TSTP Solution File: SEU235+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n013.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 22.61s 10.70s
% Output   : CNFRefutation 22.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  296 (  83 unt;  32 typ;   0 def)
%            Number of atoms       :  669 (  81 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  795 ( 390   ~; 357   |;  27   &)
%                                         (   3 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  17   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  15 con; 0-2 aty)
%            Number of variables   :  245 (; 240   !;   5   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff('#skF_1',type,
    '#skF_1': $i > $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_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('#skF_18',type,
    '#skF_18': ( $i * $i ) > $i ).

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

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

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

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

tff('#skF_3',type,
    '#skF_3': $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_4',type,
    '#skF_4': $i ).

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

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

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

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

tff(f_150,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_273,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_130,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_128,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_252,negated_conjecture,
    ~ ! [A,B] :
        ( ordinal(B)
       => ~ ( subset(A,B)
            & ( A != empty_set )
            & ! [C] :
                ( ordinal(C)
               => ~ ( in(C,A)
                    & ! [D] :
                        ( ordinal(D)
                       => ( in(D,A)
                         => ordinal_subset(C,D) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).

tff(f_90,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

tff(f_230,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(f_269,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

tff(f_256,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

tff(f_191,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_71,axiom,
    ! [A] :
      ( empty(A)
     => ( epsilon_transitive(A)
        & epsilon_connected(A)
        & ordinal(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).

tff(f_224,axiom,
    ! [A] :
      ( ordinal(A)
     => ! [B] :
          ( ordinal(B)
         => ~ ( ~ in(A,B)
              & ( A != B )
              & ~ in(B,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).

tff(f_86,axiom,
    ! [A] :
      ( epsilon_transitive(A)
    <=> ! [B] :
          ( in(B,A)
         => subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

tff(f_262,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_209,axiom,
    ! [A,B] :
      ( ordinal(B)
     => ( in(A,B)
       => ordinal(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).

tff(f_63,axiom,
    ! [A] :
      ( ( epsilon_transitive(A)
        & epsilon_connected(A) )
     => ordinal(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).

tff(f_199,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_291,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & ! [C] :
            ~ ( in(C,B)
              & ! [D] :
                  ~ ( in(D,B)
                    & in(D,C) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).

tff(f_197,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ordinal_subset(A,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).

tff(f_124,axiom,
    ? [A] :
      ( epsilon_transitive(A)
      & epsilon_connected(A)
      & ordinal(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).

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

tff(f_203,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

tff(f_278,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

tff(c_98,plain,
    empty('#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_220,plain,
    ! [A_62] :
      ( ( empty_set = A_62 )
      | ~ empty(A_62) ),
    inference(cnfTransformation,[status(thm)],[f_273]) ).

tff(c_240,plain,
    empty_set = '#skF_8',
    inference(resolution,[status(thm)],[c_98,c_220]) ).

tff(c_84,plain,
    empty('#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_130]) ).

tff(c_237,plain,
    empty_set = '#skF_6',
    inference(resolution,[status(thm)],[c_84,c_220]) ).

tff(c_263,plain,
    '#skF_6' = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_237]) ).

tff(c_82,plain,
    empty('#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_236,plain,
    empty_set = '#skF_5',
    inference(resolution,[status(thm)],[c_82,c_220]) ).

tff(c_258,plain,
    '#skF_5' = '#skF_6',
    inference(demodulation,[status(thm),theory(equality)],[c_237,c_236]) ).

tff(c_152,plain,
    empty_set != '#skF_15',
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_250,plain,
    '#skF_15' != '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_152]) ).

tff(c_296,plain,
    '#skF_15' != '#skF_6',
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_250]) ).

tff(c_298,plain,
    '#skF_15' != '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_263,c_296]) ).

tff(c_40,plain,
    ! [A_15] : element('#skF_2'(A_15),A_15),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_92,plain,
    ordinal('#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_150,plain,
    ! [A_30,B_31] :
      ( in(A_30,B_31)
      | empty(B_31)
      | ~ element(A_30,B_31) ),
    inference(cnfTransformation,[status(thm)],[f_230]) ).

tff(c_560,plain,
    ! [C_112,B_113,A_114] :
      ( ~ empty(C_112)
      | ~ element(B_113,powerset(C_112))
      | ~ in(A_114,B_113) ),
    inference(cnfTransformation,[status(thm)],[f_269]) ).

tff(c_52419,plain,
    ! [C_1209,A_1210] :
      ( ~ empty(C_1209)
      | ~ in(A_1210,'#skF_2'(powerset(C_1209))) ),
    inference(resolution,[status(thm)],[c_40,c_560]) ).

tff(c_57149,plain,
    ! [C_1476,A_1477] :
      ( ~ empty(C_1476)
      | empty('#skF_2'(powerset(C_1476)))
      | ~ element(A_1477,'#skF_2'(powerset(C_1476))) ),
    inference(resolution,[status(thm)],[c_150,c_52419]) ).

tff(c_57189,plain,
    ! [C_1478] :
      ( ~ empty(C_1478)
      | empty('#skF_2'(powerset(C_1478))) ),
    inference(resolution,[status(thm)],[c_40,c_57149]) ).

tff(c_300,plain,
    '#skF_5' = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_263,c_258]) ).

tff(c_172,plain,
    ! [A_45] :
      ( ( empty_set = A_45 )
      | ~ empty(A_45) ),
    inference(cnfTransformation,[status(thm)],[f_273]) ).

tff(c_242,plain,
    ! [A_45] :
      ( ( A_45 = '#skF_5' )
      | ~ empty(A_45) ),
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_172]) ).

tff(c_353,plain,
    ! [A_45] :
      ( ( A_45 = '#skF_8' )
      | ~ empty(A_45) ),
    inference(demodulation,[status(thm),theory(equality)],[c_300,c_242]) ).

tff(c_57197,plain,
    ! [C_1479] :
      ( ( '#skF_2'(powerset(C_1479)) = '#skF_8' )
      | ~ empty(C_1479) ),
    inference(resolution,[status(thm)],[c_57189,c_353]) ).

tff(c_403,plain,
    ! [A_87,B_88] :
      ( subset(A_87,B_88)
      | ~ element(A_87,powerset(B_88)) ),
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_413,plain,
    ! [B_88] : subset('#skF_2'(powerset(B_88)),B_88),
    inference(resolution,[status(thm)],[c_40,c_403]) ).

tff(c_57251,plain,
    ! [C_1480] :
      ( subset('#skF_8',C_1480)
      | ~ empty(C_1480) ),
    inference(superposition,[status(thm),theory(equality)],[c_57197,c_413]) ).

tff(c_136,plain,
    ! [A_17,B_18] :
      ( ordinal_subset(A_17,B_18)
      | ~ subset(A_17,B_18)
      | ~ ordinal(B_18)
      | ~ ordinal(A_17) ),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_57265,plain,
    ! [C_1480] :
      ( ordinal_subset('#skF_8',C_1480)
      | ~ ordinal(C_1480)
      | ~ ordinal('#skF_8')
      | ~ empty(C_1480) ),
    inference(resolution,[status(thm)],[c_57251,c_136]) ).

