TSTP Solution File: SEU236+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU236+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n007.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 Aug 22 10:58:07 EDT 2023

% Result   : Theorem 283.89s 257.12s
% Output   : CNFRefutation 283.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  165 (  52 unt;  38 typ;   0 def)
%            Number of atoms       :  270 (  25 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  244 ( 101   ~; 107   |;  16   &)
%                                         (   7 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  22   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  16 con; 0-2 aty)
%            Number of variables   :  112 (; 109   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > ordinal_subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > set_union2 > #nlpp > succ > singleton > powerset > empty_set > #skF_5 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_12 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(epsilon_connected,type,
    epsilon_connected: $i > $o ).

tff('#skF_5',type,
    '#skF_5': $i > $i ).

tff(relation,type,
    relation: $i > $o ).

tff('#skF_20',type,
    '#skF_20': $i ).

tff('#skF_18',type,
    '#skF_18': $i ).

tff(singleton,type,
    singleton: $i > $i ).

tff('#skF_17',type,
    '#skF_17': $i ).

tff('#skF_11',type,
    '#skF_11': $i ).

tff(relation_non_empty,type,
    relation_non_empty: $i > $o ).

tff('#skF_15',type,
    '#skF_15': $i ).

tff(epsilon_transitive,type,
    epsilon_transitive: $i > $o ).

tff(element,type,
    element: ( $i * $i ) > $o ).

tff(one_to_one,type,
    one_to_one: $i > $o ).

tff(function,type,
    function: $i > $o ).

tff('#skF_19',type,
    '#skF_19': $i ).

tff('#skF_7',type,
    '#skF_7': $i ).

tff(relation_empty_yielding,type,
    relation_empty_yielding: $i > $o ).

tff('#skF_10',type,
    '#skF_10': $i ).

tff('#skF_16',type,
    '#skF_16': $i ).

tff(ordinal,type,
    ordinal: $i > $o ).

tff(in,type,
    in: ( $i * $i ) > $o ).

tff('#skF_14',type,
    '#skF_14': $i ).

tff(subset,type,
    subset: ( $i * $i ) > $o ).

tff('#skF_6',type,
    '#skF_6': $i ).

tff('#skF_13',type,
    '#skF_13': $i ).

tff(empty,type,
    empty: $i > $o ).

tff('#skF_9',type,
    '#skF_9': $i ).

tff(empty_set,type,
    empty_set: $i ).

tff('#skF_8',type,
    '#skF_8': $i ).

tff('#skF_3',type,
    '#skF_3': $i > $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

tff(powerset,type,
    powerset: $i > $i ).

tff(ordinal_subset,type,
    ordinal_subset: ( $i * $i ) > $o ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

tff(succ,type,
    succ: $i > $i ).

tff('#skF_12',type,
    '#skF_12': $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i ) > $i ).

tff(f_280,negated_conjecture,
    ~ ! [A] :
        ( ordinal(A)
       => ! [B] :
            ( ordinal(B)
           => ( in(A,B)
            <=> ordinal_subset(succ(A),B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).

tff(f_154,axiom,
    ! [A] :
      ( ordinal(A)
     => ( ~ empty(succ(A))
        & epsilon_transitive(succ(A))
        & epsilon_connected(succ(A))
        & ordinal(succ(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).

tff(f_248,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
      <=> subset(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

tff(f_258,axiom,
    ! [A] : in(A,succ(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).

tff(f_104,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_41,axiom,
    ! [A] :
      ( ordinal(A)
     => ( epsilon_transitive(A)
        & epsilon_connected(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).

tff(f_97,axiom,
    ! [A] :
      ( epsilon_transitive(A)
    <=> ! [B] :
          ( in(B,A)
         => subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

tff(f_284,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

tff(f_270,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(f_290,axiom,
    ! [A,B,C] :
      ( ( in(A,B)
        & element(B,powerset(C)) )
     => element(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

tff(f_179,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_301,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_181,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_201,axiom,
    ? [A] :
      ( relation(A)
      & function(A)
      & one_to_one(A)
      & empty(A)
      & epsilon_transitive(A)
      & epsilon_connected(A)
      & ordinal(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).

tff(f_81,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
        | ordinal_subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).

tff(f_90,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_83,axiom,
    ! [A] : ( succ(A) = set_union2(A,singleton(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).

tff(f_320,axiom,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(C,B) )
     => subset(set_union2(A,C),B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).

