TSTP Solution File: NUM190-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM190-1 : 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 : n016.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 14:13:56 EDT 2024

% Result   : Unsatisfiable 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   47
% Syntax   : Number of formulae    :  150 (  16 unt;   0 def)
%            Number of atoms       :  305 (  42 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  260 ( 105   ~; 133   |;   0   &)
%                                         (  22 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   28 (  26 usr;  23 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   9 con; 0-2 aty)
%            Number of variables   :   67 (  67   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f575,plain,
    $false,
    inference(avatar_sat_refutation,[],[f180,f227,f237,f268,f274,f363,f383,f392,f406,f421,f434,f436,f454,f464,f479,f481,f506,f523,f531,f553,f574]) ).

fof(f574,plain,
    ~ spl0_5,
    inference(avatar_contradiction_clause,[],[f573]) ).

fof(f573,plain,
    ( $false
    | ~ spl0_5 ),
    inference(subsumption_resolution,[],[f569,f166]) ).

fof(f166,plain,
    inductive(null_class),
    inference(superposition,[],[f50,f159]) ).

fof(f159,axiom,
    null_class = omega,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_omega_is_not_null_1) ).

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

fof(f569,plain,
    ( ~ inductive(null_class)
    | ~ spl0_5 ),
    inference(superposition,[],[f562,f560]) ).

fof(f560,plain,
    ( null_class = kind_1_ordinals
    | ~ spl0_5 ),
    inference(resolution,[],[f558,f490]) ).

fof(f490,plain,
    ! [X0] :
      ( member(null_class,X0)
      | null_class = X0 ),
    inference(subsumption_resolution,[],[f487,f166]) ).

fof(f487,plain,
    ! [X0] :
      ( ~ inductive(null_class)
      | member(null_class,X0)
      | null_class = X0 ),
    inference(superposition,[],[f212,f67]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = intersection(X0,regular(X0))
      | null_class = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).

fof(f212,plain,
    ! [X0,X1] :
      ( ~ inductive(intersection(X0,X1))
      | member(null_class,X0) ),
    inference(resolution,[],[f21,f47]) ).

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

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

fof(f558,plain,
    ( ~ member(null_class,kind_1_ordinals)
    | ~ spl0_5 ),
    inference(resolution,[],[f232,f24]) ).

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

fof(f232,plain,
    ( member(null_class,complement(kind_1_ordinals))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f230,plain,
    ( spl0_5
  <=> member(null_class,complement(kind_1_ordinals)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f562,plain,
    ( ~ inductive(kind_1_ordinals)
    | ~ spl0_5 ),
    inference(resolution,[],[f558,f47]) ).

fof(f553,plain,
    ( ~ spl0_1
    | spl0_9 ),
    inference(avatar_contradiction_clause,[],[f552]) ).

fof(f552,plain,
    ( $false
    | ~ spl0_1
    | spl0_9 ),
    inference(subsumption_resolution,[],[f547,f166]) ).

fof(f547,plain,
    ( ~ inductive(null_class)
    | ~ spl0_1
    | spl0_9 ),
    inference(superposition,[],[f175,f509]) ).

fof(f509,plain,
    ( ! [X0] : null_class = recursion_equation_functions(X0)
    | spl0_9 ),
    inference(subsumption_resolution,[],[f502,f358]) ).

fof(f358,plain,
    ( ~ member(domain_of(null_class),ordinal_numbers)
    | spl0_9 ),
    inference(avatar_component_clause,[],[f357]) ).

fof(f357,plain,
    ( spl0_9
  <=> member(domain_of(null_class),ordinal_numbers) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f502,plain,
    ! [X0] :
      ( null_class = recursion_equation_functions(X0)
      | member(domain_of(null_class),ordinal_numbers) ),
    inference(resolution,[],[f490,f149]) ).

fof(f149,axiom,
    ! [X0,X4] :
      ( ~ member(X0,recursion_equation_functions(X4))
      | member(domain_of(X0),ordinal_numbers) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions3) ).

fof(f175,plain,
    ( ! [X0] : ~ inductive(recursion_equation_functions(X0))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f174,plain,
    ( spl0_1
  <=> ! [X0] : ~ inductive(recursion_equation_functions(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f531,plain,
    spl0_7,
    inference(avatar_contradiction_clause,[],[f530]) ).