tff(c_57276,plain,
    ! [C_1480] :
      ( ordinal_subset('#skF_8',C_1480)
      | ~ ordinal(C_1480)
      | ~ empty(C_1480) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_57265]) ).

tff(c_20,plain,
    ! [A_8] :
      ( ordinal(A_8)
      | ~ empty(A_8) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_156,plain,
    ordinal('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_154,plain,
    subset('#skF_15','#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_576,plain,
    ! [A_115,B_116] :
      ( ordinal_subset(A_115,B_116)
      | ~ subset(A_115,B_116)
      | ~ ordinal(B_116)
      | ~ ordinal(A_115) ),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_591,plain,
    ( ordinal_subset('#skF_15','#skF_16')
    | ~ ordinal('#skF_16')
    | ~ ordinal('#skF_15') ),
    inference(resolution,[status(thm)],[c_154,c_576]) ).

tff(c_598,plain,
    ( ordinal_subset('#skF_15','#skF_16')
    | ~ ordinal('#skF_15') ),
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_591]) ).

tff(c_599,plain,
    ~ ordinal('#skF_15'),
    inference(splitLeft,[status(thm)],[c_598]) ).

tff(c_607,plain,
    ~ empty('#skF_15'),
    inference(resolution,[status(thm)],[c_20,c_599]) ).

tff(c_162,plain,
    ! [C_35] :
      ( ordinal('#skF_17'(C_35))
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_148,plain,
    ! [B_29,A_27] :
      ( in(B_29,A_27)
      | ( B_29 = A_27 )
      | in(A_27,B_29)
      | ~ ordinal(B_29)
      | ~ ordinal(A_27) ),
    inference(cnfTransformation,[status(thm)],[f_224]) ).

tff(c_57277,plain,
    ! [C_1481] :
      ( element('#skF_8',powerset(C_1481))
      | ~ empty(C_1481) ),
    inference(superposition,[status(thm),theory(equality)],[c_57197,c_40]) ).

tff(c_170,plain,
    ! [C_44,B_43,A_42] :
      ( ~ empty(C_44)
      | ~ element(B_43,powerset(C_44))
      | ~ in(A_42,B_43) ),
    inference(cnfTransformation,[status(thm)],[f_269]) ).

tff(c_57295,plain,
    ! [A_42,C_1481] :
      ( ~ in(A_42,'#skF_8')
      | ~ empty(C_1481) ),
    inference(resolution,[status(thm)],[c_57277,c_170]) ).

tff(c_57323,plain,
    ! [C_1481] : ~ empty(C_1481),
    inference(splitLeft,[status(thm)],[c_57295]) ).

tff(c_57340,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_57323,c_98]) ).

tff(c_57342,plain,
    ! [A_1484] : ~ in(A_1484,'#skF_8'),
    inference(splitRight,[status(thm)],[c_57295]) ).

tff(c_57358,plain,
    ! [A_27] :
      ( in('#skF_8',A_27)
      | ( A_27 = '#skF_8' )
      | ~ ordinal('#skF_8')
      | ~ ordinal(A_27) ),
    inference(resolution,[status(thm)],[c_148,c_57342]) ).

tff(c_57396,plain,
    ! [A_1486] :
      ( in('#skF_8',A_1486)
      | ( A_1486 = '#skF_8' )
      | ~ ordinal(A_1486) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_57358]) ).

tff(c_28,plain,
    ! [B_14,A_11] :
      ( subset(B_14,A_11)
      | ~ in(B_14,A_11)
      | ~ epsilon_transitive(A_11) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_57081,plain,
    ! [B_1469,A_1470] :
      ( ordinal_subset(B_1469,A_1470)
      | ~ ordinal(A_1470)
      | ~ ordinal(B_1469)
      | ~ in(B_1469,A_1470)
      | ~ epsilon_transitive(A_1470) ),
    inference(resolution,[status(thm)],[c_28,c_576]) ).

tff(c_158,plain,
    ! [C_35] :
      ( ~ ordinal_subset(C_35,'#skF_17'(C_35))
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_57086,plain,
    ! [B_1469] :
      ( ~ in(B_1469,'#skF_15')
      | ~ ordinal('#skF_17'(B_1469))
      | ~ ordinal(B_1469)
      | ~ in(B_1469,'#skF_17'(B_1469))
      | ~ epsilon_transitive('#skF_17'(B_1469)) ),
    inference(resolution,[status(thm)],[c_57081,c_158]) ).

tff(c_57404,plain,
    ( ~ in('#skF_8','#skF_15')
    | ~ ordinal('#skF_8')
    | ~ epsilon_transitive('#skF_17'('#skF_8'))
    | ( '#skF_17'('#skF_8') = '#skF_8' )
    | ~ ordinal('#skF_17'('#skF_8')) ),
    inference(resolution,[status(thm)],[c_57396,c_57086]) ).

tff(c_57464,plain,
    ( ~ in('#skF_8','#skF_15')
    | ~ epsilon_transitive('#skF_17'('#skF_8'))
    | ( '#skF_17'('#skF_8') = '#skF_8' )
    | ~ ordinal('#skF_17'('#skF_8')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_57404]) ).

tff(c_59412,plain,
    ~ ordinal('#skF_17'('#skF_8')),
    inference(splitLeft,[status(thm)],[c_57464]) ).

tff(c_59421,plain,
    ( ~ in('#skF_8','#skF_15')
    | ~ ordinal('#skF_8') ),
    inference(resolution,[status(thm)],[c_162,c_59412]) ).

tff(c_59426,plain,
    ~ in('#skF_8','#skF_15'),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_59421]) ).

tff(c_59440,plain,
    ( empty('#skF_15')
    | ~ element('#skF_8','#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_59426]) ).

tff(c_59453,plain,
    ~ element('#skF_8','#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_607,c_59440]) ).

tff(c_166,plain,
    ! [A_37,B_38] :
      ( element(A_37,powerset(B_38))
      | ~ subset(A_37,B_38) ),
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_52462,plain,
    ! [B_1216,A_1217,A_1218] :
      ( ~ empty(B_1216)
      | ~ in(A_1217,A_1218)
      | ~ subset(A_1218,B_1216) ),
    inference(resolution,[status(thm)],[c_166,c_560]) ).

tff(c_52700,plain,
    ! [B_1253,B_1254,A_1255] :
      ( ~ empty(B_1253)
      | ~ subset(B_1254,B_1253)
      | empty(B_1254)
      | ~ element(A_1255,B_1254) ),
    inference(resolution,[status(thm)],[c_150,c_52462]) ).

tff(c_52714,plain,
    ! [A_1255] :
      ( ~ empty('#skF_16')
      | empty('#skF_15')
      | ~ element(A_1255,'#skF_15') ),
    inference(resolution,[status(thm)],[c_154,c_52700]) ).

tff(c_52723,plain,
    ! [A_1255] :
      ( ~ empty('#skF_16')
      | ~ element(A_1255,'#skF_15') ),
    inference(negUnitSimplification,[status(thm)],[c_607,c_52714]) ).

