TSTP Solution File: SET239-6 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET239-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n024.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 15:07:24 EDT 2024

% Result   : Unsatisfiable 0.16s 0.34s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   81
% Syntax   : Number of formulae    :  135 (  61 unt;   0 def)
%            Number of atoms       :  241 (   9 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  175 (  69   ~;  66   |;   0   &)
%                                         (  40 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   51 (  49 usr;  41 prp; 0-3 aty)
%            Number of functors    :   26 (  26 usr;  13 con; 0-3 aty)
%            Number of variables   :  127 ( 127   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f391,plain,
    $false,
    inference(avatar_sat_refutation,[],[f209,f214,f220,f225,f230,f234,f239,f243,f247,f251,f255,f260,f265,f269,f273,f278,f282,f286,f290,f294,f298,f302,f306,f310,f314,f319,f324,f330,f334,f338,f342,f346,f350,f354,f358,f362,f366,f370,f374,f389,f390]) ).

fof(f390,plain,
    ( spl0_1
    | ~ spl0_3
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f381,f348,f217,f206]) ).

fof(f206,plain,
    ( spl0_1
  <=> member(z,xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f217,plain,
    ( spl0_3
  <=> member(z,intersection(xr,cross_product(x,y))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f348,plain,
    ( spl0_33
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f381,plain,
    ( member(z,xr)
    | ~ spl0_3
    | ~ spl0_33 ),
    inference(resolution,[],[f349,f219]) ).

fof(f219,plain,
    ( member(z,intersection(xr,cross_product(x,y)))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f217]) ).

fof(f349,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f348]) ).

fof(f389,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f1,f387]) ).

fof(f387,plain,
    ( spl0_40
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).

fof(f374,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f133,f372]) ).

fof(f372,plain,
    ( spl0_39
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f133,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).

fof(f370,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f110,f368]) ).

fof(f368,plain,
    ( spl0_38
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).

fof(f366,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f88,f364]) ).

fof(f364,plain,
    ( spl0_37
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).

fof(f362,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f35,f360]) ).

fof(f360,plain,
    ( spl0_36
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).

fof(f358,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f32,f356]) ).

fof(f356,plain,
    ( spl0_35
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).

fof(f354,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f22,f352]) ).

fof(f352,plain,
    ( spl0_34
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).

fof(f350,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f21,f348]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).

fof(f346,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f10,f344]) ).

fof(f344,plain,
    ( spl0_32
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f342,plain,
    ( spl0_31
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f325,f300,f267,f340]) ).

fof(f340,plain,
    ( spl0_31
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f267,plain,
    ( spl0_14
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f300,plain,
    ( spl0_22
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f325,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(resolution,[],[f301,f268]) ).

fof(f268,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f301,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f338,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f9,f336]) ).

fof(f336,plain,
    ( spl0_30
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f334,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f3,f332]) ).

fof(f332,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f330,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f2,f328]) ).

fof(f328,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f324,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f105,f321]) ).

fof(f321,plain,
    ( spl0_27
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f105,axiom,
    subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn1) ).

fof(f319,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f95,f316]) ).

fof(f316,plain,
    ( spl0_26
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f95,axiom,
    subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function1) ).

fof(f314,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f66,f312]) ).

fof(f312,plain,
    ( spl0_25
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).

fof(f310,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f62,f308]) ).

fof(f308,plain,
    ( spl0_24
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).

fof(f306,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f57,f304]) ).

fof(f304,plain,
    ( spl0_23
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).

fof(f302,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f24,f300]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).

fof(f298,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f109,f296]) ).

fof(f296,plain,
    ( spl0_21
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).

fof(f294,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f92,f292]) ).

fof(f292,plain,
    ( spl0_20
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f92,axiom,
    ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).

fof(f290,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f87,f288]) ).

fof(f288,plain,
    ( spl0_19
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).

fof(f286,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f86,f284]) ).

fof(f284,plain,
    ( spl0_18
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).

fof(f282,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f82,f280]) ).

fof(f280,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).

fof(f278,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f98,f275]) ).

fof(f275,plain,
    ( spl0_16
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f273,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f51,f271]) ).

fof(f271,plain,
    ( spl0_15
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

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

fof(f269,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f47,f267]) ).

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

fof(f265,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f44,f262]) ).

fof(f262,plain,
    ( spl0_13
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

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

fof(f260,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f18,f257]) ).

fof(f257,plain,
    ( spl0_12
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

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

fof(f255,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f11,f253]) ).

fof(f253,plain,
    ( spl0_11
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

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

fof(f251,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f78,f249]) ).

fof(f249,plain,
    ( spl0_10
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

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

fof(f247,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f71,f245]) ).

fof(f245,plain,
    ( spl0_9
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

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

fof(f243,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f178,f241]) ).

fof(f241,plain,
    ( spl0_8
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f178,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).

fof(f239,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f52,f236]) ).

fof(f236,plain,
    ( spl0_7
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

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

fof(f234,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f4,f232]) ).

fof(f232,plain,
    ( spl0_6
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

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

fof(f230,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f69,f227]) ).

fof(f227,plain,
    ( spl0_5
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

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

fof(f225,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f50,f222]) ).

fof(f222,plain,
    ( spl0_4
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

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

fof(f220,plain,
    ( spl0_3
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f215,f211,f217]) ).

fof(f211,plain,
    ( spl0_2
  <=> member(z,intersection(cross_product(x,y),xr)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f215,plain,
    ( member(z,intersection(xr,cross_product(x,y)))
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f213,f130]) ).

fof(f130,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).

fof(f213,plain,
    ( member(z,intersection(cross_product(x,y),xr))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f214,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f128,f211]) ).

fof(f128,plain,
    member(z,intersection(cross_product(x,y),xr)),
    inference(definition_unfolding,[],[f113,f29]) ).

fof(f113,axiom,
    member(z,restrict(xr,x,y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn2_1) ).

fof(f209,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f114,f206]) ).

fof(f114,axiom,
    ~ member(z,xr),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn2_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : SET239-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.05/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n024.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Apr 30 01:18:21 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  % (30602)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (30605)WARNING: value z3 for option sas not known
% 0.16/0.33  % (30609)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  % (30604)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  % (30608)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  % (30603)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33  % (30607)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  % (30605)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  % (30606)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34  % (30607)First to succeed.
% 0.16/0.34  % (30607)Refutation found. Thanks to Tanya!
% 0.16/0.34  % SZS status Unsatisfiable for theBenchmark
% 0.16/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.34  % (30607)------------------------------
% 0.16/0.34  % (30607)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.34  % (30607)Termination reason: Refutation
% 0.16/0.34  
% 0.16/0.34  % (30607)Memory used [KB]: 1066
% 0.16/0.34  % (30607)Time elapsed: 0.011 s
% 0.16/0.34  % (30607)Instructions burned: 21 (million)
% 0.16/0.34  % (30607)------------------------------
% 0.16/0.34  % (30607)------------------------------
% 0.16/0.34  % (30602)Success in time 0.029 s
%------------------------------------------------------------------------------