TSTP Solution File: NUM401+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM401+1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n032.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 10:51:35 EDT 2023

% Result   : Theorem 16.53s 6.19s
% Output   : CNFRefutation 16.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  151 (  52 unt;  39 typ;   0 def)
%            Number of atoms       :  229 (  26 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  211 (  94   ~;  78   |;  17   &)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  23   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  16 con; 0-3 aty)
%            Number of variables   :  114 (; 112   !;   2   ?;   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_20 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_4 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_13 > #skF_5 > #skF_21 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_6 > #skF_12

%Foreground sorts:

%Background operators:

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

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_4',type,
    '#skF_4': ( $i * $i * $i ) > $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_13',type,
    '#skF_13': $i ).

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

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

tff('#skF_21',type,
    '#skF_21': $i ).

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_6',type,
    '#skF_6': $i > $i ).

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

tff(f_306,negated_conjecture,
    ~ ! [A] :
        ( ordinal(A)
       => ! [B] :
            ( ordinal(B)
           => ( in(A,succ(B))
            <=> ordinal_subset(A,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).

tff(f_262,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ordinal_subset(A,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).

tff(f_209,axiom,
    ? [A] :
      ( relation(A)
      & function(A)
      & one_to_one(A)
      & empty(A)
      & epsilon_transitive(A)
      & epsilon_connected(A)
      & ordinal(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).

tff(f_89,axiom,
    ! [A] : ( succ(A) = set_union2(A,singleton(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).

tff(f_73,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_327,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_189,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_271,axiom,
    ! [A] : ( set_union2(A,empty_set) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).

tff(f_162,axiom,
    ! [A] :
      ( ordinal(A)
     => ( ~ empty(succ(A))
        & epsilon_transitive(succ(A))
        & epsilon_connected(succ(A))
        & ordinal(succ(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).

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

tff(f_266,axiom,
    ! [A] : in(A,succ(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).

tff(f_275,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

tff(f_256,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
      <=> subset(A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

tff(f_290,axiom,
    ! [A] :
      ( ordinal(A)
     => ! [B] :
          ( ordinal(B)
         => ~ ( ~ in(A,B)
              & ( A != B )
              & ~ in(B,A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).

tff(f_112,axiom,
    ! [A,B,C] :
      ( ( C = set_union2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

tff(f_310,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

tff(f_323,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

tff(f_316,axiom,
    ! [A,B,C] :
      ( ( in(A,B)
        & element(B,powerset(C)) )
     => element(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

tff(f_296,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

tff(f_31,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

tff(f_123,axiom,
    ! [A] : ~ empty(succ(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).

tff(f_103,axiom,
    ! [A] :
      ( epsilon_transitive(A)
    <=> ! [B] :
          ( in(B,A)
         => subset(B,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).

tff(f_96,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

tff(c_214,plain,
    ordinal('#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_198,plain,
    ! [A_45,B_46] :
      ( ordinal_subset(A_45,A_45)
      | ~ ordinal(B_46)
      | ~ ordinal(A_45) ),
    inference(cnfTransformation,[status(thm)],[f_262]) ).

tff(c_21761,plain,
    ! [B_46] : ~ ordinal(B_46),
    inference(splitLeft,[status(thm)],[c_198]) ).

tff(c_144,plain,
    ordinal('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_21678,plain,
    ! [A_932] : ( set_union2(A_932,singleton(A_932)) = succ(A_932) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_21515,plain,
    ! [B_921,A_922] : ( set_union2(B_921,A_922) = set_union2(A_922,B_921) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_150,plain,
    empty('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_21349,plain,
    ! [A_901] :
      ( ( empty_set = A_901 )
      | ~ empty(A_901) ),
    inference(cnfTransformation,[status(thm)],[f_327]) ).

tff(c_21367,plain,
    empty_set = '#skF_12',
    inference(resolution,[status(thm)],[c_150,c_21349]) ).

tff(c_136,plain,
    empty('#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_189]) ).

tff(c_21365,plain,
    empty_set = '#skF_10',
    inference(resolution,[status(thm)],[c_136,c_21349]) ).

