TSTP Solution File: SEU315+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU315+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 : n011.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 10:58:23 EDT 2023

% Result   : Theorem 39.47s 25.28s
% Output   : CNFRefutation 39.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   44
% Syntax   : Number of formulae    :  165 (  58 unt;  35 typ;   0 def)
%            Number of atoms       :  330 (  20 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  369 ( 169   ~; 173   |;  15   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  29   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  18 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   6 con; 0-3 aty)
%            Number of variables   :  101 (;  95   !;   6   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > closed_subset > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > topological_space > top_str > one_sorted_str > natural > empty > #nlpp > the_carrier > powerset > empty_set > #skF_7 > #skF_4 > #skF_8 > #skF_12 > #skF_14 > #skF_5 > #skF_13 > #skF_2 > #skF_1 > #skF_3 > #skF_11 > #skF_9 > #skF_6 > #skF_10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_7',type,
    '#skF_7': $i > $i ).

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

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

tff(v1_int_1,type,
    v1_int_1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

tff(v3_membered,type,
    v3_membered: $i > $o ).

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

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

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

tff(v1_xreal_0,type,
    v1_xreal_0: $i > $o ).

tff(v5_membered,type,
    v5_membered: $i > $o ).

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

tff(v2_membered,type,
    v2_membered: $i > $o ).

tff(v1_membered,type,
    v1_membered: $i > $o ).

tff(v1_xcmplx_0,type,
    v1_xcmplx_0: $i > $o ).

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

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

tff(v1_rat_1,type,
    v1_rat_1: $i > $o ).

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

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

tff(v4_membered,type,
    v4_membered: $i > $o ).

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

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

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

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

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

tff(f_286,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_293,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_204,axiom,
    ! [A] :
    ? [B] :
      ( element(B,powerset(A))
      & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

tff(f_50,negated_conjecture,
    ~ ! [A,B] :
        ( ( topological_space(A)
          & top_str(A)
          & element(B,powerset(the_carrier(A))) )
       => ? [C] :
            ( element(C,powerset(powerset(the_carrier(A))))
            & ! [D] :
                ( element(D,powerset(the_carrier(A)))
               => ( in(D,C)
                <=> ? [E] :
                      ( element(E,powerset(the_carrier(A)))
                      & ( E = D )
                      & closed_subset(E,A)
                      & subset(B,D) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).

tff(f_298,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

tff(f_273,axiom,
    ! [A,B] :
      ( ( ~ empty(A)
       => ( element(B,A)
        <=> in(B,A) ) )
      & ( empty(A)
       => ( element(B,A)
        <=> empty(B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).

tff(f_260,axiom,
    ! [A,B] :
      ( ( topological_space(A)
        & top_str(A)
        & element(B,powerset(the_carrier(A))) )
     => ? [C] :
        ! [D] :
          ( in(D,C)
        <=> ( in(D,powerset(the_carrier(A)))
            & ? [E] :
                ( element(E,powerset(the_carrier(A)))
                & ( E = D )
                & closed_subset(E,A)
                & subset(B,D) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).

tff(f_239,axiom,
    ! [A] : ~ empty(powerset(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

tff(f_284,axiom,
    ! [A,B] :
      ( ! [C] :
          ( in(C,A)
         => in(C,B) )
     => element(A,powerset(B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).

tff(c_178,plain,
    empty('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_286]) ).

tff(c_222,plain,
    ! [A_113] :
      ( ( empty_set = A_113 )
      | ~ empty(A_113) ),
    inference(cnfTransformation,[status(thm)],[f_293]) ).

tff(c_235,plain,
    empty_set = '#skF_13',
    inference(resolution,[status(thm)],[c_178,c_222]) ).

tff(c_116,plain,
    ! [A_57] : empty('#skF_7'(A_57)),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_232,plain,
    ! [A_57] : ( '#skF_7'(A_57) = empty_set ),
    inference(resolution,[status(thm)],[c_116,c_222]) ).

tff(c_248,plain,
    ! [A_57] : ( '#skF_7'(A_57) = '#skF_13' ),
    inference(demodulation,[status(thm),theory(equality)],[c_235,c_232]) ).

tff(c_118,plain,
    ! [A_57] : element('#skF_7'(A_57),powerset(A_57)),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_285,plain,
    ! [A_57] : element('#skF_13',powerset(A_57)),
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_118]) ).

tff(c_286,plain,
    ! [A_122] : element('#skF_13',powerset(A_122)),
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_118]) ).

tff(c_24,plain,
    ! [C_12] :
      ( in('#skF_3'(C_12),C_12)
      | ( '#skF_4'(C_12) = '#skF_3'(C_12) )
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_290,plain,
    ( in('#skF_3'('#skF_13'),'#skF_13')
    | ( '#skF_4'('#skF_13') = '#skF_3'('#skF_13') ) ),
    inference(resolution,[status(thm)],[c_286,c_24]) ).

tff(c_1222,plain,
    '#skF_4'('#skF_13') = '#skF_3'('#skF_13'),
    inference(splitLeft,[status(thm)],[c_290]) ).