tff(c_52724,plain,
    ~ empty('#skF_16'),
    inference(splitLeft,[status(thm)],[c_52723]) ).

tff(c_52403,plain,
    ! [A_1206,C_1207,B_1208] :
      ( element(A_1206,C_1207)
      | ~ element(B_1208,powerset(C_1207))
      | ~ in(A_1206,B_1208) ),
    inference(cnfTransformation,[status(thm)],[f_262]) ).

tff(c_52562,plain,
    ! [A_1230,B_1231,A_1232] :
      ( element(A_1230,B_1231)
      | ~ in(A_1230,A_1232)
      | ~ subset(A_1232,B_1231) ),
    inference(resolution,[status(thm)],[c_166,c_52403]) ).

tff(c_56805,plain,
    ! [A_1452,B_1453,B_1454] :
      ( element(A_1452,B_1453)
      | ~ subset(B_1454,B_1453)
      | empty(B_1454)
      | ~ element(A_1452,B_1454) ),
    inference(resolution,[status(thm)],[c_150,c_52562]) ).

tff(c_56823,plain,
    ! [A_1452] :
      ( element(A_1452,'#skF_16')
      | empty('#skF_15')
      | ~ element(A_1452,'#skF_15') ),
    inference(resolution,[status(thm)],[c_154,c_56805]) ).

tff(c_56835,plain,
    ! [A_1455] :
      ( element(A_1455,'#skF_16')
      | ~ element(A_1455,'#skF_15') ),
    inference(negUnitSimplification,[status(thm)],[c_607,c_56823]) ).

tff(c_56877,plain,
    element('#skF_2'('#skF_15'),'#skF_16'),
    inference(resolution,[status(thm)],[c_40,c_56835]) ).

tff(c_448,plain,
    ! [A_98,B_99] :
      ( in(A_98,B_99)
      | empty(B_99)
      | ~ element(A_98,B_99) ),
    inference(cnfTransformation,[status(thm)],[f_230]) ).

tff(c_146,plain,
    ! [A_25,B_26] :
      ( ordinal(A_25)
      | ~ in(A_25,B_26)
      | ~ ordinal(B_26) ),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_467,plain,
    ! [A_98,B_99] :
      ( ordinal(A_98)
      | ~ ordinal(B_99)
      | empty(B_99)
      | ~ element(A_98,B_99) ),
    inference(resolution,[status(thm)],[c_448,c_146]) ).

tff(c_56960,plain,
    ( ordinal('#skF_2'('#skF_15'))
    | ~ ordinal('#skF_16')
    | empty('#skF_16') ),
    inference(resolution,[status(thm)],[c_56877,c_467]) ).

tff(c_56966,plain,
    ( ordinal('#skF_2'('#skF_15'))
    | empty('#skF_16') ),
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_56960]) ).

tff(c_56967,plain,
    ordinal('#skF_2'('#skF_15')),
    inference(negUnitSimplification,[status(thm)],[c_52724,c_56966]) ).

tff(c_18,plain,
    ! [A_7] :
      ( ordinal(A_7)
      | ~ epsilon_connected(A_7)
      | ~ epsilon_transitive(A_7) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_606,plain,
    ( ~ epsilon_connected('#skF_15')
    | ~ epsilon_transitive('#skF_15') ),
    inference(resolution,[status(thm)],[c_18,c_599]) ).

tff(c_608,plain,
    ~ epsilon_transitive('#skF_15'),
    inference(splitLeft,[status(thm)],[c_606]) ).

tff(c_32,plain,
    ! [A_11] :
      ( in('#skF_1'(A_11),A_11)
      | epsilon_transitive(A_11) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_142,plain,
    ! [A_21] : subset(A_21,A_21),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_630,plain,
    ! [B_120,A_121,A_122] :
      ( ~ empty(B_120)
      | ~ in(A_121,A_122)
      | ~ subset(A_122,B_120) ),
    inference(resolution,[status(thm)],[c_166,c_560]) ).

tff(c_643,plain,
    ! [B_123,A_124] :
      ( ~ empty(B_123)
      | ~ subset(A_124,B_123)
      | epsilon_transitive(A_124) ),
    inference(resolution,[status(thm)],[c_32,c_630]) ).

tff(c_658,plain,
    ( ~ empty('#skF_16')
    | epsilon_transitive('#skF_15') ),
    inference(resolution,[status(thm)],[c_154,c_643]) ).

tff(c_665,plain,
    ~ empty('#skF_16'),
    inference(negUnitSimplification,[status(thm)],[c_608,c_658]) ).

tff(c_178,plain,
    ! [A_48,B_49] :
      ( in('#skF_18'(A_48,B_49),B_49)
      | ~ in(A_48,B_49) ),
    inference(cnfTransformation,[status(thm)],[f_291]) ).

tff(c_666,plain,
    ! [A_125,C_126,B_127] :
      ( element(A_125,C_126)
      | ~ element(B_127,powerset(C_126))
      | ~ in(A_125,B_127) ),
    inference(cnfTransformation,[status(thm)],[f_262]) ).

tff(c_754,plain,
    ! [A_139,B_140,A_141] :
      ( element(A_139,B_140)
      | ~ in(A_139,A_141)
      | ~ subset(A_141,B_140) ),
    inference(resolution,[status(thm)],[c_166,c_666]) ).

tff(c_763,plain,
    ! [A_48,B_49,B_140] :
      ( element('#skF_18'(A_48,B_49),B_140)
      | ~ subset(B_49,B_140)
      | ~ in(A_48,B_49) ),
    inference(resolution,[status(thm)],[c_178,c_754]) ).

tff(c_4614,plain,
    ! [A_340,B_341,B_342] :
      ( element(A_340,B_341)
      | ~ subset(B_342,B_341)
      | empty(B_342)
      | ~ element(A_340,B_342) ),
    inference(resolution,[status(thm)],[c_150,c_754]) ).

tff(c_4632,plain,
    ! [A_340] :
      ( element(A_340,'#skF_16')
      | empty('#skF_15')
      | ~ element(A_340,'#skF_15') ),
    inference(resolution,[status(thm)],[c_154,c_4614]) ).

tff(c_4644,plain,
    ! [A_343] :
      ( element(A_343,'#skF_16')
      | ~ element(A_343,'#skF_15') ),
    inference(negUnitSimplification,[status(thm)],[c_607,c_4632]) ).

tff(c_6225,plain,
    ! [A_411,B_412] :
      ( element('#skF_18'(A_411,B_412),'#skF_16')
      | ~ subset(B_412,'#skF_15')
      | ~ in(A_411,B_412) ),
    inference(resolution,[status(thm)],[c_763,c_4644]) ).

tff(c_6230,plain,
    ! [A_411,B_412] :
      ( ordinal('#skF_18'(A_411,B_412))
      | ~ ordinal('#skF_16')
      | empty('#skF_16')
      | ~ subset(B_412,'#skF_15')
      | ~ in(A_411,B_412) ),
    inference(resolution,[status(thm)],[c_6225,c_467]) ).