tff(c_21395,plain,
    '#skF_10' = '#skF_12',
    inference(demodulation,[status(thm),theory(equality)],[c_21367,c_21365]) ).

tff(c_206,plain,
    ! [A_51] : ( set_union2(A_51,empty_set) = A_51 ),
    inference(cnfTransformation,[status(thm)],[f_271]) ).

tff(c_21372,plain,
    ! [A_51] : ( set_union2(A_51,'#skF_10') = A_51 ),
    inference(demodulation,[status(thm),theory(equality)],[c_21365,c_206]) ).

tff(c_21473,plain,
    ! [A_51] : ( set_union2(A_51,'#skF_12') = A_51 ),
    inference(demodulation,[status(thm),theory(equality)],[c_21395,c_21372]) ).

tff(c_21543,plain,
    ! [A_922] : ( set_union2('#skF_12',A_922) = A_922 ),
    inference(superposition,[status(thm),theory(equality)],[c_21515,c_21473]) ).

tff(c_21685,plain,
    succ('#skF_12') = singleton('#skF_12'),
    inference(superposition,[status(thm),theory(equality)],[c_21678,c_21543]) ).

tff(c_106,plain,
    ! [A_38] :
      ( ordinal(succ(A_38))
      | ~ ordinal(A_38) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_21711,plain,
    ( ordinal(singleton('#skF_12'))
    | ~ ordinal('#skF_12') ),
    inference(superposition,[status(thm),theory(equality)],[c_21685,c_106]) ).

tff(c_21730,plain,
    ordinal(singleton('#skF_12')),
    inference(demodulation,[status(thm),theory(equality)],[c_144,c_21711]) ).

tff(c_21771,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_21761,c_21730]) ).

tff(c_21772,plain,
    ! [A_45] :
      ( ordinal_subset(A_45,A_45)
      | ~ ordinal(A_45) ),
    inference(splitRight,[status(thm)],[c_198]) ).

tff(c_21282,plain,
    ! [A_892] :
      ( epsilon_transitive(A_892)
      | ~ ordinal(A_892) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_21313,plain,
    epsilon_transitive('#skF_21'),
    inference(resolution,[status(thm)],[c_214,c_21282]) ).

tff(c_224,plain,
    ( in('#skF_20',succ('#skF_21'))
    | ordinal_subset('#skF_20','#skF_21') ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_247,plain,
    ordinal_subset('#skF_20','#skF_21'),
    inference(splitLeft,[status(thm)],[c_224]) ).

tff(c_202,plain,
    ! [A_49] : in(A_49,succ(A_49)),
    inference(cnfTransformation,[status(thm)],[f_266]) ).

tff(c_713,plain,
    ! [A_115,B_116] :
      ( element(A_115,B_116)
      | ~ in(A_115,B_116) ),
    inference(cnfTransformation,[status(thm)],[f_275]) ).

tff(c_724,plain,
    ! [A_49] : element(A_49,succ(A_49)),
    inference(resolution,[status(thm)],[c_202,c_713]) ).

tff(c_216,plain,
    ordinal('#skF_20'),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_196,plain,
    ! [A_43,B_44] :
      ( subset(A_43,B_44)
      | ~ ordinal_subset(A_43,B_44)
      | ~ ordinal(B_44)
      | ~ ordinal(A_43) ),
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_1760,plain,
    ! [B_210,A_211] :
      ( in(B_210,A_211)
      | ( B_210 = A_211 )
      | in(A_211,B_210)
      | ~ ordinal(B_210)
      | ~ ordinal(A_211) ),
    inference(cnfTransformation,[status(thm)],[f_290]) ).

tff(c_36,plain,
    ! [A_15] : ( set_union2(A_15,singleton(A_15)) = succ(A_15) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_872,plain,
    ! [D_140,A_141,B_142] :
      ( ~ in(D_140,A_141)
      | in(D_140,set_union2(A_141,B_142)) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_1306,plain,
    ! [D_176,A_177] :
      ( ~ in(D_176,A_177)
      | in(D_176,succ(A_177)) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_872]) ).