fof(f530,plain,
    ( $false
    | spl0_7 ),
    inference(subsumption_resolution,[],[f529,f166]) ).

fof(f529,plain,
    ( ~ inductive(null_class)
    | spl0_7 ),
    inference(superposition,[],[f516,f514]) ).

fof(f514,plain,
    ( null_class = kind_1_ordinals
    | spl0_7 ),
    inference(resolution,[],[f507,f490]) ).

fof(f507,plain,
    ( ~ member(null_class,kind_1_ordinals)
    | spl0_7 ),
    inference(subsumption_resolution,[],[f500,f262]) ).

fof(f262,plain,
    ( null_class != limit_ordinals
    | spl0_7 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f261,plain,
    ( spl0_7
  <=> null_class = limit_ordinals ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f500,plain,
    ( null_class = limit_ordinals
    | ~ member(null_class,kind_1_ordinals) ),
    inference(resolution,[],[f490,f251]) ).

fof(f251,plain,
    ! [X0] :
      ( ~ member(X0,limit_ordinals)
      | ~ member(X0,kind_1_ordinals) ),
    inference(resolution,[],[f216,f24]) ).

fof(f216,plain,
    ! [X0] :
      ( member(X0,complement(kind_1_ordinals))
      | ~ member(X0,limit_ordinals) ),
    inference(superposition,[],[f21,f139]) ).

fof(f139,axiom,
    intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_ordinals) ).

fof(f516,plain,
    ( ~ inductive(kind_1_ordinals)
    | spl0_7 ),
    inference(resolution,[],[f507,f47]) ).

fof(f523,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_contradiction_clause,[],[f522]) ).

fof(f522,plain,
    ( $false
    | spl0_3
    | spl0_4 ),
    inference(subsumption_resolution,[],[f521,f166]) ).

fof(f521,plain,
    ( ~ inductive(null_class)
    | spl0_3
    | spl0_4 ),
    inference(superposition,[],[f226,f493]) ).

fof(f493,plain,
    ( null_class = identity_relation
    | spl0_3 ),
    inference(resolution,[],[f490,f249]) ).

fof(f249,plain,
    ( ~ member(null_class,identity_relation)
    | spl0_3 ),
    inference(resolution,[],[f215,f221]) ).

fof(f221,plain,
    ( ~ member(null_class,inverse(subset_relation))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f220]) ).

fof(f220,plain,
    ( spl0_3
  <=> member(null_class,inverse(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f215,plain,
    ! [X0] :
      ( member(X0,inverse(subset_relation))
      | ~ member(X0,identity_relation) ),
    inference(superposition,[],[f21,f75]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).

fof(f226,plain,
    ( ~ inductive(identity_relation)
    | spl0_4 ),
    inference(avatar_component_clause,[],[f224]) ).

fof(f224,plain,
    ( spl0_4
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f506,plain,
    ( spl0_5
    | spl0_7 ),
    inference(avatar_contradiction_clause,[],[f505]) ).

fof(f505,plain,
    ( $false
    | spl0_5
    | spl0_7 ),
    inference(subsumption_resolution,[],[f494,f262]) ).

fof(f494,plain,
    ( null_class = limit_ordinals
    | spl0_5 ),
    inference(resolution,[],[f490,f253]) ).

fof(f253,plain,
    ( ~ member(null_class,limit_ordinals)
    | spl0_5 ),
    inference(resolution,[],[f216,f231]) ).

fof(f231,plain,
    ( ~ member(null_class,complement(kind_1_ordinals))
    | spl0_5 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f481,plain,
    ( ~ spl0_1
    | spl0_21 ),
    inference(avatar_contradiction_clause,[],[f480]) ).

fof(f480,plain,
    ( $false
    | ~ spl0_1
    | spl0_21 ),
    inference(subsumption_resolution,[],[f470,f166]) ).

fof(f470,plain,
    ( ~ inductive(null_class)
    | ~ spl0_1
    | spl0_21 ),
    inference(superposition,[],[f175,f465]) ).

fof(f465,plain,
    ( null_class = recursion_equation_functions(universal_class)
    | spl0_21 ),
    inference(resolution,[],[f459,f183]) ).

fof(f183,plain,
    ! [X0] :
      ( function(X0)
      | null_class = recursion_equation_functions(X0) ),
    inference(resolution,[],[f66,f147]) ).

fof(f147,axiom,
    ! [X0,X4] :
      ( ~ member(X0,recursion_equation_functions(X4))
      | function(X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions1) ).

