TSTP Solution File: SEU146+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU146+2 : 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/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 : n008.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 10:57:45 EDT 2023

% Result   : Theorem 10.19s 3.44s
% Output   : CNFRefutation 10.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  139 (  62 unt;  33 typ;   0 def)
%            Number of atoms       :  161 (  77 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   97 (  42   ~;  43   |;   1   &)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   57 (  26   >;  31   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;   7 con; 0-3 aty)
%            Number of variables   :   83 (;  82   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > #nlpp > singleton > empty_set > #skF_22 > #skF_18 > #skF_17 > #skF_6 > #skF_15 > #skF_20 > #skF_12 > #skF_4 > #skF_16 > #skF_14 > #skF_19 > #skF_13 > #skF_5 > #skF_8 > #skF_11 > #skF_7 > #skF_9 > #skF_3 > #skF_2 > #skF_1 > #skF_21 > #skF_10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_22',type,
    '#skF_22': ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_19',type,
    '#skF_19': ( $i * $i ) > $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(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

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

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

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i ) > $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('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

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

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

tff(f_168,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_144,lemma,
    ! [A,B] :
      ( subset(singleton(A),B)
    <=> in(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).

tff(f_161,negated_conjecture,
    ~ ! [A,B] :
        ( subset(A,singleton(B))
      <=> ( ( A = empty_set )
          | ( A = singleton(B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).

tff(f_163,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_288,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_61,axiom,
    ! [A] :
      ( ( A = empty_set )
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

tff(f_223,lemma,
    ! [A,B] : ( set_union2(A,set_difference(B,A)) = set_union2(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).

tff(f_253,lemma,
    ! [A,B] :
      ( subset(A,B)
     => ( B = set_union2(A,set_difference(B,A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).

tff(f_79,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_55,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_48,axiom,
    ! [A,B] :
      ( ( A = B )
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

tff(f_211,lemma,
    ! [A] : subset(empty_set,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).

tff(f_200,lemma,
    ! [A,B] :
      ( subset(A,B)
     => ( set_intersection2(A,B) = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

tff(f_40,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_42,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(f_178,lemma,
    ! [A,B] : subset(set_intersection2(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).

tff(c_174,plain,
    ! [A_73] : subset(A_73,A_73),
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_150,plain,
    ! [A_66,B_67] :
      ( subset(singleton(A_66),B_67)
      | ~ in(A_66,B_67) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_158,plain,
    ( ~ subset('#skF_13',singleton('#skF_14'))
    | ( singleton('#skF_16') != '#skF_15' ) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_435,plain,
    singleton('#skF_16') != '#skF_15',
    inference(splitLeft,[status(thm)],[c_158]) ).

tff(c_170,plain,
    empty('#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_299,plain,
    ! [A_152] :
      ( ( empty_set = A_152 )
      | ~ empty(A_152) ),
    inference(cnfTransformation,[status(thm)],[f_288]) ).

tff(c_308,plain,
    empty_set = '#skF_17',
    inference(resolution,[status(thm)],[c_170,c_299]) ).

tff(c_162,plain,
    ( ~ subset('#skF_13',singleton('#skF_14'))
    | ( empty_set != '#skF_15' ) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_272,plain,
    empty_set != '#skF_15',
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_312,plain,
    '#skF_17' != '#skF_15',
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_272]) ).

tff(c_32,plain,
    ! [A_18] :
      ( ( empty_set = A_18 )
      | in('#skF_3'(A_18),A_18) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_885,plain,
    ! [A_18] :
      ( ( A_18 = '#skF_17' )
      | in('#skF_3'(A_18),A_18) ),
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_32]) ).

tff(c_168,plain,
    ( ( singleton('#skF_14') = '#skF_13' )
    | ( empty_set = '#skF_13' )
    | subset('#skF_15',singleton('#skF_16')) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_762,plain,
    ( ( singleton('#skF_14') = '#skF_13' )
    | ( '#skF_17' = '#skF_13' )
    | subset('#skF_15',singleton('#skF_16')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_168]) ).

tff(c_763,plain,
    subset('#skF_15',singleton('#skF_16')),
    inference(splitLeft,[status(thm)],[c_762]) ).

tff(c_212,plain,
    ! [A_105,B_106] : ( set_union2(A_105,set_difference(B_106,A_105)) = set_union2(A_105,B_106) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_226,plain,
    ! [A_116,B_117] :
      ( ( set_union2(A_116,set_difference(B_117,A_116)) = B_117 )
      | ~ subset(A_116,B_117) ),
    inference(cnfTransformation,[status(thm)],[f_253]) ).