tff(c_218,plain,
    ( ~ ordinal_subset('#skF_20','#skF_21')
    | ~ in('#skF_20',succ('#skF_21')) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_248,plain,
    ~ in('#skF_20',succ('#skF_21')),
    inference(splitLeft,[status(thm)],[c_218]) ).

tff(c_1364,plain,
    ~ in('#skF_20','#skF_21'),
    inference(resolution,[status(thm)],[c_1306,c_248]) ).

tff(c_1803,plain,
    ( ( '#skF_20' = '#skF_21' )
    | in('#skF_21','#skF_20')
    | ~ ordinal('#skF_20')
    | ~ ordinal('#skF_21') ),
    inference(resolution,[status(thm)],[c_1760,c_1364]) ).

tff(c_1967,plain,
    ( ( '#skF_20' = '#skF_21' )
    | in('#skF_21','#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_214,c_216,c_1803]) ).

tff(c_2017,plain,
    in('#skF_21','#skF_20'),
    inference(splitLeft,[status(thm)],[c_1967]) ).

tff(c_228,plain,
    ! [A_60,B_61] :
      ( element(A_60,powerset(B_61))
      | ~ subset(A_60,B_61) ),
    inference(cnfTransformation,[status(thm)],[f_310]) ).

tff(c_1180,plain,
    ! [C_158,B_159,A_160] :
      ( ~ empty(C_158)
      | ~ element(B_159,powerset(C_158))
      | ~ in(A_160,B_159) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_3403,plain,
    ! [B_270,A_271,A_272] :
      ( ~ empty(B_270)
      | ~ in(A_271,A_272)
      | ~ subset(A_272,B_270) ),
    inference(resolution,[status(thm)],[c_228,c_1180]) ).

tff(c_3464,plain,
    ! [B_273] :
      ( ~ empty(B_273)
      | ~ subset('#skF_20',B_273) ),
    inference(resolution,[status(thm)],[c_2017,c_3403]) ).

tff(c_3468,plain,
    ! [B_44] :
      ( ~ empty(B_44)
      | ~ ordinal_subset('#skF_20',B_44)
      | ~ ordinal(B_44)
      | ~ ordinal('#skF_20') ),
    inference(resolution,[status(thm)],[c_196,c_3464]) ).

tff(c_3516,plain,
    ! [B_278] :
      ( ~ empty(B_278)
      | ~ ordinal_subset('#skF_20',B_278)
      | ~ ordinal(B_278) ),
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_3468]) ).

tff(c_3531,plain,
    ( ~ empty('#skF_21')
    | ~ ordinal('#skF_21') ),
    inference(resolution,[status(thm)],[c_247,c_3516]) ).

tff(c_3543,plain,
    ~ empty('#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_214,c_3531]) ).

tff(c_1445,plain,
    ! [A_184,C_185,B_186] :
      ( element(A_184,C_185)
      | ~ element(B_186,powerset(C_185))
      | ~ in(A_184,B_186) ),
    inference(cnfTransformation,[status(thm)],[f_316]) ).

tff(c_4187,plain,
    ! [A_306,B_307,A_308] :
      ( element(A_306,B_307)
      | ~ in(A_306,A_308)
      | ~ subset(A_308,B_307) ),
    inference(resolution,[status(thm)],[c_228,c_1445]) ).

tff(c_4251,plain,
    ! [B_309] :
      ( element('#skF_21',B_309)
      | ~ subset('#skF_20',B_309) ),
    inference(resolution,[status(thm)],[c_2017,c_4187]) ).

tff(c_4255,plain,
    ! [B_44] :
      ( element('#skF_21',B_44)
      | ~ ordinal_subset('#skF_20',B_44)
      | ~ ordinal(B_44)
      | ~ ordinal('#skF_20') ),
    inference(resolution,[status(thm)],[c_196,c_4251]) ).

tff(c_4423,plain,
    ! [B_317] :
      ( element('#skF_21',B_317)
      | ~ ordinal_subset('#skF_20',B_317)
      | ~ ordinal(B_317) ),
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_4255]) ).