tff(c_293,plain,
    ! [C_127] :
      ( in('#skF_3'(C_127),C_127)
      | closed_subset('#skF_4'(C_127),'#skF_1')
      | ~ element(C_127,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_300,plain,
    ( in('#skF_3'('#skF_13'),'#skF_13')
    | closed_subset('#skF_4'('#skF_13'),'#skF_1') ),
    inference(resolution,[status(thm)],[c_285,c_293]) ).

tff(c_1123,plain,
    closed_subset('#skF_4'('#skF_13'),'#skF_1'),
    inference(splitLeft,[status(thm)],[c_300]) ).

tff(c_1223,plain,
    closed_subset('#skF_3'('#skF_13'),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_1222,c_1123]) ).

tff(c_369,plain,
    ! [C_138] :
      ( in('#skF_3'(C_138),C_138)
      | subset('#skF_2','#skF_3'(C_138))
      | ~ element(C_138,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_382,plain,
    ( in('#skF_3'('#skF_13'),'#skF_13')
    | subset('#skF_2','#skF_3'('#skF_13')) ),
    inference(resolution,[status(thm)],[c_285,c_369]) ).

tff(c_1146,plain,
    subset('#skF_2','#skF_3'('#skF_13')),
    inference(splitLeft,[status(thm)],[c_382]) ).

tff(c_440,plain,
    ! [C_147] :
      ( in('#skF_3'(C_147),C_147)
      | element('#skF_4'(C_147),powerset(the_carrier('#skF_1')))
      | ~ element(C_147,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_184,plain,
    ! [B_99,A_98] :
      ( ~ empty(B_99)
      | ~ in(A_98,B_99) ),
    inference(cnfTransformation,[status(thm)],[f_298]) ).

tff(c_3349,plain,
    ! [C_340] :
      ( ~ empty(C_340)
      | element('#skF_4'(C_340),powerset(the_carrier('#skF_1')))
      | ~ element(C_340,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_440,c_184]) ).

tff(c_3448,plain,
    ( ~ empty('#skF_13')
    | element('#skF_3'('#skF_13'),powerset(the_carrier('#skF_1')))
    | ~ element('#skF_13',powerset(powerset(the_carrier('#skF_1')))) ),
    inference(superposition,[status(thm),theory(equality)],[c_1222,c_3349]) ).

tff(c_3481,plain,
    element('#skF_3'('#skF_13'),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_285,c_178,c_3448]) ).

tff(c_10,plain,
    ! [C_12] :
      ( ~ subset('#skF_2','#skF_3'(C_12))
      | ~ closed_subset('#skF_3'(C_12),'#skF_1')
      | ~ element('#skF_3'(C_12),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_3'(C_12),C_12)
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_3534,plain,
    ( ~ subset('#skF_2','#skF_3'('#skF_13'))
    | ~ closed_subset('#skF_3'('#skF_13'),'#skF_1')
    | ~ in('#skF_3'('#skF_13'),'#skF_13')
    | ~ element('#skF_13',powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_3481,c_10]) ).

tff(c_3602,plain,
    ~ in('#skF_3'('#skF_13'),'#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_285,c_1223,c_1146,c_3534]) ).

tff(c_6,plain,
    topological_space('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_4,plain,
    top_str('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_2,plain,
    element('#skF_2',powerset(the_carrier('#skF_1'))),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_162,plain,
    ! [B_91,A_90] :
      ( in(B_91,A_90)
      | ~ element(B_91,A_90)
      | empty(A_90) ),
    inference(cnfTransformation,[status(thm)],[f_273]) ).

tff(c_2849,plain,
    ! [B_285,D_286,A_287] :
      ( subset(B_285,D_286)
      | ~ in(D_286,'#skF_9'(A_287,B_285))
      | ~ element(B_285,powerset(the_carrier(A_287)))
      | ~ top_str(A_287)
      | ~ topological_space(A_287) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_65861,plain,
    ! [B_1473,B_1474,A_1475] :
      ( subset(B_1473,B_1474)
      | ~ element(B_1473,powerset(the_carrier(A_1475)))
      | ~ top_str(A_1475)
      | ~ topological_space(A_1475)
      | ~ element(B_1474,'#skF_9'(A_1475,B_1473))
      | empty('#skF_9'(A_1475,B_1473)) ),
    inference(resolution,[status(thm)],[c_162,c_2849]) ).

tff(c_65905,plain,
    ! [B_1474] :
      ( subset('#skF_2',B_1474)
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | ~ element(B_1474,'#skF_9'('#skF_1','#skF_2'))
      | empty('#skF_9'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_2,c_65861]) ).

tff(c_65943,plain,
    ! [B_1474] :
      ( subset('#skF_2',B_1474)
      | ~ element(B_1474,'#skF_9'('#skF_1','#skF_2'))
      | empty('#skF_9'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_65905]) ).

tff(c_68950,plain,
    empty('#skF_9'('#skF_1','#skF_2')),
    inference(splitLeft,[status(thm)],[c_65943]) ).

tff(c_182,plain,
    ! [A_97] :
      ( ( empty_set = A_97 )
      | ~ empty(A_97) ),
    inference(cnfTransformation,[status(thm)],[f_293]) ).

