TSTP Solution File: SEU290+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU290+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 : n027.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 10:58:17 EDT 2023

% Result   : Theorem 6.12s 2.48s
% Output   : CNFRefutation 6.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   61
% Syntax   : Number of formulae    :  132 (  41 unt;  43 typ;   0 def)
%            Number of atoms       :  174 (  47 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives :  137 (  52   ~;  49   |;  14   &)
%                                         (   5 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   50 (  28   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   32 (  32 usr;  15 con; 0-3 aty)
%            Number of variables   :   88 (;  84   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_dom_as_subset > cartesian_product2 > apply > #nlpp > relation_rng > relation_dom > powerset > empty_set > #skF_20 > #skF_18 > #skF_11 > #skF_25 > #skF_19 > #skF_4 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_13 > #skF_21 > #skF_8 > #skF_17 > #skF_22 > #skF_2 > #skF_24 > #skF_23 > #skF_12 > #skF_7 > #skF_1 > #skF_9 > #skF_5 > #skF_15 > #skF_6

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff('#skF_25',type,
    '#skF_25': $i ).

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

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

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

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

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(relation_dom_as_subset,type,
    relation_dom_as_subset: ( $i * $i * $i ) > $i ).

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

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

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

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

tff(relation_of2,type,
    relation_of2: ( $i * $i * $i ) > $o ).

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

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

tff('#skF_22',type,
    '#skF_22': $i ).

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

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

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

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

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

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

tff(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

tff(relation_of2_as_subset,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

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

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

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

tff(f_287,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( function(D)
          & quasi_total(D,A,B)
          & relation_of2_as_subset(D,A,B) )
       => ( in(C,A)
         => ( ( B = empty_set )
            | in(apply(D,C),relation_rng(D)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).

tff(f_247,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

tff(f_191,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_274,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_197,axiom,
    ? [A] :
      ( relation(A)
      & empty(A)
      & function(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

tff(f_176,axiom,
    ? [A] :
      ( relation(A)
      & function(A)
      & one_to_one(A)
      & empty(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).

tff(f_241,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
    <=> relation_of2(C,A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

tff(f_237,axiom,
    ! [A,B,C] :
      ( relation_of2(C,A,B)
     => ( relation_dom_as_subset(A,B,C) = relation_dom(C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).

tff(f_73,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
     => ( ( ( ( B = empty_set )
           => ( A = empty_set ) )
         => ( quasi_total(C,A,B)
          <=> ( A = relation_dom_as_subset(A,B,C) ) ) )
        & ( ( B = empty_set )
         => ( ( A = empty_set )
            | ( quasi_total(C,A,B)
            <=> ( C = empty_set ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).

tff(f_292,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

tff(f_97,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
     => element(C,powerset(cartesian_product2(A,B))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

tff(f_43,axiom,
    ! [A,B,C] :
      ( element(C,powerset(cartesian_product2(A,B)))
     => relation(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

tff(f_253,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(f_93,axiom,
    ! [A,B,C] :
      ( relation_of2(C,A,B)
     => element(relation_dom_as_subset(A,B,C),powerset(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).

tff(f_263,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_135,axiom,
    ! [A] :
      ( ( ~ empty(A)
        & relation(A) )
     => ~ empty(relation_dom(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).

tff(f_149,axiom,
    ! [A] :
      ( empty(A)
     => ( empty(relation_dom(A))
        & relation(relation_dom(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).

tff(f_88,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B] :
          ( ( B = relation_rng(A) )
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] :
                  ( in(D,relation_dom(A))
                  & ( C = apply(A,D) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

tff(c_194,plain,
    in('#skF_24','#skF_22'),
    inference(cnfTransformation,[status(thm)],[f_287]) ).

tff(c_388,plain,
    ! [A_137,B_138] :
      ( element(A_137,B_138)
      | ~ in(A_137,B_138) ),
    inference(cnfTransformation,[status(thm)],[f_247]) ).

tff(c_392,plain,
    element('#skF_24','#skF_22'),
    inference(resolution,[status(thm)],[c_194,c_388]) ).

tff(c_128,plain,
    empty('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_211,plain,
    ! [A_111] :
      ( ( empty_set = A_111 )
      | ~ empty(A_111) ),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_235,plain,
    empty_set = '#skF_13',
    inference(resolution,[status(thm)],[c_128,c_211]) ).

tff(c_132,plain,
    empty('#skF_14'),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_236,plain,
    empty_set = '#skF_14',
    inference(resolution,[status(thm)],[c_132,c_211]) ).

tff(c_254,plain,
    '#skF_14' = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_235,c_236]) ).

tff(c_112,plain,
    empty('#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_176]) ).