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

fof(f459,plain,
    ( ~ function(universal_class)
    | spl0_21 ),
    inference(avatar_component_clause,[],[f457]) ).

fof(f457,plain,
    ( spl0_21
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f479,plain,
    spl0_21,
    inference(avatar_contradiction_clause,[],[f478]) ).

fof(f478,plain,
    ( $false
    | spl0_21 ),
    inference(subsumption_resolution,[],[f477,f459]) ).

fof(f477,plain,
    ( function(universal_class)
    | spl0_21 ),
    inference(subsumption_resolution,[],[f469,f166]) ).

fof(f469,plain,
    ( ~ inductive(null_class)
    | function(universal_class)
    | spl0_21 ),
    inference(superposition,[],[f171,f465]) ).

fof(f171,plain,
    ! [X0] :
      ( ~ inductive(recursion_equation_functions(X0))
      | function(X0) ),
    inference(resolution,[],[f147,f47]) ).

fof(f464,plain,
    ( ~ spl0_21
    | spl0_22 ),
    inference(avatar_split_clause,[],[f346,f461,f457]) ).

fof(f461,plain,
    ( spl0_22
  <=> universal_class = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f346,plain,
    ( universal_class = cross_product(universal_class,universal_class)
    | ~ function(universal_class) ),
    inference(resolution,[],[f324,f62]) ).

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

fof(f324,plain,
    ! [X0] :
      ( ~ subclass(universal_class,X0)
      | universal_class = X0 ),
    inference(resolution,[],[f7,f4]) ).

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

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X1,X0)
      | ~ subclass(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f454,plain,
    ( spl0_19
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f441,f451,f448]) ).

fof(f448,plain,
    ( spl0_19
  <=> ! [X0] : singleton(X0) = integer_of(singleton(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f451,plain,
    ( spl0_20
  <=> subclass(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f441,plain,
    ! [X0] :
      ( ~ subclass(universal_class,null_class)
      | singleton(X0) = integer_of(singleton(X0)) ),
    inference(resolution,[],[f289,f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ member(X0,null_class)
      | integer_of(X0) = X0 ),
    inference(forward_demodulation,[],[f157,f159]) ).

fof(f157,axiom,
    ! [X0] :
      ( ~ member(X0,omega)
      | integer_of(X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function1) ).

fof(f289,plain,
    ! [X0,X1] :
      ( member(singleton(X1),X0)
      | ~ subclass(universal_class,X0) ),
    inference(resolution,[],[f1,f169]) ).

fof(f169,plain,
    ! [X0] : member(singleton(X0),universal_class),
    inference(superposition,[],[f11,f12]) ).

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

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

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

fof(f436,plain,
    ( spl0_1
    | spl0_9 ),
    inference(avatar_split_clause,[],[f435,f357,f174]) ).

fof(f435,plain,
    ( ! [X0] : ~ inductive(recursion_equation_functions(X0))
    | spl0_9 ),
    inference(subsumption_resolution,[],[f282,f358]) ).

fof(f282,plain,
    ! [X0] :
      ( member(domain_of(null_class),ordinal_numbers)
      | ~ inductive(recursion_equation_functions(X0)) ),
    inference(resolution,[],[f149,f47]) ).

fof(f434,plain,
    ( ~ spl0_17
    | spl0_18 ),
    inference(avatar_split_clause,[],[f355,f431,f427]) ).

fof(f427,plain,
    ( spl0_17
  <=> inductive(image(successor_relation,null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f431,plain,
    ( spl0_18
  <=> null_class = image(successor_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f355,plain,
    ( null_class = image(successor_relation,null_class)
    | ~ inductive(image(successor_relation,null_class)) ),
    inference(subsumption_resolution,[],[f351,f166]) ).