tff(c_1378,plain,
    ! [A_256,B_257] :
      ( ( set_union2(A_256,B_257) = B_257 )
      | ~ subset(A_256,B_257) ),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_226]) ).

tff(c_1416,plain,
    set_union2('#skF_15',singleton('#skF_16')) = singleton('#skF_16'),
    inference(resolution,[status(thm)],[c_763,c_1378]) ).

tff(c_1861,plain,
    ! [D_271,A_272,B_273] :
      ( ~ in(D_271,A_272)
      | in(D_271,set_union2(A_272,B_273)) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_2279,plain,
    ! [D_288] :
      ( ~ in(D_288,'#skF_15')
      | in(D_288,singleton('#skF_16')) ),
    inference(superposition,[status(thm),theory(equality)],[c_1416,c_1861]) ).

tff(c_18,plain,
    ! [C_17,A_13] :
      ( ( C_17 = A_13 )
      | ~ in(C_17,singleton(A_13)) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_2311,plain,
    ! [D_289] :
      ( ( D_289 = '#skF_16' )
      | ~ in(D_289,'#skF_15') ),
    inference(resolution,[status(thm)],[c_2279,c_18]) ).

tff(c_2319,plain,
    ( ( '#skF_3'('#skF_15') = '#skF_16' )
    | ( '#skF_17' = '#skF_15' ) ),
    inference(resolution,[status(thm)],[c_885,c_2311]) ).

tff(c_2323,plain,
    '#skF_3'('#skF_15') = '#skF_16',
    inference(negUnitSimplification,[status(thm)],[c_312,c_2319]) ).

tff(c_2330,plain,
    ( ( '#skF_17' = '#skF_15' )
    | in('#skF_16','#skF_15') ),
    inference(superposition,[status(thm),theory(equality)],[c_2323,c_885]) ).

tff(c_2334,plain,
    in('#skF_16','#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_312,c_2330]) ).

tff(c_5247,plain,
    ! [B_400,A_401] :
      ( ( B_400 = A_401 )
      | ~ subset(B_400,A_401)
      | ~ subset(A_401,B_400) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_5261,plain,
    ( ( singleton('#skF_16') = '#skF_15' )
    | ~ subset(singleton('#skF_16'),'#skF_15') ),
    inference(resolution,[status(thm)],[c_763,c_5247]) ).

tff(c_5280,plain,
    ~ subset(singleton('#skF_16'),'#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_435,c_5261]) ).

tff(c_5300,plain,
    ~ in('#skF_16','#skF_15'),
    inference(resolution,[status(thm)],[c_150,c_5280]) ).

tff(c_5310,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_5300]) ).

tff(c_5311,plain,
    ( ( '#skF_17' = '#skF_13' )
    | ( singleton('#skF_14') = '#skF_13' ) ),
    inference(splitRight,[status(thm)],[c_762]) ).

tff(c_5314,plain,
    singleton('#skF_14') = '#skF_13',
    inference(splitLeft,[status(thm)],[c_5311]) ).

tff(c_166,plain,
    ( ~ subset('#skF_13',singleton('#skF_14'))
    | subset('#skF_15',singleton('#skF_16')) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_505,plain,
    ~ subset('#skF_13',singleton('#skF_14')),
    inference(splitLeft,[status(thm)],[c_166]) ).

tff(c_5315,plain,
    ~ subset('#skF_13','#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_5314,c_505]) ).

tff(c_5318,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_174,c_5315]) ).

tff(c_5319,plain,
    '#skF_17' = '#skF_13',
    inference(splitRight,[status(thm)],[c_5311]) ).

tff(c_202,plain,
    ! [A_97] : subset(empty_set,A_97),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_315,plain,
    ! [A_97] : subset('#skF_17',A_97),
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_202]) ).

tff(c_5331,plain,
    ! [A_97] : subset('#skF_13',A_97),
    inference(demodulation,[status(thm),theory(equality)],[c_5319,c_315]) ).

tff(c_5349,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5331,c_505]) ).

tff(c_5350,plain,
    subset('#skF_15',singleton('#skF_16')),
    inference(splitRight,[status(thm)],[c_166]) ).

tff(c_7266,plain,
    ! [B_507,A_508] :
      ( ( B_507 = A_508 )
      | ~ subset(B_507,A_508)
      | ~ subset(A_508,B_507) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_7280,plain,
    ( ( singleton('#skF_16') = '#skF_15' )
    | ~ subset(singleton('#skF_16'),'#skF_15') ),
    inference(resolution,[status(thm)],[c_5350,c_7266]) ).