tff(c_233,plain,
    empty_set = '#skF_10',
    inference(resolution,[status(thm)],[c_112,c_211]) ).

tff(c_249,plain,
    '#skF_10' = '#skF_14',
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_233]) ).

tff(c_267,plain,
    '#skF_10' = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_254,c_249]) ).

tff(c_192,plain,
    empty_set != '#skF_23',
    inference(cnfTransformation,[status(thm)],[f_287]) ).

tff(c_241,plain,
    '#skF_10' != '#skF_23',
    inference(demodulation,[status(thm),theory(equality)],[c_233,c_192]) ).

tff(c_268,plain,
    '#skF_13' != '#skF_23',
    inference(demodulation,[status(thm),theory(equality)],[c_267,c_241]) ).

tff(c_198,plain,
    quasi_total('#skF_25','#skF_22','#skF_23'),
    inference(cnfTransformation,[status(thm)],[f_287]) ).

tff(c_196,plain,
    relation_of2_as_subset('#skF_25','#skF_22','#skF_23'),
    inference(cnfTransformation,[status(thm)],[f_287]) ).

tff(c_761,plain,
    ! [C_185,A_186,B_187] :
      ( relation_of2(C_185,A_186,B_187)
      | ~ relation_of2_as_subset(C_185,A_186,B_187) ),
    inference(cnfTransformation,[status(thm)],[f_241]) ).

tff(c_769,plain,
    relation_of2('#skF_25','#skF_22','#skF_23'),
    inference(resolution,[status(thm)],[c_196,c_761]) ).

tff(c_898,plain,
    ! [A_225,B_226,C_227] :
      ( ( relation_dom_as_subset(A_225,B_226,C_227) = relation_dom(C_227) )
      | ~ relation_of2(C_227,A_225,B_226) ),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_915,plain,
    relation_dom_as_subset('#skF_22','#skF_23','#skF_25') = relation_dom('#skF_25'),
    inference(resolution,[status(thm)],[c_769,c_898]) ).

tff(c_26,plain,
    ! [B_10,A_9,C_11] :
      ( ( empty_set = B_10 )
      | ( relation_dom_as_subset(A_9,B_10,C_11) = A_9 )
      | ~ quasi_total(C_11,A_9,B_10)
      | ~ relation_of2_as_subset(C_11,A_9,B_10) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_1661,plain,
    ! [B_331,A_332,C_333] :
      ( ( B_331 = '#skF_13' )
      | ( relation_dom_as_subset(A_332,B_331,C_333) = A_332 )
      | ~ quasi_total(C_333,A_332,B_331)
      | ~ relation_of2_as_subset(C_333,A_332,B_331) ),
    inference(demodulation,[status(thm),theory(equality)],[c_235,c_26]) ).

tff(c_1670,plain,
    ( ( '#skF_13' = '#skF_23' )
    | ( relation_dom_as_subset('#skF_22','#skF_23','#skF_25') = '#skF_22' )
    | ~ quasi_total('#skF_25','#skF_22','#skF_23') ),
    inference(resolution,[status(thm)],[c_196,c_1661]) ).

tff(c_1675,plain,
    ( ( '#skF_13' = '#skF_23' )
    | ( relation_dom('#skF_25') = '#skF_22' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_198,c_915,c_1670]) ).

tff(c_1676,plain,
    relation_dom('#skF_25') = '#skF_22',
    inference(negUnitSimplification,[status(thm)],[c_268,c_1675]) ).

tff(c_316,plain,
    ! [B_127,A_128] :
      ( ~ empty(B_127)
      | ~ in(A_128,B_127) ),
    inference(cnfTransformation,[status(thm)],[f_292]) ).

tff(c_320,plain,
    ~ empty('#skF_22'),
    inference(resolution,[status(thm)],[c_194,c_316]) ).

tff(c_846,plain,
    ! [C_212,A_213,B_214] :
      ( element(C_212,powerset(cartesian_product2(A_213,B_214)))
      | ~ relation_of2_as_subset(C_212,A_213,B_214) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_8,plain,
    ! [C_7,A_5,B_6] :
      ( relation(C_7)
      | ~ element(C_7,powerset(cartesian_product2(A_5,B_6))) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_858,plain,
    ! [C_215,A_216,B_217] :
      ( relation(C_215)
      | ~ relation_of2_as_subset(C_215,A_216,B_217) ),
    inference(resolution,[status(thm)],[c_846,c_8]) ).

tff(c_870,plain,
    relation('#skF_25'),
    inference(resolution,[status(thm)],[c_196,c_858]) ).