tff(f_306,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

tff(f_264,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

tff(c_194,plain,
    ordinal('#skF_19'),
    inference(cnfTransformation,[status(thm)],[f_280]) ).

tff(c_88,plain,
    ! [A_35] :
      ( ordinal(succ(A_35))
      | ~ ordinal(A_35) ),
    inference(cnfTransformation,[status(thm)],[f_154]) ).

tff(c_196,plain,
    ( ~ ordinal_subset(succ('#skF_19'),'#skF_20')
    | ~ in('#skF_19','#skF_20') ),
    inference(cnfTransformation,[status(thm)],[f_280]) ).

tff(c_225,plain,
    ~ in('#skF_19','#skF_20'),
    inference(splitLeft,[status(thm)],[c_196]) ).

tff(c_192,plain,
    ordinal('#skF_20'),
    inference(cnfTransformation,[status(thm)],[f_280]) ).

tff(c_202,plain,
    ( in('#skF_19','#skF_20')
    | ordinal_subset(succ('#skF_19'),'#skF_20') ),
    inference(cnfTransformation,[status(thm)],[f_280]) ).

tff(c_226,plain,
    ordinal_subset(succ('#skF_19'),'#skF_20'),
    inference(splitLeft,[status(thm)],[c_202]) ).

tff(c_1047,plain,
    ! [A_160,B_161] :
      ( subset(A_160,B_161)
      | ~ ordinal_subset(A_160,B_161)
      | ~ ordinal(B_161)
      | ~ ordinal(A_160) ),
    inference(cnfTransformation,[status(thm)],[f_248]) ).

tff(c_184,plain,
    ! [A_46] : in(A_46,succ(A_46)),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_949,plain,
    ! [C_143,B_144,A_145] :
      ( in(C_143,B_144)
      | ~ in(C_143,A_145)
      | ~ subset(A_145,B_144) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_963,plain,
    ! [A_46,B_144] :
      ( in(A_46,B_144)
      | ~ subset(succ(A_46),B_144) ),
    inference(resolution,[status(thm)],[c_184,c_949]) ).

tff(c_7665,plain,
    ! [A_436,B_437] :
      ( in(A_436,B_437)
      | ~ ordinal_subset(succ(A_436),B_437)
      | ~ ordinal(B_437)
      | ~ ordinal(succ(A_436)) ),
    inference(resolution,[status(thm)],[c_1047,c_963]) ).

tff(c_7695,plain,
    ( in('#skF_19','#skF_20')
    | ~ ordinal('#skF_20')
    | ~ ordinal(succ('#skF_19')) ),
    inference(resolution,[status(thm)],[c_226,c_7665]) ).

tff(c_7710,plain,
    ( in('#skF_19','#skF_20')
    | ~ ordinal(succ('#skF_19')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_192,c_7695]) ).

tff(c_7711,plain,
    ~ ordinal(succ('#skF_19')),
    inference(negUnitSimplification,[status(thm)],[c_225,c_7710]) ).

tff(c_7717,plain,
    ~ ordinal('#skF_19'),
    inference(resolution,[status(thm)],[c_88,c_7711]) ).

tff(c_7725,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_194,c_7717]) ).

tff(c_7726,plain,
    in('#skF_19','#skF_20'),
    inference(splitRight,[status(thm)],[c_202]) ).

tff(c_7729,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7726,c_225]) ).

tff(c_7730,plain,
    ~ ordinal_subset(succ('#skF_19'),'#skF_20'),
    inference(splitRight,[status(thm)],[c_196]) ).

tff(c_7732,plain,
    ordinal_subset(succ('#skF_19'),'#skF_20'),
    inference(splitLeft,[status(thm)],[c_202]) ).

tff(c_7768,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7730,c_7732]) ).

tff(c_7770,plain,
    ~ ordinal_subset(succ('#skF_19'),'#skF_20'),
    inference(splitRight,[status(thm)],[c_202]) ).

tff(c_7731,plain,
    in('#skF_19','#skF_20'),
    inference(splitRight,[status(thm)],[c_196]) ).

tff(c_7775,plain,
    ! [A_448] :
      ( epsilon_transitive(A_448)
      | ~ ordinal(A_448) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_7800,plain,
    epsilon_transitive('#skF_20'),
    inference(resolution,[status(thm)],[c_192,c_7775]) ).