tff(c_7299,plain,
    ~ subset(singleton('#skF_16'),'#skF_15'),
    inference(negUnitSimplification,[status(thm)],[c_435,c_7280]) ).

tff(c_7317,plain,
    ~ in('#skF_16','#skF_15'),
    inference(resolution,[status(thm)],[c_150,c_7299]) ).

tff(c_5377,plain,
    ! [A_18] :
      ( ( A_18 = '#skF_17' )
      | in('#skF_3'(A_18),A_18) ),
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_32]) ).

tff(c_6298,plain,
    ! [A_472,B_473] :
      ( ( set_intersection2(A_472,B_473) = A_472 )
      | ~ subset(A_472,B_473) ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_6333,plain,
    set_intersection2('#skF_15',singleton('#skF_16')) = '#skF_15',
    inference(resolution,[status(thm)],[c_5350,c_6298]) ).

tff(c_8,plain,
    ! [B_8,A_7] : ( set_union2(B_8,A_7) = set_union2(A_7,B_8) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_5542,plain,
    ! [B_420,A_421] : ( set_intersection2(B_420,A_421) = set_intersection2(A_421,B_420) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_180,plain,
    ! [A_79,B_80] : subset(set_intersection2(A_79,B_80),A_79),
    inference(cnfTransformation,[status(thm)],[f_178]) ).

tff(c_5565,plain,
    ! [B_420,A_421] : subset(set_intersection2(B_420,A_421),A_421),
    inference(superposition,[status(thm),theory(equality)],[c_5542,c_180]) ).

tff(c_5905,plain,
    ! [A_458,B_459] :
      ( ( set_union2(A_458,B_459) = B_459 )
      | ~ subset(A_458,B_459) ),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_226]) ).

tff(c_6130,plain,
    ! [B_464,A_465] : ( set_union2(set_intersection2(B_464,A_465),A_465) = A_465 ),
    inference(resolution,[status(thm)],[c_5565,c_5905]) ).

tff(c_11600,plain,
    ! [B_684,B_685] : ( set_union2(B_684,set_intersection2(B_685,B_684)) = B_684 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_6130]) ).

tff(c_11690,plain,
    set_union2(singleton('#skF_16'),'#skF_15') = singleton('#skF_16'),
    inference(superposition,[status(thm),theory(equality)],[c_6333,c_11600]) ).

tff(c_54,plain,
    ! [D_33,B_29,A_28] :
      ( ~ in(D_33,B_29)
      | in(D_33,set_union2(A_28,B_29)) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_12100,plain,
    ! [D_701] :
      ( ~ in(D_701,'#skF_15')
      | in(D_701,singleton('#skF_16')) ),
    inference(superposition,[status(thm),theory(equality)],[c_11690,c_54]) ).

tff(c_12147,plain,
    ! [D_702] :
      ( ( D_702 = '#skF_16' )
      | ~ in(D_702,'#skF_15') ),
    inference(resolution,[status(thm)],[c_12100,c_18]) ).

tff(c_12151,plain,
    ( ( '#skF_3'('#skF_15') = '#skF_16' )
    | ( '#skF_17' = '#skF_15' ) ),
    inference(resolution,[status(thm)],[c_5377,c_12147]) ).

tff(c_12154,plain,
    '#skF_3'('#skF_15') = '#skF_16',
    inference(negUnitSimplification,[status(thm)],[c_312,c_12151]) ).

tff(c_12161,plain,
    ( ( '#skF_17' = '#skF_15' )
    | in('#skF_16','#skF_15') ),
    inference(superposition,[status(thm),theory(equality)],[c_12154,c_5377]) ).

tff(c_12166,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7317,c_312,c_12161]) ).

tff(c_12168,plain,
    singleton('#skF_16') = '#skF_15',
    inference(splitRight,[status(thm)],[c_158]) ).

tff(c_160,plain,
    ( ( singleton('#skF_14') = '#skF_13' )
    | ( empty_set = '#skF_13' )
    | ( singleton('#skF_16') != '#skF_15' ) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_12288,plain,
    ( ( singleton('#skF_14') = '#skF_13' )
    | ( '#skF_17' = '#skF_13' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12168,c_308,c_160]) ).

tff(c_12289,plain,
    '#skF_17' = '#skF_13',
    inference(splitLeft,[status(thm)],[c_12288]) ).

tff(c_12299,plain,
    ! [A_97] : subset('#skF_13',A_97),
    inference(demodulation,[status(thm),theory(equality)],[c_12289,c_315]) ).