tff(c_6236,plain,
    ! [A_411,B_412] :
      ( ordinal('#skF_18'(A_411,B_412))
      | empty('#skF_16')
      | ~ subset(B_412,'#skF_15')
      | ~ in(A_411,B_412) ),
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_6230]) ).

tff(c_6237,plain,
    ! [A_411,B_412] :
      ( ordinal('#skF_18'(A_411,B_412))
      | ~ subset(B_412,'#skF_15')
      | ~ in(A_411,B_412) ),
    inference(negUnitSimplification,[status(thm)],[c_665,c_6236]) ).

tff(c_140,plain,
    ! [A_19,B_20] :
      ( ordinal_subset(A_19,A_19)
      | ~ ordinal(B_20)
      | ~ ordinal(A_19) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_429,plain,
    ! [B_20] : ~ ordinal(B_20),
    inference(splitLeft,[status(thm)],[c_140]) ).

tff(c_74,plain,
    ordinal('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_124]) ).

tff(c_438,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_429,c_74]) ).

tff(c_439,plain,
    ! [A_19] :
      ( ordinal_subset(A_19,A_19)
      | ~ ordinal(A_19) ),
    inference(splitRight,[status(thm)],[c_140]) ).

tff(c_318,plain,
    ! [A_66] :
      ( epsilon_transitive(A_66)
      | ~ ordinal(A_66) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_340,plain,
    ! [C_35] :
      ( epsilon_transitive('#skF_17'(C_35))
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(resolution,[status(thm)],[c_162,c_318]) ).

tff(c_160,plain,
    ! [C_35] :
      ( in('#skF_17'(C_35),'#skF_15')
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_1058,plain,
    ! [B_177,A_178] :
      ( in(B_177,A_178)
      | ( B_177 = A_178 )
      | in(A_178,B_177)
      | ~ ordinal(B_177)
      | ~ ordinal(A_178) ),
    inference(cnfTransformation,[status(thm)],[f_224]) ).

tff(c_176,plain,
    ! [D_54,A_48,B_49] :
      ( ~ in(D_54,'#skF_18'(A_48,B_49))
      | ~ in(D_54,B_49)
      | ~ in(A_48,B_49) ),
    inference(cnfTransformation,[status(thm)],[f_291]) ).

tff(c_5438,plain,
    ! [B_383,B_384,A_385] :
      ( ~ in(B_383,B_384)
      | ~ in(A_385,B_384)
      | ( B_383 = '#skF_18'(A_385,B_384) )
      | in('#skF_18'(A_385,B_384),B_383)
      | ~ ordinal(B_383)
      | ~ ordinal('#skF_18'(A_385,B_384)) ),
    inference(resolution,[status(thm)],[c_1058,c_176]) ).

tff(c_4738,plain,
    ! [B_345,A_346] :
      ( ordinal_subset(B_345,A_346)
      | ~ ordinal(A_346)
      | ~ ordinal(B_345)
      | ~ in(B_345,A_346)
      | ~ epsilon_transitive(A_346) ),
    inference(resolution,[status(thm)],[c_28,c_576]) ).

tff(c_4743,plain,
    ! [B_345] :
      ( ~ in(B_345,'#skF_15')
      | ~ ordinal('#skF_17'(B_345))
      | ~ ordinal(B_345)
      | ~ in(B_345,'#skF_17'(B_345))
      | ~ epsilon_transitive('#skF_17'(B_345)) ),
    inference(resolution,[status(thm)],[c_4738,c_158]) ).

tff(c_41395,plain,
    ! [A_1111,B_1112] :
      ( ~ in('#skF_18'(A_1111,B_1112),'#skF_15')
      | ~ epsilon_transitive('#skF_17'('#skF_18'(A_1111,B_1112)))
      | ~ in('#skF_17'('#skF_18'(A_1111,B_1112)),B_1112)
      | ~ in(A_1111,B_1112)
      | ( '#skF_17'('#skF_18'(A_1111,B_1112)) = '#skF_18'(A_1111,B_1112) )
      | ~ ordinal('#skF_17'('#skF_18'(A_1111,B_1112)))
      | ~ ordinal('#skF_18'(A_1111,B_1112)) ),
    inference(resolution,[status(thm)],[c_5438,c_4743]) ).

tff(c_42399,plain,
    ! [A_1121] :
      ( ~ epsilon_transitive('#skF_17'('#skF_18'(A_1121,'#skF_15')))
      | ~ in(A_1121,'#skF_15')
      | ( '#skF_17'('#skF_18'(A_1121,'#skF_15')) = '#skF_18'(A_1121,'#skF_15') )
      | ~ ordinal('#skF_17'('#skF_18'(A_1121,'#skF_15')))
      | ~ in('#skF_18'(A_1121,'#skF_15'),'#skF_15')
      | ~ ordinal('#skF_18'(A_1121,'#skF_15')) ),
    inference(resolution,[status(thm)],[c_160,c_41395]) ).

tff(c_42751,plain,
    ! [A_1127] :
      ( ~ epsilon_transitive('#skF_17'('#skF_18'(A_1127,'#skF_15')))
      | ~ in(A_1127,'#skF_15')
      | ( '#skF_17'('#skF_18'(A_1127,'#skF_15')) = '#skF_18'(A_1127,'#skF_15') )
      | ~ in('#skF_18'(A_1127,'#skF_15'),'#skF_15')
      | ~ ordinal('#skF_18'(A_1127,'#skF_15')) ),
    inference(resolution,[status(thm)],[c_162,c_42399]) ).

tff(c_43874,plain,
    ! [A_1135] :
      ( ~ in(A_1135,'#skF_15')
      | ( '#skF_17'('#skF_18'(A_1135,'#skF_15')) = '#skF_18'(A_1135,'#skF_15') )
      | ~ in('#skF_18'(A_1135,'#skF_15'),'#skF_15')
      | ~ ordinal('#skF_18'(A_1135,'#skF_15')) ),
    inference(resolution,[status(thm)],[c_340,c_42751]) ).

tff(c_51080,plain,
    ! [A_1192] :
      ( ( '#skF_17'('#skF_18'(A_1192,'#skF_15')) = '#skF_18'(A_1192,'#skF_15') )
      | ~ ordinal('#skF_18'(A_1192,'#skF_15'))
      | ~ in(A_1192,'#skF_15') ),
    inference(resolution,[status(thm)],[c_178,c_43874]) ).

tff(c_51084,plain,
    ! [A_411] :
      ( ( '#skF_17'('#skF_18'(A_411,'#skF_15')) = '#skF_18'(A_411,'#skF_15') )
      | ~ subset('#skF_15','#skF_15')
      | ~ in(A_411,'#skF_15') ),
    inference(resolution,[status(thm)],[c_6237,c_51080]) ).

tff(c_51299,plain,
    ! [A_1196] :
      ( ( '#skF_17'('#skF_18'(A_1196,'#skF_15')) = '#skF_18'(A_1196,'#skF_15') )
      | ~ in(A_1196,'#skF_15') ),
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_51084]) ).

