TSTP Solution File: SET923+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET923+1 : 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_sat --cores 0 -t %d %s

% Computer : n021.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 18:26:06 EDT 2022

% Result   : Theorem 0.19s 0.46s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   24 (   6 unt;   0 def)
%            Number of atoms       :   69 (  51 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   80 (  35   ~;  19   |;  22   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (  24   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f47,plain,
    $false,
    inference(subsumption_resolution,[],[f46,f30]) ).

fof(f30,plain,
    empty_set != sK2,
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( empty_set = set_difference(sK2,singleton(sK1))
    & empty_set != sK2
    & sK2 != singleton(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0,X1] :
        ( empty_set = set_difference(X1,singleton(X0))
        & empty_set != X1
        & singleton(X0) != X1 )
   => ( empty_set = set_difference(sK2,singleton(sK1))
      & empty_set != sK2
      & sK2 != singleton(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1] :
      ( empty_set = set_difference(X1,singleton(X0))
      & empty_set != X1
      & singleton(X0) != X1 ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ? [X1,X0] :
      ( empty_set = set_difference(X0,singleton(X1))
      & empty_set != X0
      & singleton(X1) != X0 ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ~ ( empty_set = set_difference(X0,singleton(X1))
          & empty_set != X0
          & singleton(X1) != X0 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ~ ( empty_set = set_difference(X0,singleton(X1))
        & empty_set != X0
        & singleton(X1) != X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).

fof(f46,plain,
    empty_set = sK2,
    inference(subsumption_resolution,[],[f44,f29]) ).

fof(f29,plain,
    sK2 != singleton(sK1),
    inference(cnf_transformation,[],[f18]) ).

fof(f44,plain,
    ( sK2 = singleton(sK1)
    | empty_set = sK2 ),
    inference(resolution,[],[f41,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ subset(X1,singleton(X0))
      | singleton(X0) = X1
      | empty_set = X1 ),
    inference(cnf_transformation,[],[f21]) ).

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

fof(f20,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,[],[f19]) ).

fof(f19,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,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ( empty_set = X0
        | singleton(X1) = X0 )
    <=> subset(X0,singleton(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).

fof(f41,plain,
    subset(sK2,singleton(sK1)),
    inference(trivial_inequality_removal,[],[f40]) ).

fof(f40,plain,
    ( empty_set != empty_set
    | subset(sK2,singleton(sK1)) ),
    inference(superposition,[],[f25,f31]) ).

fof(f31,plain,
    empty_set = set_difference(sK2,singleton(sK1)),
    inference(cnf_transformation,[],[f18]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( empty_set != set_difference(X0,X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | empty_set != set_difference(X0,X1) )
      & ( empty_set = set_difference(X0,X1)
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | empty_set != set_difference(X1,X0) )
      & ( empty_set = set_difference(X1,X0)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> empty_set = set_difference(X1,X0) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X0] :
      ( empty_set = set_difference(X0,X1)
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET923+1 : 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_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 14:27:11 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.45  % (30092)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.45  % (30092)First to succeed.
% 0.19/0.46  % (30108)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.46  % (30092)Refutation found. Thanks to Tanya!
% 0.19/0.46  % SZS status Theorem for theBenchmark
% 0.19/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46  % (30092)------------------------------
% 0.19/0.46  % (30092)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.46  % (30092)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.46  % (30092)Termination reason: Refutation
% 0.19/0.46  
% 0.19/0.46  % (30092)Memory used [KB]: 5373
% 0.19/0.46  % (30092)Time elapsed: 0.061 s
% 0.19/0.46  % (30092)Instructions burned: 2 (million)
% 0.19/0.46  % (30092)------------------------------
% 0.19/0.46  % (30092)------------------------------
% 0.19/0.46  % (30084)Success in time 0.118 s
%------------------------------------------------------------------------------