tff(c_12167,plain,
    ~ subset('#skF_13',singleton('#skF_14')),
    inference(splitRight,[status(thm)],[c_158]) ).

tff(c_12332,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12299,c_12167]) ).

tff(c_12333,plain,
    singleton('#skF_14') = '#skF_13',
    inference(splitRight,[status(thm)],[c_12288]) ).

tff(c_12336,plain,
    ~ subset('#skF_13','#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_12333,c_12167]) ).

tff(c_12339,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_174,c_12336]) ).

tff(c_12341,plain,
    empty_set = '#skF_15',
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_164,plain,
    ( ( singleton('#skF_14') = '#skF_13' )
    | ( empty_set = '#skF_13' )
    | ( empty_set != '#skF_15' ) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_12342,plain,
    empty_set != '#skF_15',
    inference(splitLeft,[status(thm)],[c_164]) ).

tff(c_12352,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12341,c_12342]) ).

tff(c_12353,plain,
    ( ( empty_set = '#skF_13' )
    | ( singleton('#skF_14') = '#skF_13' ) ),
    inference(splitRight,[status(thm)],[c_164]) ).

tff(c_12487,plain,
    ( ( '#skF_15' = '#skF_13' )
    | ( singleton('#skF_14') = '#skF_13' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12341,c_12353]) ).

tff(c_12488,plain,
    singleton('#skF_14') = '#skF_13',
    inference(splitLeft,[status(thm)],[c_12487]) ).

tff(c_12340,plain,
    ~ subset('#skF_13',singleton('#skF_14')),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_12489,plain,
    ~ subset('#skF_13','#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_12488,c_12340]) ).

tff(c_12492,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_174,c_12489]) ).

tff(c_12493,plain,
    '#skF_15' = '#skF_13',
    inference(splitRight,[status(thm)],[c_12487]) ).

tff(c_12357,plain,
    ! [A_97] : subset('#skF_15',A_97),
    inference(demodulation,[status(thm),theory(equality)],[c_12341,c_202]) ).

tff(c_12503,plain,
    ! [A_97] : subset('#skF_13',A_97),
    inference(demodulation,[status(thm),theory(equality)],[c_12493,c_12357]) ).

tff(c_12522,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12503,c_12340]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU146+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 11:32:33 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 10.19/3.44  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.19/3.46  
% 10.19/3.46  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.62/3.49  
% 10.62/3.49  Inference rules
% 10.62/3.49  ----------------------
% 10.62/3.49  #Ref     : 0
% 10.62/3.49  #Sup     : 3079
% 10.62/3.49  #Fact    : 0
% 10.62/3.49  #Define  : 0
% 10.62/3.49  #Split   : 14
% 10.62/3.49  #Chain   : 0
% 10.62/3.49  #Close   : 0
% 10.62/3.49  
% 10.62/3.49  Ordering : KBO
% 10.62/3.49  
% 10.62/3.49  Simplification rules
% 10.62/3.49  ----------------------
% 10.62/3.49  #Subsume      : 895
% 10.62/3.49  #Demod        : 1202
% 10.62/3.49  #Tautology    : 1482
% 10.62/3.49  #SimpNegUnit  : 60
% 10.62/3.49  #BackRed      : 111
% 10.62/3.49  
% 10.62/3.49  #Partial instantiations: 0
% 10.62/3.49  #Strategies tried      : 1
% 10.62/3.49  
% 10.62/3.49  Timing (in seconds)
% 10.62/3.49  ----------------------
% 10.62/3.50  Preprocessing        : 0.77
% 10.62/3.50  Parsing              : 0.39
% 10.62/3.50  CNF conversion       : 0.07
% 10.62/3.50  Main loop            : 1.62
% 10.62/3.50  Inferencing          : 0.51
% 10.62/3.50  Reduction            : 0.60
% 10.62/3.50  Demodulation         : 0.42
% 10.62/3.50  BG Simplification    : 0.06
% 10.62/3.50  Subsumption          : 0.33
% 10.62/3.50  Abstraction          : 0.05
% 10.62/3.50  MUC search           : 0.00
% 10.62/3.50  Cooper               : 0.00
% 10.62/3.50  Total                : 2.46
% 10.62/3.50  Index Insertion      : 0.00
% 10.62/3.50  Index Deletion       : 0.00
% 10.77/3.50  Index Matching       : 0.00
% 10.77/3.50  BG Taut test         : 0.00
%------------------------------------------------------------------------------