tff(c_178,plain,
    ! [A_93,B_94] :
      ( in(A_93,B_94)
      | empty(B_94)
      | ~ element(A_93,B_94) ),
    inference(cnfTransformation,[status(thm)],[f_253]) ).

tff(c_980,plain,
    ! [A_244,B_245,C_246] :
      ( element(relation_dom_as_subset(A_244,B_245,C_246),powerset(A_244))
      | ~ relation_of2(C_246,A_244,B_245) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_994,plain,
    ( element(relation_dom('#skF_25'),powerset('#skF_22'))
    | ~ relation_of2('#skF_25','#skF_22','#skF_23') ),
    inference(superposition,[status(thm),theory(equality)],[c_915,c_980]) ).

tff(c_1000,plain,
    element(relation_dom('#skF_25'),powerset('#skF_22')),
    inference(demodulation,[status(thm),theory(equality)],[c_769,c_994]) ).

tff(c_184,plain,
    ! [A_97,C_99,B_98] :
      ( element(A_97,C_99)
      | ~ element(B_98,powerset(C_99))
      | ~ in(A_97,B_98) ),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_1011,plain,
    ! [A_247] :
      ( element(A_247,'#skF_22')
      | ~ in(A_247,relation_dom('#skF_25')) ),
    inference(resolution,[status(thm)],[c_1000,c_184]) ).

tff(c_1016,plain,
    ! [A_93] :
      ( element(A_93,'#skF_22')
      | empty(relation_dom('#skF_25'))
      | ~ element(A_93,relation_dom('#skF_25')) ),
    inference(resolution,[status(thm)],[c_178,c_1011]) ).

tff(c_1017,plain,
    empty(relation_dom('#skF_25')),
    inference(splitLeft,[status(thm)],[c_1016]) ).

tff(c_88,plain,
    ! [A_69] :
      ( ~ empty(relation_dom(A_69))
      | ~ relation(A_69)
      | empty(A_69) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_1030,plain,
    ( ~ relation('#skF_25')
    | empty('#skF_25') ),
    inference(resolution,[status(thm)],[c_1017,c_88]) ).

tff(c_1049,plain,
    empty('#skF_25'),
    inference(demodulation,[status(thm),theory(equality)],[c_870,c_1030]) ).

tff(c_188,plain,
    ! [A_103] :
      ( ( empty_set = A_103 )
      | ~ empty(A_103) ),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_238,plain,
    ! [A_103] :
      ( ( A_103 = '#skF_10' )
      | ~ empty(A_103) ),
    inference(demodulation,[status(thm),theory(equality)],[c_233,c_188]) ).

tff(c_307,plain,
    ! [A_103] :
      ( ( A_103 = '#skF_13' )
      | ~ empty(A_103) ),
    inference(demodulation,[status(thm),theory(equality)],[c_267,c_238]) ).

tff(c_1083,plain,
    '#skF_25' = '#skF_13',
    inference(resolution,[status(thm)],[c_1049,c_307]) ).

tff(c_1094,plain,
    quasi_total('#skF_13','#skF_22','#skF_23'),
    inference(demodulation,[status(thm),theory(equality)],[c_1083,c_198]) ).

tff(c_328,plain,
    ! [A_132] :
      ( empty(relation_dom(A_132))
      | ~ empty(A_132) ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_361,plain,
    ! [A_136] :
      ( ( relation_dom(A_136) = '#skF_13' )
      | ~ empty(A_136) ),
    inference(resolution,[status(thm)],[c_328,c_307]) ).

tff(c_373,plain,
    relation_dom('#skF_13') = '#skF_13',
    inference(resolution,[status(thm)],[c_128,c_361]) ).

tff(c_1089,plain,
    relation_dom_as_subset('#skF_22','#skF_23','#skF_13') = relation_dom('#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_1083,c_1083,c_915]) ).

tff(c_1102,plain,
    relation_dom_as_subset('#skF_22','#skF_23','#skF_13') = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_373,c_1089]) ).

tff(c_1095,plain,
    relation_of2_as_subset('#skF_13','#skF_22','#skF_23'),
    inference(demodulation,[status(thm),theory(equality)],[c_1083,c_196]) ).

tff(c_1369,plain,
    ! [B_284,A_285,C_286] :
      ( ( B_284 = '#skF_13' )
      | ( relation_dom_as_subset(A_285,B_284,C_286) = A_285 )
      | ~ quasi_total(C_286,A_285,B_284)
      | ~ relation_of2_as_subset(C_286,A_285,B_284) ),
    inference(demodulation,[status(thm),theory(equality)],[c_235,c_26]) ).

tff(c_1372,plain,
    ( ( '#skF_13' = '#skF_23' )
    | ( relation_dom_as_subset('#skF_22','#skF_23','#skF_13') = '#skF_22' )
    | ~ quasi_total('#skF_13','#skF_22','#skF_23') ),
    inference(resolution,[status(thm)],[c_1095,c_1369]) ).

