X1) = X0 ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f55,plain,
    ~ in(sK1,singleton(sK1)),
    inference(backward_demodulation,[],[f47,f54]) ).

fof(f54,plain,
    singleton(sK1) = singleton(sK2),
    inference(unit_resulting_resolution,[],[f38,f37,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ subset(X1,singleton(X0))
      | singleton(X0) = X1
      | empty_set = X1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( empty_set = X1
        | singleton(X0) = X1
        | ~ subset(X1,singleton(X0)) )
      & ( subset(X1,singleton(X0))
        | ( empty_set != X1
          & singleton(X0) != X1 ) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0] :
      ( ( empty_set = X0
        | singleton(X1) = X0
        | ~ subset(X0,singleton(X1)) )
      & ( subset(X0,singleton(X1))
        | ( empty_set != X0
          & singleton(X1) != X0 ) ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ( empty_set = X0
        | singleton(X1) = X0
        | ~ subset(X0,singleton(X1)) )
      & ( subset(X0,singleton(X1))
        | ( empty_set != X0
          & singleton(X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( ( empty_set = X0
        | singleton(X1) = X0 )
    <=> subset(X0,singleton(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).

fof(f37,plain,
    subset(singleton(sK1),singleton(sK2)),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ( subset(singleton(sK1),singleton(sK2))
    & sK2 != sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f24,f25]) ).

fof(f25,plain,
    ( ? [X0,X1] :
        ( subset(singleton(X0),singleton(X1))
        & X0 != X1 )
   => ( subset(singleton(sK1),singleton(sK2))
      & sK2 != sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ? [X0,X1] :
      ( subset(singleton(X0),singleton(X1))
      & X0 != X1 ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ? [X1,X0] :
      ( subset(singleton(X1),singleton(X0))
      & X0 != X1 ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X0,X1] :
        ( subset(singleton(X1),singleton(X0))
       => X0 = X1 ),
    inference(rectify,[],[f10]) ).

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

fof(f9,conjecture,
    ! [X1,X0] :
      ( subset(singleton(X0),singleton(X1))
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).

fof(f38,plain,
    ! [X0] : singleton(X0) != empty_set,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : singleton(X0) != empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).

fof(f47,plain,
    ~ in(sK1,singleton(sK2)),
    inference(unit_resulting_resolution,[],[f36,f42]) ).

fof(f42,plain,
    ! [X2,X0] :
      ( ~ in(X2,singleton(X0))
      | X0 = X2 ),
    inference(equality_resolution,[],[f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | ~ in(X2,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f36,plain,
    sK2 != sK1,
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.33  % Computer : n008.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Tue Aug 30 14:49:40 EDT 2022
% 0.11/0.33  % CPUTime    : 
% 0.18/0.49  % (947)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)
% 0.18/0.50  % (938)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)
% 0.18/0.50  % (928)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)
% 0.18/0.50  % (936)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.50  % (936)First to succeed.
% 0.18/0.50  % (927)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)
% 0.18/0.50  % (936)Refutation found. Thanks to Tanya!
% 0.18/0.50  % SZS status Theorem for theBenchmark
% 0.18/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50  % (936)------------------------------
% 0.18/0.50  % (936)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (936)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (936)Termination reason: Refutation
% 0.18/0.50  
% 0.18/0.50  % (936)Memory used [KB]: 6012
% 0.18/0.50  % (936)Time elapsed: 0.103 s
% 0.18/0.50  % (936)Instructions burned: 2 (million)
% 0.18/0.50  % (936)------------------------------
% 0.18/0.50  % (936)------------------------------
% 0.18/0.50  % (922)Success in time 0.167 s
%------------------------------------------------------------------------------