tff(c_51444,plain,
    ! [A_1200] :
      ( ~ ordinal_subset('#skF_18'(A_1200,'#skF_15'),'#skF_18'(A_1200,'#skF_15'))
      | ~ in('#skF_18'(A_1200,'#skF_15'),'#skF_15')
      | ~ ordinal('#skF_18'(A_1200,'#skF_15'))
      | ~ in(A_1200,'#skF_15') ),
    inference(superposition,[status(thm),theory(equality)],[c_51299,c_158]) ).

tff(c_52250,plain,
    ! [A_1203] :
      ( ~ in('#skF_18'(A_1203,'#skF_15'),'#skF_15')
      | ~ in(A_1203,'#skF_15')
      | ~ ordinal('#skF_18'(A_1203,'#skF_15')) ),
    inference(resolution,[status(thm)],[c_439,c_51444]) ).

tff(c_52284,plain,
    ! [A_1204] :
      ( ~ ordinal('#skF_18'(A_1204,'#skF_15'))
      | ~ in(A_1204,'#skF_15') ),
    inference(resolution,[status(thm)],[c_178,c_52250]) ).

tff(c_52288,plain,
    ! [A_411] :
      ( ~ subset('#skF_15','#skF_15')
      | ~ in(A_411,'#skF_15') ),
    inference(resolution,[status(thm)],[c_6237,c_52284]) ).

tff(c_52310,plain,
    ! [A_1205] : ~ in(A_1205,'#skF_15'),
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_52288]) ).

tff(c_52374,plain,
    epsilon_transitive('#skF_15'),
    inference(resolution,[status(thm)],[c_32,c_52310]) ).

tff(c_52396,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_608,c_52374]) ).

tff(c_52398,plain,
    epsilon_transitive('#skF_15'),
    inference(splitRight,[status(thm)],[c_606]) ).

tff(c_52416,plain,
    ! [A_1206,B_38,A_37] :
      ( element(A_1206,B_38)
      | ~ in(A_1206,A_37)
      | ~ subset(A_37,B_38) ),
    inference(resolution,[status(thm)],[c_166,c_52403]) ).

tff(c_57854,plain,
    ! [B_1506,A_1507] :
      ( element('#skF_8',B_1506)
      | ~ subset(A_1507,B_1506)
      | ( A_1507 = '#skF_8' )
      | ~ ordinal(A_1507) ),
    inference(resolution,[status(thm)],[c_57396,c_52416]) ).

tff(c_59542,plain,
    ! [A_1581,B_1582] :
      ( element('#skF_8',A_1581)
      | ( B_1582 = '#skF_8' )
      | ~ ordinal(B_1582)
      | ~ in(B_1582,A_1581)
      | ~ epsilon_transitive(A_1581) ),
    inference(resolution,[status(thm)],[c_28,c_57854]) ).

tff(c_59572,plain,
    ! [C_35] :
      ( element('#skF_8','#skF_15')
      | ( '#skF_17'(C_35) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_35))
      | ~ epsilon_transitive('#skF_15')
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(resolution,[status(thm)],[c_160,c_59542]) ).

tff(c_59586,plain,
    ! [C_35] :
      ( element('#skF_8','#skF_15')
      | ( '#skF_17'(C_35) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_35))
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_52398,c_59572]) ).

tff(c_59588,plain,
    ! [C_1583] :
      ( ( '#skF_17'(C_1583) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_1583))
      | ~ in(C_1583,'#skF_15')
      | ~ ordinal(C_1583) ),
    inference(negUnitSimplification,[status(thm)],[c_59453,c_59586]) ).

tff(c_59601,plain,
    ! [C_1584] :
      ( ( '#skF_17'(C_1584) = '#skF_8' )
      | ~ in(C_1584,'#skF_15')
      | ~ ordinal(C_1584) ),
    inference(resolution,[status(thm)],[c_162,c_59588]) ).

tff(c_59633,plain,
    ! [A_30] :
      ( ( '#skF_17'(A_30) = '#skF_8' )
      | ~ ordinal(A_30)
      | empty('#skF_15')
      | ~ element(A_30,'#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_59601]) ).

tff(c_59657,plain,
    ! [A_1585] :
      ( ( '#skF_17'(A_1585) = '#skF_8' )
      | ~ ordinal(A_1585)
      | ~ element(A_1585,'#skF_15') ),
    inference(negUnitSimplification,[status(thm)],[c_607,c_59633]) ).

tff(c_59712,plain,
    ( ( '#skF_17'('#skF_2'('#skF_15')) = '#skF_8' )
    | ~ ordinal('#skF_2'('#skF_15')) ),
    inference(resolution,[status(thm)],[c_40,c_59657]) ).

tff(c_59737,plain,
    '#skF_17'('#skF_2'('#skF_15')) = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_56967,c_59712]) ).

tff(c_374,plain,
    ! [A_76,B_77] :
      ( element(A_76,B_77)
      | ~ in(A_76,B_77) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_378,plain,
    ! [C_35] :
      ( element('#skF_17'(C_35),'#skF_15')
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(resolution,[status(thm)],[c_160,c_374]) ).

tff(c_59770,plain,
    ( element('#skF_8','#skF_15')
    | ~ in('#skF_2'('#skF_15'),'#skF_15')
    | ~ ordinal('#skF_2'('#skF_15')) ),
    inference(superposition,[status(thm),theory(equality)],[c_59737,c_378]) ).

tff(c_59812,plain,
    ( element('#skF_8','#skF_15')
    | ~ in('#skF_2'('#skF_15'),'#skF_15') ),
    inference(demodulation,[status(thm),theory(equality)],[c_56967,c_59770]) ).

tff(c_59813,plain,
    ~ in('#skF_2'('#skF_15'),'#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_59453,c_59812]) ).

tff(c_59842,plain,
    ( empty('#skF_15')
    | ~ element('#skF_2'('#skF_15'),'#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_59813]) ).

tff(c_59857,plain,
    empty('#skF_15'),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_59842]) ).

tff(c_59859,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_607,c_59857]) ).

tff(c_59861,plain,
    ordinal('#skF_17'('#skF_8')),
    inference(splitRight,[status(thm)],[c_57464]) ).

tff(c_8,plain,
    ! [A_4] :
      ( epsilon_transitive(A_4)
      | ~ ordinal(A_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_59868,plain,
    epsilon_transitive('#skF_17'('#skF_8')),
    inference(resolution,[status(thm)],[c_59861,c_8]) ).

tff(c_59860,plain,
    ( ~ epsilon_transitive('#skF_17'('#skF_8'))
    | ~ in('#skF_8','#skF_15')
    | ( '#skF_17'('#skF_8') = '#skF_8' ) ),
    inference(splitRight,[status(thm)],[c_57464]) ).

tff(c_59871,plain,
    ( ~ in('#skF_8','#skF_15')
    | ( '#skF_17'('#skF_8') = '#skF_8' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_59868,c_59860]) ).

tff(c_59872,plain,
    ~ in('#skF_8','#skF_15'),
    inference(splitLeft,[status(thm)],[c_59871]) ).

tff(c_59886,plain,
    ( empty('#skF_15')
    | ~ element('#skF_8','#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_59872]) ).