tff(c_4442,plain,
    ( element('#skF_21','#skF_21')
    | ~ ordinal('#skF_21') ),
    inference(resolution,[status(thm)],[c_247,c_4423]) ).

tff(c_4457,plain,
    element('#skF_21','#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_214,c_4442]) ).

tff(c_212,plain,
    ! [A_57,B_58] :
      ( in(A_57,B_58)
      | empty(B_58)
      | ~ element(A_57,B_58) ),
    inference(cnfTransformation,[status(thm)],[f_296]) ).

tff(c_1094,plain,
    ! [A_155,B_156] :
      ( in(A_155,B_156)
      | empty(B_156)
      | ~ element(A_155,B_156) ),
    inference(cnfTransformation,[status(thm)],[f_296]) ).

tff(c_2,plain,
    ! [B_2,A_1] :
      ( ~ in(B_2,A_1)
      | ~ in(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_3113,plain,
    ! [B_257,A_258] :
      ( ~ in(B_257,A_258)
      | empty(B_257)
      | ~ element(A_258,B_257) ),
    inference(resolution,[status(thm)],[c_1094,c_2]) ).

tff(c_20946,plain,
    ! [A_884,B_885] :
      ( empty(A_884)
      | ~ element(B_885,A_884)
      | empty(B_885)
      | ~ element(A_884,B_885) ),
    inference(resolution,[status(thm)],[c_212,c_3113]) ).

tff(c_21054,plain,
    ( empty('#skF_21')
    | ~ element('#skF_21','#skF_21') ),
    inference(resolution,[status(thm)],[c_4457,c_20946]) ).

tff(c_21216,plain,
    empty('#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_4457,c_21054]) ).

tff(c_21218,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3543,c_21216]) ).

tff(c_21219,plain,
    '#skF_20' = '#skF_21',
    inference(splitRight,[status(thm)],[c_1967]) ).

tff(c_82,plain,
    ! [A_33] : ~ empty(succ(A_33)),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_1154,plain,
    ( empty(succ('#skF_21'))
    | ~ element('#skF_20',succ('#skF_21')) ),
    inference(resolution,[status(thm)],[c_1094,c_248]) ).

tff(c_1178,plain,
    ~ element('#skF_20',succ('#skF_21')),
    inference(negUnitSimplification,[status(thm)],[c_82,c_1154]) ).

tff(c_21223,plain,
    ~ element('#skF_21',succ('#skF_21')),
    inference(demodulation,[status(thm),theory(equality)],[c_21219,c_1178]) ).

tff(c_21231,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_724,c_21223]) ).

tff(c_21232,plain,
    ~ ordinal_subset('#skF_20','#skF_21'),
    inference(splitRight,[status(thm)],[c_218]) ).

tff(c_21235,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_247,c_21232]) ).

tff(c_21236,plain,
    in('#skF_20',succ('#skF_21')),
    inference(splitRight,[status(thm)],[c_224]) ).

tff(c_22358,plain,
    ! [D_998,B_999,A_1000] :
      ( in(D_998,B_999)
      | in(D_998,A_1000)
      | ~ in(D_998,set_union2(A_1000,B_999)) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_26509,plain,
    ! [D_1171,A_1172] :
      ( in(D_1171,singleton(A_1172))
      | in(D_1171,A_1172)
      | ~ in(D_1171,succ(A_1172)) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_22358]) ).

tff(c_26607,plain,
    ( in('#skF_20',singleton('#skF_21'))
    | in('#skF_20','#skF_21') ),
    inference(resolution,[status(thm)],[c_21236,c_26509]) ).

tff(c_26608,plain,
    in('#skF_20','#skF_21'),
    inference(splitLeft,[status(thm)],[c_26607]) ).