fof(f351,plain,
    ( null_class = image(successor_relation,null_class)
    | ~ inductive(image(successor_relation,null_class))
    | ~ inductive(null_class) ),
    inference(resolution,[],[f328,f48]) ).

fof(f48,axiom,
    ! [X0] :
      ( subclass(image(successor_relation,X0),X0)
      | ~ inductive(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).

fof(f328,plain,
    ! [X0] :
      ( ~ subclass(X0,null_class)
      | null_class = X0
      | ~ inductive(X0) ),
    inference(resolution,[],[f7,f168]) ).

fof(f168,plain,
    ! [X1] :
      ( subclass(null_class,X1)
      | ~ inductive(X1) ),
    inference(forward_demodulation,[],[f51,f159]) ).

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

fof(f421,plain,
    ( spl0_15
    | spl0_16 ),
    inference(avatar_split_clause,[],[f347,f418,f414]) ).

fof(f414,plain,
    ( spl0_15
  <=> null_class = integer_of(not_subclass_element(universal_class,null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f418,plain,
    ( spl0_16
  <=> universal_class = null_class ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f347,plain,
    ( universal_class = null_class
    | null_class = integer_of(not_subclass_element(universal_class,null_class)) ),
    inference(resolution,[],[f324,f208]) ).

fof(f208,plain,
    ! [X0] :
      ( subclass(X0,null_class)
      | null_class = integer_of(not_subclass_element(X0,null_class)) ),
    inference(resolution,[],[f3,f189]) ).

fof(f189,plain,
    ! [X0] :
      ( member(X0,null_class)
      | null_class = integer_of(X0) ),
    inference(forward_demodulation,[],[f158,f159]) ).

fof(f158,axiom,
    ! [X0] :
      ( member(X0,omega)
      | null_class = integer_of(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function2) ).

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

fof(f406,plain,
    spl0_13,
    inference(avatar_contradiction_clause,[],[f405]) ).

fof(f405,plain,
    ( $false
    | spl0_13 ),
    inference(subsumption_resolution,[],[f404,f387]) ).

fof(f387,plain,
    ( ~ function(domain_of(null_class))
    | spl0_13 ),
    inference(avatar_component_clause,[],[f386]) ).

fof(f386,plain,
    ( spl0_13
  <=> function(domain_of(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f404,plain,
    ( function(domain_of(null_class))
    | spl0_13 ),
    inference(subsumption_resolution,[],[f397,f166]) ).

fof(f397,plain,
    ( ~ inductive(null_class)
    | function(domain_of(null_class))
    | spl0_13 ),
    inference(superposition,[],[f171,f393]) ).

fof(f393,plain,
    ( null_class = recursion_equation_functions(domain_of(null_class))
    | spl0_13 ),
    inference(resolution,[],[f387,f183]) ).

fof(f392,plain,
    ( spl0_13
    | spl0_14
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f373,f357,f390,f386]) ).

fof(f390,plain,
    ( spl0_14
  <=> ! [X0] : ~ subclass(ordinal_numbers,recursion_equation_functions(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f373,plain,
    ( ! [X0] :
        ( ~ subclass(ordinal_numbers,recursion_equation_functions(X0))
        | function(domain_of(null_class)) )
    | ~ spl0_9 ),
    inference(resolution,[],[f364,f148]) ).

fof(f148,axiom,
    ! [X0,X4] :
      ( ~ member(X0,recursion_equation_functions(X4))
      | function(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions2) ).

fof(f364,plain,
    ( ! [X0] :
        ( member(domain_of(null_class),X0)
        | ~ subclass(ordinal_numbers,X0) )
    | ~ spl0_9 ),
    inference(resolution,[],[f359,f1]) ).

fof(f359,plain,
    ( member(domain_of(null_class),ordinal_numbers)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f357]) ).

fof(f383,plain,
    ( ~ spl0_11
    | ~ spl0_12
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f370,f357,f380,f376]) ).