tff(c_59899,plain,
    ~ element('#skF_8','#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_607,c_59886]) ).

tff(c_59977,plain,
    ! [A_1591,B_1592] :
      ( element('#skF_8',A_1591)
      | ( B_1592 = '#skF_8' )
      | ~ ordinal(B_1592)
      | ~ in(B_1592,A_1591)
      | ~ epsilon_transitive(A_1591) ),
    inference(resolution,[status(thm)],[c_28,c_57854]) ).

tff(c_60007,plain,
    ! [C_35] :
      ( element('#skF_8','#skF_15')
      | ( '#skF_17'(C_35) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_35))
      | ~ epsilon_transitive('#skF_15')
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(resolution,[status(thm)],[c_160,c_59977]) ).

tff(c_60021,plain,
    ! [C_35] :
      ( element('#skF_8','#skF_15')
      | ( '#skF_17'(C_35) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_35))
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_52398,c_60007]) ).

tff(c_60023,plain,
    ! [C_1593] :
      ( ( '#skF_17'(C_1593) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_1593))
      | ~ in(C_1593,'#skF_15')
      | ~ ordinal(C_1593) ),
    inference(negUnitSimplification,[status(thm)],[c_59899,c_60021]) ).

tff(c_60042,plain,
    ! [C_1594] :
      ( ( '#skF_17'(C_1594) = '#skF_8' )
      | ~ in(C_1594,'#skF_15')
      | ~ ordinal(C_1594) ),
    inference(resolution,[status(thm)],[c_162,c_60023]) ).

tff(c_60074,plain,
    ! [A_30] :
      ( ( '#skF_17'(A_30) = '#skF_8' )
      | ~ ordinal(A_30)
      | empty('#skF_15')
      | ~ element(A_30,'#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_60042]) ).

tff(c_60098,plain,
    ! [A_1595] :
      ( ( '#skF_17'(A_1595) = '#skF_8' )
      | ~ ordinal(A_1595)
      | ~ element(A_1595,'#skF_15') ),
    inference(negUnitSimplification,[status(thm)],[c_607,c_60074]) ).

tff(c_60153,plain,
    ( ( '#skF_17'('#skF_2'('#skF_15')) = '#skF_8' )
    | ~ ordinal('#skF_2'('#skF_15')) ),
    inference(resolution,[status(thm)],[c_40,c_60098]) ).

tff(c_60178,plain,
    '#skF_17'('#skF_2'('#skF_15')) = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_56967,c_60153]) ).

tff(c_60211,plain,
    ( element('#skF_8','#skF_15')
    | ~ in('#skF_2'('#skF_15'),'#skF_15')
    | ~ ordinal('#skF_2'('#skF_15')) ),
    inference(superposition,[status(thm),theory(equality)],[c_60178,c_378]) ).

tff(c_60253,plain,
    ( element('#skF_8','#skF_15')
    | ~ in('#skF_2'('#skF_15'),'#skF_15') ),
    inference(demodulation,[status(thm),theory(equality)],[c_56967,c_60211]) ).

tff(c_60254,plain,
    ~ in('#skF_2'('#skF_15'),'#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_59899,c_60253]) ).

tff(c_60283,plain,
    ( empty('#skF_15')
    | ~ element('#skF_2'('#skF_15'),'#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_60254]) ).

tff(c_60298,plain,
    empty('#skF_15'),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_60283]) ).

tff(c_60300,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_607,c_60298]) ).

tff(c_60301,plain,
    '#skF_17'('#skF_8') = '#skF_8',
    inference(splitRight,[status(thm)],[c_59871]) ).

tff(c_57388,plain,
    ! [C_1485] :
      ( ordinal_subset('#skF_8',C_1485)
      | ~ ordinal(C_1485)
      | ~ empty(C_1485) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_57265]) ).

tff(c_57392,plain,
    ( ~ in('#skF_8','#skF_15')
    | ~ ordinal('#skF_8')
    | ~ ordinal('#skF_17'('#skF_8'))
    | ~ empty('#skF_17'('#skF_8')) ),
    inference(resolution,[status(thm)],[c_57388,c_158]) ).

tff(c_57395,plain,
    ( ~ in('#skF_8','#skF_15')
    | ~ ordinal('#skF_17'('#skF_8'))
    | ~ empty('#skF_17'('#skF_8')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_57392]) ).

tff(c_57585,plain,
    ~ empty('#skF_17'('#skF_8')),
    inference(splitLeft,[status(thm)],[c_57395]) ).

tff(c_60332,plain,
    ~ empty('#skF_8'),
    inference(demodulation,[status(thm),theory(equality)],[c_60301,c_57585]) ).

tff(c_60338,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_98,c_60332]) ).

tff(c_60340,plain,
    empty('#skF_17'('#skF_8')),
    inference(splitRight,[status(thm)],[c_57395]) ).

tff(c_60350,plain,
    '#skF_17'('#skF_8') = '#skF_8',
    inference(resolution,[status(thm)],[c_60340,c_353]) ).

tff(c_60388,plain,
    ( ~ ordinal_subset('#skF_8','#skF_8')
    | ~ in('#skF_8','#skF_15')
    | ~ ordinal('#skF_8') ),
    inference(superposition,[status(thm),theory(equality)],[c_60350,c_158]) ).

tff(c_60420,plain,
    ( ~ ordinal_subset('#skF_8','#skF_8')
    | ~ in('#skF_8','#skF_15') ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_60388]) ).

tff(c_60426,plain,
    ~ in('#skF_8','#skF_15'),
    inference(splitLeft,[status(thm)],[c_60420]) ).

tff(c_60440,plain,
    ( empty('#skF_15')
    | ~ element('#skF_8','#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_60426]) ).

tff(c_60453,plain,
    ~ element('#skF_8','#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_607,c_60440]) ).

tff(c_60830,plain,
    ! [B_1614,A_1615] :
      ( element('#skF_8',B_1614)
      | ~ subset(A_1615,B_1614)
      | ( A_1615 = '#skF_8' )
      | ~ ordinal(A_1615) ),
    inference(resolution,[status(thm)],[c_57396,c_52416]) ).

tff(c_62341,plain,
    ! [A_1681,B_1682] :
      ( element('#skF_8',A_1681)
      | ( B_1682 = '#skF_8' )
      | ~ ordinal(B_1682)
      | ~ in(B_1682,A_1681)
      | ~ epsilon_transitive(A_1681) ),
    inference(resolution,[status(thm)],[c_28,c_60830]) ).

tff(c_62371,plain,
    ! [C_35] :
      ( element('#skF_8','#skF_15')
      | ( '#skF_17'(C_35) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_35))
      | ~ epsilon_transitive('#skF_15')
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(resolution,[status(thm)],[c_160,c_62341]) ).

tff(c_62385,plain,
    ! [C_35] :
      ( element('#skF_8','#skF_15')
      | ( '#skF_17'(C_35) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_35))
      | ~ in(C_35,'#skF_15')
      | ~ ordinal(C_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_52398,c_62371]) ).