tff(c_50,plain,
    ! [B_24,A_21] :
      ( subset(B_24,A_21)
      | ~ in(B_24,A_21)
      | ~ epsilon_transitive(A_21) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_22206,plain,
    ! [A_979,B_980] :
      ( ordinal_subset(A_979,B_980)
      | ~ subset(A_979,B_980)
      | ~ ordinal(B_980)
      | ~ ordinal(A_979) ),
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_28387,plain,
    ! [B_1215,A_1216] :
      ( ordinal_subset(B_1215,A_1216)
      | ~ ordinal(A_1216)
      | ~ ordinal(B_1215)
      | ~ in(B_1215,A_1216)
      | ~ epsilon_transitive(A_1216) ),
    inference(resolution,[status(thm)],[c_50,c_22206]) ).

tff(c_21237,plain,
    ~ ordinal_subset('#skF_20','#skF_21'),
    inference(splitRight,[status(thm)],[c_224]) ).

tff(c_28402,plain,
    ( ~ ordinal('#skF_21')
    | ~ ordinal('#skF_20')
    | ~ in('#skF_20','#skF_21')
    | ~ epsilon_transitive('#skF_21') ),
    inference(resolution,[status(thm)],[c_28387,c_21237]) ).

tff(c_28415,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_21313,c_26608,c_216,c_214,c_28402]) ).

tff(c_28416,plain,
    in('#skF_20',singleton('#skF_21')),
    inference(splitRight,[status(thm)],[c_26607]) ).

tff(c_38,plain,
    ! [C_20,A_16] :
      ( ( C_20 = A_16 )
      | ~ in(C_20,singleton(A_16)) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_28466,plain,
    '#skF_20' = '#skF_21',
    inference(resolution,[status(thm)],[c_28416,c_38]) ).

tff(c_28483,plain,
    ~ ordinal_subset('#skF_21','#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_28466,c_21237]) ).

tff(c_28499,plain,
    ~ ordinal('#skF_21'),
    inference(resolution,[status(thm)],[c_21772,c_28483]) ).

tff(c_28503,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_214,c_28499]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu Aug  3 15:12:21 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 16.53/6.19  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.53/6.20  
% 16.53/6.20  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.69/6.24  
% 16.69/6.24  Inference rules
% 16.69/6.24  ----------------------
% 16.69/6.24  #Ref     : 0
% 16.69/6.24  #Sup     : 6185
% 16.69/6.24  #Fact    : 26
% 16.69/6.24  #Define  : 0
% 16.69/6.24  #Split   : 44
% 16.69/6.24  #Chain   : 0
% 16.69/6.24  #Close   : 0
% 16.69/6.24  
% 16.69/6.24  Ordering : KBO
% 16.69/6.24  
% 16.69/6.24  Simplification rules
% 16.69/6.24  ----------------------
% 16.69/6.24  #Subsume      : 2350
% 16.69/6.24  #Demod        : 1185
% 16.69/6.24  #Tautology    : 595
% 16.69/6.24  #SimpNegUnit  : 361
% 16.69/6.24  #BackRed      : 84
% 16.69/6.24  
% 16.69/6.24  #Partial instantiations: 0
% 16.69/6.24  #Strategies tried      : 1
% 16.69/6.24  
% 16.69/6.24  Timing (in seconds)
% 16.69/6.24  ----------------------
% 16.69/6.24  Preprocessing        : 0.63
% 16.69/6.24  Parsing              : 0.31
% 16.69/6.24  CNF conversion       : 0.06
% 16.69/6.24  Main loop            : 4.58
% 16.69/6.24  Inferencing          : 1.08
% 16.69/6.24  Reduction            : 1.78
% 16.69/6.24  Demodulation         : 1.15
% 16.69/6.24  BG Simplification    : 0.09
% 16.69/6.24  Subsumption          : 1.27
% 16.69/6.24  Abstraction          : 0.10
% 16.69/6.24  MUC search           : 0.00
% 16.69/6.24  Cooper               : 0.00
% 16.69/6.24  Total                : 5.28
% 16.69/6.24  Index Insertion      : 0.00
% 16.69/6.24  Index Deletion       : 0.00
% 16.69/6.24  Index Matching       : 0.00
% 16.69/6.24  BG Taut test         : 0.00
%------------------------------------------------------------------------------