tff(c_44,plain,
    ! [B_22,A_19] :
      ( subset(B_22,A_19)
      | ~ in(B_22,A_19)
      | ~ epsilon_transitive(A_19) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_54,plain,
    ! [A_23,B_24] :
      ( in('#skF_4'(A_23,B_24),A_23)
      | subset(A_23,B_24) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_206,plain,
    ! [A_53,B_54] :
      ( element(A_53,powerset(B_54))
      | ~ subset(A_53,B_54) ),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_190,plain,
    ! [A_50,B_51] :
      ( in(A_50,B_51)
      | empty(B_51)
      | ~ element(A_50,B_51) ),
    inference(cnfTransformation,[status(thm)],[f_270]) ).

tff(c_8488,plain,
    ! [A_517,B_518] :
      ( ~ in('#skF_4'(A_517,B_518),B_518)
      | subset(A_517,B_518) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_10253,plain,
    ! [A_635,B_636] :
      ( subset(A_635,B_636)
      | empty(B_636)
      | ~ element('#skF_4'(A_635,B_636),B_636) ),
    inference(resolution,[status(thm)],[c_190,c_8488]) ).

tff(c_29811,plain,
    ! [A_1140,B_1141] :
      ( subset(A_1140,powerset(B_1141))
      | empty(powerset(B_1141))
      | ~ subset('#skF_4'(A_1140,powerset(B_1141)),B_1141) ),
    inference(resolution,[status(thm)],[c_206,c_10253]) ).

tff(c_847697,plain,
    ! [A_297482,A_297483] :
      ( subset(A_297482,powerset(A_297483))
      | empty(powerset(A_297483))
      | ~ in('#skF_4'(A_297482,powerset(A_297483)),A_297483)
      | ~ epsilon_transitive(A_297483) ),
    inference(resolution,[status(thm)],[c_44,c_29811]) ).

tff(c_848022,plain,
    ! [A_297510] :
      ( empty(powerset(A_297510))
      | ~ epsilon_transitive(A_297510)
      | subset(A_297510,powerset(A_297510)) ),
    inference(resolution,[status(thm)],[c_54,c_847697]) ).

tff(c_9011,plain,
    ! [A_561,C_562,B_563] :
      ( element(A_561,C_562)
      | ~ element(B_563,powerset(C_562))
      | ~ in(A_561,B_563) ),
    inference(cnfTransformation,[status(thm)],[f_290]) ).

tff(c_9125,plain,
    ! [A_574,B_575,A_576] :
      ( element(A_574,B_575)
      | ~ in(A_574,A_576)
      | ~ subset(A_576,B_575) ),
    inference(resolution,[status(thm)],[c_206,c_9011]) ).

tff(c_9149,plain,
    ! [B_575] :
      ( element('#skF_19',B_575)
      | ~ subset('#skF_20',B_575) ),
    inference(resolution,[status(thm)],[c_7731,c_9125]) ).

tff(c_848328,plain,
    ( element('#skF_19',powerset('#skF_20'))
    | empty(powerset('#skF_20'))
    | ~ epsilon_transitive('#skF_20') ),
    inference(resolution,[status(thm)],[c_848022,c_9149]) ).

tff(c_848521,plain,
    ( element('#skF_19',powerset('#skF_20'))
    | empty(powerset('#skF_20')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7800,c_848328]) ).

tff(c_848538,plain,
    empty(powerset('#skF_20')),
    inference(splitLeft,[status(thm)],[c_848521]) ).

tff(c_116,plain,
    empty('#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_179]) ).

tff(c_7856,plain,
    ! [A_457] :
      ( ( empty_set = A_457 )
      | ~ empty(A_457) ),
    inference(cnfTransformation,[status(thm)],[f_301]) ).

tff(c_7876,plain,
    empty_set = '#skF_8',
    inference(resolution,[status(thm)],[c_116,c_7856]) ).

tff(c_118,plain,
    empty('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_181]) ).

tff(c_7877,plain,
    empty_set = '#skF_9',
    inference(resolution,[status(thm)],[c_118,c_7856]) ).

tff(c_7904,plain,
    '#skF_9' = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_7876,c_7877]) ).

tff(c_132,plain,
    empty('#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_201]) ).

tff(c_7874,plain,
    empty_set = '#skF_11',
    inference(resolution,[status(thm)],[c_132,c_7856]) ).

tff(c_7899,plain,
    '#skF_11' = '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_7877,c_7874]) ).

tff(c_7952,plain,
    '#skF_11' = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_7904,c_7899]) ).

tff(c_212,plain,
    ! [A_61] :
      ( ( empty_set = A_61 )
      | ~ empty(A_61) ),
    inference(cnfTransformation,[status(thm)],[f_301]) ).