tff(c_1381,plain,
    ( ( '#skF_13' = '#skF_23' )
    | ( '#skF_13' = '#skF_22' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1094,c_1102,c_1372]) ).

tff(c_1382,plain,
    '#skF_13' = '#skF_22',
    inference(negUnitSimplification,[status(thm)],[c_268,c_1381]) ).

tff(c_1419,plain,
    empty('#skF_22'),
    inference(demodulation,[status(thm),theory(equality)],[c_1382,c_128]) ).

tff(c_1421,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_320,c_1419]) ).

tff(c_1423,plain,
    ~ empty(relation_dom('#skF_25')),
    inference(splitRight,[status(thm)],[c_1016]) ).

tff(c_200,plain,
    function('#skF_25'),
    inference(cnfTransformation,[status(thm)],[f_287]) ).

tff(c_1599,plain,
    ! [A_323,D_324] :
      ( in(apply(A_323,D_324),relation_rng(A_323))
      | ~ in(D_324,relation_dom(A_323))
      | ~ function(A_323)
      | ~ relation(A_323) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_190,plain,
    ~ in(apply('#skF_25','#skF_24'),relation_rng('#skF_25')),
    inference(cnfTransformation,[status(thm)],[f_287]) ).

tff(c_1617,plain,
    ( ~ in('#skF_24',relation_dom('#skF_25'))
    | ~ function('#skF_25')
    | ~ relation('#skF_25') ),
    inference(resolution,[status(thm)],[c_1599,c_190]) ).

tff(c_1635,plain,
    ~ in('#skF_24',relation_dom('#skF_25')),
    inference(demodulation,[status(thm),theory(equality)],[c_870,c_200,c_1617]) ).

tff(c_1643,plain,
    ( empty(relation_dom('#skF_25'))
    | ~ element('#skF_24',relation_dom('#skF_25')) ),
    inference(resolution,[status(thm)],[c_178,c_1635]) ).

tff(c_1646,plain,
    ~ element('#skF_24',relation_dom('#skF_25')),
    inference(negUnitSimplification,[status(thm)],[c_1423,c_1643]) ).

tff(c_1677,plain,
    ~ element('#skF_24','#skF_22'),
    inference(demodulation,[status(thm),theory(equality)],[c_1676,c_1646]) ).

tff(c_1688,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_1677]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 11:56:38 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 6.12/2.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.12/2.49  
% 6.12/2.49  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.50/2.53  
% 6.50/2.53  Inference rules
% 6.50/2.53  ----------------------
% 6.50/2.53  #Ref     : 0
% 6.50/2.53  #Sup     : 309
% 6.50/2.53  #Fact    : 0
% 6.50/2.53  #Define  : 0
% 6.50/2.53  #Split   : 7
% 6.50/2.53  #Chain   : 0
% 6.50/2.53  #Close   : 0
% 6.50/2.53  
% 6.50/2.53  Ordering : KBO
% 6.50/2.53  
% 6.50/2.53  Simplification rules
% 6.50/2.53  ----------------------
% 6.50/2.53  #Subsume      : 48
% 6.50/2.53  #Demod        : 302
% 6.50/2.53  #Tautology    : 127
% 6.50/2.53  #SimpNegUnit  : 11
% 6.50/2.53  #BackRed      : 74
% 6.50/2.53  
% 6.50/2.53  #Partial instantiations: 0
% 6.50/2.53  #Strategies tried      : 1
% 6.50/2.53  
% 6.50/2.53  Timing (in seconds)
% 6.50/2.53  ----------------------
% 6.50/2.53  Preprocessing        : 0.66
% 6.50/2.53  Parsing              : 0.32
% 6.50/2.53  CNF conversion       : 0.06
% 6.50/2.53  Main loop            : 0.75
% 6.50/2.53  Inferencing          : 0.26
% 6.50/2.53  Reduction            : 0.23
% 6.50/2.53  Demodulation         : 0.16
% 6.50/2.53  BG Simplification    : 0.04
% 6.50/2.53  Subsumption          : 0.16
% 6.50/2.53  Abstraction          : 0.02
% 6.50/2.53  MUC search           : 0.00
% 6.50/2.53  Cooper               : 0.00
% 6.50/2.53  Total                : 1.47
% 6.50/2.53  Index Insertion      : 0.00
% 6.50/2.53  Index Deletion       : 0.00
% 6.50/2.53  Index Matching       : 0.00
% 6.50/2.53  BG Taut test         : 0.00
%------------------------------------------------------------------------------