TSTP Solution File: SET093-7 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET093-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.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 May 21 03:16:02 EDT 2024

% Result   : Unsatisfiable 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   62 (  36 unt;   0 def)
%            Number of atoms       :   94 (   5 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   50 (  18   ~;  14   |;   0   &)
%                                         (  18 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   26 (  24 usr;  19 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   23 (  23   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f322,plain,
    $false,
    inference(avatar_sat_refutation,[],[f242,f247,f252,f257,f261,f266,f270,f274,f278,f283,f287,f291,f295,f300,f305,f309,f313,f318,f321]) ).

fof(f321,plain,
    ( spl0_1
    | ~ spl0_2
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f319,f293,f244,f239]) ).

fof(f239,plain,
    ( spl0_1
  <=> member(x,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f244,plain,
    ( spl0_2
  <=> x = unordered_pair(member_of(x),member_of(x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f293,plain,
    ( spl0_13
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f319,plain,
    ( member(x,universal_class)
    | ~ spl0_2
    | ~ spl0_13 ),
    inference(superposition,[],[f294,f246]) ).

fof(f246,plain,
    ( x = unordered_pair(member_of(x),member_of(x))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f294,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f293]) ).

fof(f318,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f150,f315]) ).

fof(f315,plain,
    ( spl0_18
  <=> member(null_class,unordered_pair(null_class,null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f150,plain,
    member(null_class,unordered_pair(null_class,null_class)),
    inference(definition_unfolding,[],[f124,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).

fof(f124,axiom,
    member(null_class,singleton(null_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_in_its_singleton) ).

fof(f313,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f51,f311]) ).

fof(f311,plain,
    ( spl0_17
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f309,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f47,f307]) ).

fof(f307,plain,
    ( spl0_16
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).

fof(f305,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f44,f302]) ).

fof(f302,plain,
    ( spl0_15
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).

fof(f300,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f18,f297]) ).

fof(f297,plain,
    ( spl0_14
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).

fof(f295,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f11,f293]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f291,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f78,f289]) ).

fof(f289,plain,
    ( spl0_12
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).

fof(f287,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f71,f285]) ).

fof(f285,plain,
    ( spl0_11
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).

fof(f283,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f107,f280]) ).

fof(f280,plain,
    ( spl0_10
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f107,axiom,
    member(null_class,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).

fof(f278,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f104,f276]) ).

fof(f276,plain,
    ( spl0_9
  <=> ! [X0] : subclass(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f104,axiom,
    ! [X0] : subclass(null_class,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).

fof(f274,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f103,f272]) ).

fof(f272,plain,
    ( spl0_8
  <=> ! [X4] : ~ member(X4,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f103,axiom,
    ! [X4] : ~ member(X4,null_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).

fof(f270,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f96,f268]) ).

fof(f268,plain,
    ( spl0_7
  <=> ! [X0] : subclass(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f96,axiom,
    ! [X0] : subclass(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).

fof(f266,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f52,f263]) ).

fof(f263,plain,
    ( spl0_6
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f261,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f4,f259]) ).

fof(f259,plain,
    ( spl0_5
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f257,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f69,f254]) ).

fof(f254,plain,
    ( spl0_4
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).

fof(f252,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f50,f249]) ).

fof(f249,plain,
    ( spl0_3
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f247,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f149,f244]) ).

fof(f149,plain,
    x = unordered_pair(member_of(x),member_of(x)),
    inference(definition_unfolding,[],[f137,f12]) ).

fof(f137,axiom,
    x = singleton(member_of(x)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_singletons_are_sets_1) ).

fof(f242,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f138,f239]) ).

fof(f138,axiom,
    ~ member(x,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_singletons_are_sets_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SET093-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon May 20 13:05:38 EDT 2024
% 0.13/0.33  % CPUTime    : 
% 0.13/0.34  % (22609)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (22614)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)
% 0.13/0.37  % (22610)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (22612)WARNING: value z3 for option sas not known
% 0.13/0.37  % (22612)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)
% 0.13/0.37  % (22611)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (22614)First to succeed.
% 0.13/0.37  % (22614)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22609"
% 0.13/0.37  % (22612)Also succeeded, but the first one will report.
% 0.13/0.38  % (22614)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (22614)------------------------------
% 0.13/0.38  % (22614)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38  % (22614)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (22614)Memory used [KB]: 1029
% 0.13/0.38  % (22614)Time elapsed: 0.014 s
% 0.13/0.38  % (22614)Instructions burned: 19 (million)
% 0.13/0.38  % (22609)Success in time 0.038 s
%------------------------------------------------------------------------------