tff(c_7879,plain,
    ! [A_61] :
      ( ( A_61 = '#skF_11' )
      | ~ empty(A_61) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7874,c_212]) ).

tff(c_7991,plain,
    ! [A_61] :
      ( ( A_61 = '#skF_8' )
      | ~ empty(A_61) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7952,c_7879]) ).

tff(c_848554,plain,
    powerset('#skF_20') = '#skF_8',
    inference(resolution,[status(thm)],[c_848538,c_7991]) ).

tff(c_862910,plain,
    ! [A_314857] :
      ( element(A_314857,'#skF_8')
      | ~ subset(A_314857,'#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_848554,c_206]) ).

tff(c_863005,plain,
    ! [B_22] :
      ( element(B_22,'#skF_8')
      | ~ in(B_22,'#skF_20')
      | ~ epsilon_transitive('#skF_20') ),
    inference(resolution,[status(thm)],[c_44,c_862910]) ).

tff(c_864799,plain,
    ! [B_315331] :
      ( element(B_315331,'#skF_8')
      | ~ in(B_315331,'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_7800,c_863005]) ).

tff(c_864935,plain,
    element('#skF_19','#skF_8'),
    inference(resolution,[status(thm)],[c_7731,c_864799]) ).

tff(c_204,plain,
    ! [A_53,B_54] :
      ( subset(A_53,B_54)
      | ~ element(A_53,powerset(B_54)) ),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_848955,plain,
    ! [A_53] :
      ( subset(A_53,'#skF_20')
      | ~ element(A_53,'#skF_8') ),
    inference(superposition,[status(thm),theory(equality)],[c_848554,c_204]) ).

tff(c_9188,plain,
    ! [B_578,A_579] :
      ( ordinal_subset(B_578,A_579)
      | ordinal_subset(A_579,B_578)
      | ~ ordinal(B_578)
      | ~ ordinal(A_579) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_9199,plain,
    ( ordinal_subset('#skF_20',succ('#skF_19'))
    | ~ ordinal(succ('#skF_19'))
    | ~ ordinal('#skF_20') ),
    inference(resolution,[status(thm)],[c_9188,c_7770]) ).

tff(c_9219,plain,
    ( ordinal_subset('#skF_20',succ('#skF_19'))
    | ~ ordinal(succ('#skF_19')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_192,c_9199]) ).

tff(c_9229,plain,
    ~ ordinal(succ('#skF_19')),
    inference(splitLeft,[status(thm)],[c_9219]) ).

tff(c_9235,plain,
    ~ ordinal('#skF_19'),
    inference(resolution,[status(thm)],[c_88,c_9229]) ).

tff(c_9243,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_194,c_9235]) ).

tff(c_9245,plain,
    ordinal(succ('#skF_19')),
    inference(splitRight,[status(thm)],[c_9219]) ).

tff(c_8312,plain,
    ! [A_501,B_502] :
      ( in('#skF_4'(A_501,B_502),A_501)
      | subset(A_501,B_502) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_32,plain,
    ! [C_18,A_14] :
      ( ( C_18 = A_14 )
      | ~ in(C_18,singleton(A_14)) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_8325,plain,
    ! [A_14,B_502] :
      ( ( '#skF_4'(singleton(A_14),B_502) = A_14 )
      | subset(singleton(A_14),B_502) ),
    inference(resolution,[status(thm)],[c_8312,c_32]) ).

tff(c_30,plain,
    ! [A_13] : ( set_union2(A_13,singleton(A_13)) = succ(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_9316,plain,
    ! [A_584,C_585,B_586] :
      ( subset(set_union2(A_584,C_585),B_586)
      | ~ subset(C_585,B_586)
      | ~ subset(A_584,B_586) ),
    inference(cnfTransformation,[status(thm)],[f_320]) ).

tff(c_10356,plain,
    ! [A_638,B_639] :
      ( subset(succ(A_638),B_639)
      | ~ subset(singleton(A_638),B_639)
      | ~ subset(A_638,B_639) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_9316]) ).

tff(c_176,plain,
    ! [A_40,B_41] :
      ( ordinal_subset(A_40,B_41)
      | ~ subset(A_40,B_41)
      | ~ ordinal(B_41)
      | ~ ordinal(A_40) ),
    inference(cnfTransformation,[status(thm)],[f_248]) ).

tff(c_484378,plain,
    ! [A_164560,B_164561] :
      ( ordinal_subset(succ(A_164560),B_164561)
      | ~ ordinal(B_164561)
      | ~ ordinal(succ(A_164560))
      | ~ subset(singleton(A_164560),B_164561)
      | ~ subset(A_164560,B_164561) ),
    inference(resolution,[status(thm)],[c_10356,c_176]) ).