tff(c_62387,plain,
    ! [C_1683] :
      ( ( '#skF_17'(C_1683) = '#skF_8' )
      | ~ ordinal('#skF_17'(C_1683))
      | ~ in(C_1683,'#skF_15')
      | ~ ordinal(C_1683) ),
    inference(negUnitSimplification,[status(thm)],[c_60453,c_62385]) ).

tff(c_62405,plain,
    ! [C_1684] :
      ( ( '#skF_17'(C_1684) = '#skF_8' )
      | ~ in(C_1684,'#skF_15')
      | ~ ordinal(C_1684) ),
    inference(resolution,[status(thm)],[c_162,c_62387]) ).

tff(c_62437,plain,
    ! [A_30] :
      ( ( '#skF_17'(A_30) = '#skF_8' )
      | ~ ordinal(A_30)
      | empty('#skF_15')
      | ~ element(A_30,'#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_62405]) ).

tff(c_62461,plain,
    ! [A_1685] :
      ( ( '#skF_17'(A_1685) = '#skF_8' )
      | ~ ordinal(A_1685)
      | ~ element(A_1685,'#skF_15') ),
    inference(negUnitSimplification,[status(thm)],[c_607,c_62437]) ).

tff(c_62516,plain,
    ( ( '#skF_17'('#skF_2'('#skF_15')) = '#skF_8' )
    | ~ ordinal('#skF_2'('#skF_15')) ),
    inference(resolution,[status(thm)],[c_40,c_62461]) ).

tff(c_62541,plain,
    '#skF_17'('#skF_2'('#skF_15')) = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_56967,c_62516]) ).

tff(c_62574,plain,
    ( element('#skF_8','#skF_15')
    | ~ in('#skF_2'('#skF_15'),'#skF_15')
    | ~ ordinal('#skF_2'('#skF_15')) ),
    inference(superposition,[status(thm),theory(equality)],[c_62541,c_378]) ).

tff(c_62616,plain,
    ( element('#skF_8','#skF_15')
    | ~ in('#skF_2'('#skF_15'),'#skF_15') ),
    inference(demodulation,[status(thm),theory(equality)],[c_56967,c_62574]) ).

tff(c_62617,plain,
    ~ in('#skF_2'('#skF_15'),'#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_60453,c_62616]) ).

tff(c_62672,plain,
    ( empty('#skF_15')
    | ~ element('#skF_2'('#skF_15'),'#skF_15') ),
    inference(resolution,[status(thm)],[c_150,c_62617]) ).

tff(c_62687,plain,
    empty('#skF_15'),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_62672]) ).

tff(c_62689,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_607,c_62687]) ).

tff(c_62690,plain,
    ~ ordinal_subset('#skF_8','#skF_8'),
    inference(splitRight,[status(thm)],[c_60420]) ).

tff(c_62694,plain,
    ( ~ ordinal('#skF_8')
    | ~ empty('#skF_8') ),
    inference(resolution,[status(thm)],[c_57276,c_62690]) ).

tff(c_62706,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_98,c_92,c_62694]) ).

tff(c_62731,plain,
    ! [A_1688] : ~ element(A_1688,'#skF_15'),
    inference(splitRight,[status(thm)],[c_52723]) ).

tff(c_62759,plain,
    $false,
    inference(resolution,[status(thm)],[c_40,c_62731]) ).

tff(c_62761,plain,
    ordinal('#skF_15'),
    inference(splitRight,[status(thm)],[c_598]) ).

tff(c_62780,plain,
    ! [C_1691,A_1692] :
      ( ~ empty(C_1691)
      | ~ in(A_1692,'#skF_2'(powerset(C_1691))) ),
    inference(resolution,[status(thm)],[c_40,c_560]) ).

tff(c_66151,plain,
    ! [C_1883,A_1884] :
      ( ~ empty(C_1883)
      | empty('#skF_2'(powerset(C_1883)))
      | ~ element(A_1884,'#skF_2'(powerset(C_1883))) ),
    inference(resolution,[status(thm)],[c_150,c_62780]) ).

tff(c_66212,plain,
    ! [C_1887] :
      ( ~ empty(C_1887)
      | empty('#skF_2'(powerset(C_1887))) ),
    inference(resolution,[status(thm)],[c_40,c_66151]) ).

tff(c_66220,plain,
    ! [C_1888] :
      ( ( '#skF_2'(powerset(C_1888)) = '#skF_8' )
      | ~ empty(C_1888) ),
    inference(resolution,[status(thm)],[c_66212,c_353]) ).

tff(c_66309,plain,
    ! [C_1891] :
      ( element('#skF_8',powerset(C_1891))
      | ~ empty(C_1891) ),
    inference(superposition,[status(thm),theory(equality)],[c_66220,c_40]) ).

tff(c_66327,plain,
    ! [A_42,C_1891] :
      ( ~ in(A_42,'#skF_8')
      | ~ empty(C_1891) ),
    inference(resolution,[status(thm)],[c_66309,c_170]) ).

tff(c_66329,plain,
    ! [C_1891] : ~ empty(C_1891),
    inference(splitLeft,[status(thm)],[c_66327]) ).

tff(c_66345,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_66329,c_98]) ).

tff(c_66347,plain,
    ! [A_1892] : ~ in(A_1892,'#skF_8'),
    inference(splitRight,[status(thm)],[c_66327]) ).

tff(c_66363,plain,
    ! [A_27] :
      ( in('#skF_8',A_27)
      | ( A_27 = '#skF_8' )
      | ~ ordinal('#skF_8')
      | ~ ordinal(A_27) ),
    inference(resolution,[status(thm)],[c_148,c_66347]) ).

tff(c_66387,plain,
    ! [A_27] :
      ( in('#skF_8',A_27)
      | ( A_27 = '#skF_8' )
      | ~ ordinal(A_27) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_66363]) ).

tff(c_63112,plain,
    ! [B_1739,A_1740] :
      ( in(B_1739,A_1740)
      | ( B_1739 = A_1740 )
      | in(A_1740,B_1739)
      | ~ ordinal(B_1739)
      | ~ ordinal(A_1740) ),
    inference(cnfTransformation,[status(thm)],[f_224]) ).

tff(c_174,plain,
    ! [B_47,A_46] :
      ( ~ empty(B_47)
      | ~ in(A_46,B_47) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_63202,plain,
    ! [B_1739,A_1740] :
      ( ~ empty(B_1739)
      | in(B_1739,A_1740)
      | ( B_1739 = A_1740 )
      | ~ ordinal(B_1739)
      | ~ ordinal(A_1740) ),
    inference(resolution,[status(thm)],[c_63112,c_174]) ).

tff(c_66043,plain,
    ! [B_1870,A_1871] :
      ( ordinal_subset(B_1870,A_1871)
      | ~ ordinal(A_1871)
      | ~ ordinal(B_1870)
      | ~ in(B_1870,A_1871)
      | ~ epsilon_transitive(A_1871) ),
    inference(resolution,[status(thm)],[c_28,c_576]) ).