fof(f376,plain,
    ( spl0_11
  <=> member(domain_of(null_class),kind_1_ordinals) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f380,plain,
    ( spl0_12
  <=> subclass(ordinal_numbers,limit_ordinals) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f370,plain,
    ( ~ subclass(ordinal_numbers,limit_ordinals)
    | ~ member(domain_of(null_class),kind_1_ordinals)
    | ~ spl0_9 ),
    inference(resolution,[],[f364,f251]) ).

fof(f363,plain,
    ( spl0_9
    | spl0_10 ),
    inference(avatar_split_clause,[],[f312,f361,f357]) ).

fof(f361,plain,
    ( spl0_10
  <=> ! [X0] : ~ subclass(universal_class,recursion_equation_functions(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f312,plain,
    ! [X0] :
      ( ~ subclass(universal_class,recursion_equation_functions(X0))
      | member(domain_of(null_class),ordinal_numbers) ),
    inference(resolution,[],[f290,f149]) ).

fof(f290,plain,
    ! [X0] :
      ( member(null_class,X0)
      | ~ subclass(universal_class,X0) ),
    inference(resolution,[],[f1,f167]) ).

fof(f167,plain,
    member(null_class,universal_class),
    inference(forward_demodulation,[],[f52,f159]) ).

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

fof(f274,plain,
    ( spl0_6
    | ~ spl0_7 ),
    inference(avatar_contradiction_clause,[],[f273]) ).

fof(f273,plain,
    ( $false
    | spl0_6
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f272,f166]) ).

fof(f272,plain,
    ( ~ inductive(null_class)
    | spl0_6
    | ~ spl0_7 ),
    inference(superposition,[],[f236,f263]) ).

fof(f263,plain,
    ( null_class = limit_ordinals
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f236,plain,
    ( ~ inductive(limit_ordinals)
    | spl0_6 ),
    inference(avatar_component_clause,[],[f234]) ).

fof(f234,plain,
    ( spl0_6
  <=> inductive(limit_ordinals) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f268,plain,
    ( spl0_7
    | spl0_8 ),
    inference(avatar_split_clause,[],[f246,f265,f261]) ).

fof(f265,plain,
    ( spl0_8
  <=> member(regular(limit_ordinals),ordinal_numbers) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f246,plain,
    ( member(regular(limit_ordinals),ordinal_numbers)
    | null_class = limit_ordinals ),
    inference(resolution,[],[f243,f66]) ).

fof(f243,plain,
    ! [X0] :
      ( ~ member(X0,limit_ordinals)
      | member(X0,ordinal_numbers) ),
    inference(superposition,[],[f22,f139]) ).

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

fof(f237,plain,
    ( spl0_5
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f218,f234,f230]) ).

fof(f218,plain,
    ( ~ inductive(limit_ordinals)
    | member(null_class,complement(kind_1_ordinals)) ),
    inference(superposition,[],[f212,f139]) ).

fof(f227,plain,
    ( spl0_3
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f217,f224,f220]) ).

fof(f217,plain,
    ( ~ inductive(identity_relation)
    | member(null_class,inverse(subset_relation)) ),
    inference(superposition,[],[f212,f75]) ).

fof(f180,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f172,f177,f174]) ).

fof(f177,plain,
    ( spl0_2
  <=> function(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f172,plain,
    ! [X0] :
      ( function(null_class)
      | ~ inductive(recursion_equation_functions(X0)) ),
    inference(resolution,[],[f148,f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM190-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 00:39:40 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (17773)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (17776)WARNING: value z3 for option sas not known
% 0.14/0.37  % (17776)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)
% 0.14/0.38  % (17775)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (17778)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)
% 0.14/0.38  % (17774)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (17779)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)
% 0.14/0.38  % (17777)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (17780)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)
% 0.14/0.39  % (17776)First to succeed.
% 0.14/0.39  % (17776)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (17776)------------------------------
% 0.14/0.39  % (17776)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (17776)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (17776)Memory used [KB]: 1231
% 0.14/0.39  % (17776)Time elapsed: 0.020 s
% 0.14/0.39  % (17776)Instructions burned: 33 (million)
% 0.14/0.39  % (17776)------------------------------
% 0.14/0.39  % (17776)------------------------------
% 0.14/0.39  % (17773)Success in time 0.036 s
%------------------------------------------------------------------------------