tff(c_921862,plain,
    ! [A_331336,B_331337] :
      ( ordinal_subset(succ(A_331336),B_331337)
      | ~ ordinal(B_331337)
      | ~ ordinal(succ(A_331336))
      | ~ subset(A_331336,B_331337)
      | ( '#skF_4'(singleton(A_331336),B_331337) = A_331336 ) ),
    inference(resolution,[status(thm)],[c_8325,c_484378]) ).

tff(c_921969,plain,
    ( ~ ordinal('#skF_20')
    | ~ ordinal(succ('#skF_19'))
    | ~ subset('#skF_19','#skF_20')
    | ( '#skF_4'(singleton('#skF_19'),'#skF_20') = '#skF_19' ) ),
    inference(resolution,[status(thm)],[c_921862,c_7770]) ).

tff(c_922135,plain,
    ( ~ subset('#skF_19','#skF_20')
    | ( '#skF_4'(singleton('#skF_19'),'#skF_20') = '#skF_19' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9245,c_192,c_921969]) ).

tff(c_922140,plain,
    ~ subset('#skF_19','#skF_20'),
    inference(splitLeft,[status(thm)],[c_922135]) ).

tff(c_922143,plain,
    ~ element('#skF_19','#skF_8'),
    inference(resolution,[status(thm)],[c_848955,c_922140]) ).

tff(c_922160,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_864935,c_922143]) ).

tff(c_922162,plain,
    subset('#skF_19','#skF_20'),
    inference(splitRight,[status(thm)],[c_922135]) ).

tff(c_7998,plain,
    ! [B_464,A_465] :
      ( ~ empty(B_464)
      | ~ in(A_465,B_464) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_8010,plain,
    ~ empty('#skF_20'),
    inference(resolution,[status(thm)],[c_7731,c_7998]) ).

tff(c_8019,plain,
    ! [A_469,B_470] :
      ( element(A_469,B_470)
      | ~ in(A_469,B_470) ),
    inference(cnfTransformation,[status(thm)],[f_264]) ).

tff(c_8031,plain,
    element('#skF_19','#skF_20'),
    inference(resolution,[status(thm)],[c_7731,c_8019]) ).

tff(c_922161,plain,
    '#skF_4'(singleton('#skF_19'),'#skF_20') = '#skF_19',
    inference(splitRight,[status(thm)],[c_922135]) ).

tff(c_8497,plain,
    ! [A_517,B_51] :
      ( subset(A_517,B_51)
      | empty(B_51)
      | ~ element('#skF_4'(A_517,B_51),B_51) ),
    inference(resolution,[status(thm)],[c_190,c_8488]) ).

tff(c_922681,plain,
    ( subset(singleton('#skF_19'),'#skF_20')
    | empty('#skF_20')
    | ~ element('#skF_19','#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_922161,c_8497]) ).

tff(c_922841,plain,
    ( subset(singleton('#skF_19'),'#skF_20')
    | empty('#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_8031,c_922681]) ).

tff(c_922842,plain,
    subset(singleton('#skF_19'),'#skF_20'),
    inference(negUnitSimplification,[status(thm)],[c_8010,c_922841]) ).

tff(c_10406,plain,
    ! [A_638,B_639] :
      ( ordinal_subset(succ(A_638),B_639)
      | ~ ordinal(B_639)
      | ~ ordinal(succ(A_638))
      | ~ subset(singleton(A_638),B_639)
      | ~ subset(A_638,B_639) ),
    inference(resolution,[status(thm)],[c_10356,c_176]) ).

tff(c_922933,plain,
    ( ordinal_subset(succ('#skF_19'),'#skF_20')
    | ~ ordinal('#skF_20')
    | ~ ordinal(succ('#skF_19'))
    | ~ subset('#skF_19','#skF_20') ),
    inference(resolution,[status(thm)],[c_922842,c_10406]) ).

tff(c_923044,plain,
    ordinal_subset(succ('#skF_19'),'#skF_20'),
    inference(demodulation,[status(thm),theory(equality)],[c_922162,c_9245,c_192,c_922933]) ).

tff(c_923046,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7770,c_923044]) ).

tff(c_923047,plain,
    element('#skF_19',powerset('#skF_20')),
    inference(splitRight,[status(thm)],[c_848521]) ).