tff(c_66056,plain,
    ! [B_1872] :
      ( ~ in(B_1872,'#skF_15')
      | ~ ordinal('#skF_17'(B_1872))
      | ~ ordinal(B_1872)
      | ~ in(B_1872,'#skF_17'(B_1872))
      | ~ epsilon_transitive('#skF_17'(B_1872)) ),
    inference(resolution,[status(thm)],[c_66043,c_158]) ).

tff(c_66135,plain,
    ! [B_1880] :
      ( ~ in(B_1880,'#skF_15')
      | ~ epsilon_transitive('#skF_17'(B_1880))
      | ~ empty(B_1880)
      | ( '#skF_17'(B_1880) = B_1880 )
      | ~ ordinal(B_1880)
      | ~ ordinal('#skF_17'(B_1880)) ),
    inference(resolution,[status(thm)],[c_63202,c_66056]) ).

tff(c_66300,plain,
    ! [C_1890] :
      ( ~ epsilon_transitive('#skF_17'(C_1890))
      | ~ empty(C_1890)
      | ( '#skF_17'(C_1890) = C_1890 )
      | ~ in(C_1890,'#skF_15')
      | ~ ordinal(C_1890) ),
    inference(resolution,[status(thm)],[c_162,c_66135]) ).

tff(c_66667,plain,
    ! [C_1906] :
      ( ~ empty(C_1906)
      | ( '#skF_17'(C_1906) = C_1906 )
      | ~ in(C_1906,'#skF_15')
      | ~ ordinal(C_1906) ),
    inference(resolution,[status(thm)],[c_340,c_66300]) ).

tff(c_66671,plain,
    ( ~ empty('#skF_8')
    | ( '#skF_17'('#skF_8') = '#skF_8' )
    | ~ ordinal('#skF_8')
    | ( '#skF_15' = '#skF_8' )
    | ~ ordinal('#skF_15') ),
    inference(resolution,[status(thm)],[c_66387,c_66667]) ).

tff(c_66705,plain,
    ( ( '#skF_17'('#skF_8') = '#skF_8' )
    | ( '#skF_15' = '#skF_8' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_62761,c_92,c_98,c_66671]) ).

tff(c_66706,plain,
    '#skF_17'('#skF_8') = '#skF_8',
    inference(negUnitSimplification,[status(thm)],[c_298,c_66705]) ).

tff(c_66274,plain,
    ! [C_1889] :
      ( subset('#skF_8',C_1889)
      | ~ empty(C_1889) ),
    inference(superposition,[status(thm),theory(equality)],[c_66220,c_413]) ).

tff(c_66288,plain,
    ! [C_1889] :
      ( ordinal_subset('#skF_8',C_1889)
      | ~ ordinal(C_1889)
      | ~ ordinal('#skF_8')
      | ~ empty(C_1889) ),
    inference(resolution,[status(thm)],[c_66274,c_136]) ).

tff(c_66429,plain,
    ! [C_1896] :
      ( ordinal_subset('#skF_8',C_1896)
      | ~ ordinal(C_1896)
      | ~ empty(C_1896) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_66288]) ).

tff(c_66433,plain,
    ( ~ in('#skF_8','#skF_15')
    | ~ ordinal('#skF_8')
    | ~ ordinal('#skF_17'('#skF_8'))
    | ~ empty('#skF_17'('#skF_8')) ),
    inference(resolution,[status(thm)],[c_66429,c_158]) ).

tff(c_66436,plain,
    ( ~ in('#skF_8','#skF_15')
    | ~ ordinal('#skF_17'('#skF_8'))
    | ~ empty('#skF_17'('#skF_8')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_66433]) ).

tff(c_66526,plain,
    ~ empty('#skF_17'('#skF_8')),
    inference(splitLeft,[status(thm)],[c_66436]) ).

tff(c_66726,plain,
    ~ empty('#skF_8'),
    inference(demodulation,[status(thm),theory(equality)],[c_66706,c_66526]) ).

tff(c_66729,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_98,c_66726]) ).

tff(c_66731,plain,
    empty('#skF_17'('#skF_8')),
    inference(splitRight,[status(thm)],[c_66436]) ).

tff(c_66738,plain,
    '#skF_17'('#skF_8') = '#skF_8',
    inference(resolution,[status(thm)],[c_66731,c_353]) ).

tff(c_66730,plain,
    ( ~ ordinal('#skF_17'('#skF_8'))
    | ~ in('#skF_8','#skF_15') ),
    inference(splitRight,[status(thm)],[c_66436]) ).

tff(c_66816,plain,
    ~ in('#skF_8','#skF_15'),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_66738,c_66730]) ).

tff(c_66819,plain,
    ( ( '#skF_15' = '#skF_8' )
    | ~ ordinal('#skF_15') ),
    inference(resolution,[status(thm)],[c_66387,c_66816]) ).

tff(c_66833,plain,
    '#skF_15' = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_62761,c_66819]) ).

tff(c_66835,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_298,c_66833]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.14/0.36  % Computer : n013.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 11:32:33 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 22.61/10.70  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.66/10.74  
% 22.66/10.74  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.82/10.79  
% 22.82/10.79  Inference rules
% 22.82/10.79  ----------------------
% 22.82/10.79  #Ref     : 0
% 22.82/10.79  #Sup     : 14103
% 22.82/10.79  #Fact    : 24
% 22.82/10.79  #Define  : 0
% 22.82/10.79  #Split   : 129
% 22.82/10.79  #Chain   : 0
% 22.82/10.79  #Close   : 0
% 22.82/10.79  
% 22.82/10.79  Ordering : KBO
% 22.82/10.79  
% 22.82/10.79  Simplification rules
% 22.82/10.79  ----------------------
% 22.82/10.79  #Subsume      : 6019
% 22.82/10.79  #Demod        : 8824
% 22.82/10.79  #Tautology    : 2675
% 22.82/10.79  #SimpNegUnit  : 1775
% 22.82/10.79  #BackRed      : 497
% 22.82/10.79  
% 22.82/10.79  #Partial instantiations: 0
% 22.82/10.79  #Strategies tried      : 1
% 22.82/10.79  
% 22.82/10.79  Timing (in seconds)
% 22.82/10.79  ----------------------
% 22.82/10.80  Preprocessing        : 0.57
% 22.82/10.80  Parsing              : 0.29
% 22.82/10.80  CNF conversion       : 0.05
% 22.82/10.80  Main loop            : 9.11
% 22.82/10.80  Inferencing          : 2.22
% 22.82/10.80  Reduction            : 3.33
% 22.82/10.80  Demodulation         : 2.38
% 22.82/10.80  BG Simplification    : 0.12
% 22.82/10.80  Subsumption          : 2.83
% 22.82/10.80  Abstraction          : 0.18
% 22.82/10.80  MUC search           : 0.00
% 22.82/10.80  Cooper               : 0.00
% 22.82/10.80  Total                : 9.79
% 22.82/10.80  Index Insertion      : 0.00
% 22.82/10.80  Index Deletion       : 0.00
% 22.82/10.80  Index Matching       : 0.00
% 22.82/10.80  BG Taut test         : 0.00
%------------------------------------------------------------------------------