tff(c_923083,plain,
    subset('#skF_19','#skF_20'),
    inference(resolution,[status(thm)],[c_923047,c_204]) ).

tff(c_995896,plain,
    ! [A_345697,B_345698] :
      ( ordinal_subset(succ(A_345697),B_345698)
      | ~ ordinal(B_345698)
      | ~ ordinal(succ(A_345697))
      | ~ subset(A_345697,B_345698)
      | ( '#skF_4'(singleton(A_345697),B_345698) = A_345697 ) ),
    inference(resolution,[status(thm)],[c_8325,c_484378]) ).

tff(c_995998,plain,
    ( ~ ordinal('#skF_20')
    | ~ ordinal(succ('#skF_19'))
    | ~ subset('#skF_19','#skF_20')
    | ( '#skF_4'(singleton('#skF_19'),'#skF_20') = '#skF_19' ) ),
    inference(resolution,[status(thm)],[c_995896,c_7770]) ).

tff(c_996133,plain,
    '#skF_4'(singleton('#skF_19'),'#skF_20') = '#skF_19',
    inference(demodulation,[status(thm),theory(equality)],[c_923083,c_9245,c_192,c_995998]) ).

tff(c_996198,plain,
    ( subset(singleton('#skF_19'),'#skF_20')
    | empty('#skF_20')
    | ~ element('#skF_19','#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_996133,c_8497]) ).

tff(c_996327,plain,
    ( subset(singleton('#skF_19'),'#skF_20')
    | empty('#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_8031,c_996198]) ).

tff(c_996328,plain,
    subset(singleton('#skF_19'),'#skF_20'),
    inference(negUnitSimplification,[status(thm)],[c_8010,c_996327]) ).

tff(c_996405,plain,
    ( ordinal_subset(succ('#skF_19'),'#skF_20')
    | ~ ordinal('#skF_20')
    | ~ ordinal(succ('#skF_19'))
    | ~ subset('#skF_19','#skF_20') ),
    inference(resolution,[status(thm)],[c_996328,c_10406]) ).

tff(c_996506,plain,
    ordinal_subset(succ('#skF_19'),'#skF_20'),
    inference(demodulation,[status(thm),theory(equality)],[c_923083,c_9245,c_192,c_996405]) ).

tff(c_996508,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7770,c_996506]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU236+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 11:32:08 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 283.89/257.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 283.97/257.14  
% 283.97/257.14  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 283.97/257.18  
% 283.97/257.18  Inference rules
% 283.97/257.18  ----------------------
% 283.97/257.18  #Ref     : 0
% 283.97/257.18  #Sup     : 200053
% 283.97/257.18  #Fact    : 30
% 283.97/257.18  #Define  : 0
% 283.97/257.18  #Split   : 559
% 283.97/257.18  #Chain   : 0
% 283.97/257.18  #Close   : 0
% 283.97/257.18  
% 283.97/257.18  Ordering : KBO
% 283.97/257.18  
% 283.97/257.18  Simplification rules
% 283.97/257.18  ----------------------
% 283.97/257.18  #Subsume      : 79659
% 283.97/257.18  #Demod        : 74508
% 283.97/257.18  #Tautology    : 25594
% 283.97/257.18  #SimpNegUnit  : 30445
% 283.97/257.18  #BackRed      : 1497
% 283.97/257.18  
% 283.97/257.18  #Partial instantiations: 651050
% 283.97/257.18  #Strategies tried      : 1
% 283.97/257.18  
% 283.97/257.18  Timing (in seconds)
% 283.97/257.18  ----------------------
% 283.97/257.18  Preprocessing        : 0.60
% 283.97/257.18  Parsing              : 0.31
% 283.97/257.18  CNF conversion       : 0.05
% 283.97/257.18  Main loop            : 255.49
% 283.97/257.18  Inferencing          : 27.53
% 283.97/257.18  Reduction            : 117.04
% 283.97/257.18  Demodulation         : 72.63
% 283.97/257.18  BG Simplification    : 0.97
% 283.97/257.18  Subsumption          : 94.83
% 283.97/257.18  Abstraction          : 1.72
% 283.97/257.18  MUC search           : 0.00
% 283.97/257.18  Cooper               : 0.00
% 283.97/257.18  Total                : 256.17
% 283.97/257.18  Index Insertion      : 0.00
% 283.97/257.18  Index Deletion       : 0.00
% 283.97/257.18  Index Matching       : 0.00
% 283.97/257.18  BG Taut test         : 0.00
%------------------------------------------------------------------------------