tff(c_241,plain,
    ! [A_97] :
      ( ( A_97 = '#skF_13' )
      | ~ empty(A_97) ),
    inference(demodulation,[status(thm),theory(equality)],[c_235,c_182]) ).

tff(c_69011,plain,
    '#skF_9'('#skF_1','#skF_2') = '#skF_13',
    inference(resolution,[status(thm)],[c_68950,c_241]) ).

tff(c_146,plain,
    ! [A_67] : ~ empty(powerset(A_67)),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_3321,plain,
    ! [E_336,A_337,B_338] :
      ( in(E_336,'#skF_9'(A_337,B_338))
      | ~ subset(B_338,E_336)
      | ~ closed_subset(E_336,A_337)
      | ~ element(E_336,powerset(the_carrier(A_337)))
      | ~ in(E_336,powerset(the_carrier(A_337)))
      | ~ element(B_338,powerset(the_carrier(A_337)))
      | ~ top_str(A_337)
      | ~ topological_space(A_337) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_3327,plain,
    ! [B_91,A_337,B_338] :
      ( in(B_91,'#skF_9'(A_337,B_338))
      | ~ subset(B_338,B_91)
      | ~ closed_subset(B_91,A_337)
      | ~ element(B_338,powerset(the_carrier(A_337)))
      | ~ top_str(A_337)
      | ~ topological_space(A_337)
      | ~ element(B_91,powerset(the_carrier(A_337)))
      | empty(powerset(the_carrier(A_337))) ),
    inference(resolution,[status(thm)],[c_162,c_3321]) ).

tff(c_73186,plain,
    ! [B_1712,A_1713,B_1714] :
      ( in(B_1712,'#skF_9'(A_1713,B_1714))
      | ~ subset(B_1714,B_1712)
      | ~ closed_subset(B_1712,A_1713)
      | ~ element(B_1714,powerset(the_carrier(A_1713)))
      | ~ top_str(A_1713)
      | ~ topological_space(A_1713)
      | ~ element(B_1712,powerset(the_carrier(A_1713))) ),
    inference(negUnitSimplification,[status(thm)],[c_146,c_3327]) ).

tff(c_73274,plain,
    ! [B_1712] :
      ( in(B_1712,'#skF_9'('#skF_1','#skF_2'))
      | ~ subset('#skF_2',B_1712)
      | ~ closed_subset(B_1712,'#skF_1')
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | ~ element(B_1712,powerset(the_carrier('#skF_1'))) ),
    inference(resolution,[status(thm)],[c_2,c_73186]) ).

tff(c_105682,plain,
    ! [B_2097] :
      ( in(B_2097,'#skF_13')
      | ~ subset('#skF_2',B_2097)
      | ~ closed_subset(B_2097,'#skF_1')
      | ~ element(B_2097,powerset(the_carrier('#skF_1'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_69011,c_73274]) ).

tff(c_105893,plain,
    ( in('#skF_3'('#skF_13'),'#skF_13')
    | ~ subset('#skF_2','#skF_3'('#skF_13'))
    | ~ closed_subset('#skF_3'('#skF_13'),'#skF_1') ),
    inference(resolution,[status(thm)],[c_3481,c_105682]) ).

tff(c_106002,plain,
    in('#skF_3'('#skF_13'),'#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_1223,c_1146,c_105893]) ).

tff(c_106004,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3602,c_106002]) ).

tff(c_106006,plain,
    ~ empty('#skF_9'('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_65943]) ).

tff(c_2214,plain,
    ! [A_270,B_271] :
      ( in('#skF_12'(A_270,B_271),A_270)
      | element(A_270,powerset(B_271)) ),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_160,plain,
    ! [B_91,A_90] :
      ( element(B_91,A_90)
      | ~ in(B_91,A_90)
      | empty(A_90) ),
    inference(cnfTransformation,[status(thm)],[f_273]) ).

tff(c_2228,plain,
    ! [A_270,B_271] :
      ( element('#skF_12'(A_270,B_271),A_270)
      | empty(A_270)
      | element(A_270,powerset(B_271)) ),
    inference(resolution,[status(thm)],[c_2214,c_160]) ).

tff(c_3003,plain,
    ! [D_306,A_307,B_308] :
      ( in(D_306,powerset(the_carrier(A_307)))
      | ~ in(D_306,'#skF_9'(A_307,B_308))
      | ~ element(B_308,powerset(the_carrier(A_307)))
      | ~ top_str(A_307)
      | ~ topological_space(A_307) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_108793,plain,
    ! [B_2222,A_2223,B_2224] :
      ( in(B_2222,powerset(the_carrier(A_2223)))
      | ~ element(B_2224,powerset(the_carrier(A_2223)))
      | ~ top_str(A_2223)
      | ~ topological_space(A_2223)
      | ~ element(B_2222,'#skF_9'(A_2223,B_2224))
      | empty('#skF_9'(A_2223,B_2224)) ),
    inference(resolution,[status(thm)],[c_162,c_3003]) ).

tff(c_108870,plain,
    ! [B_2222] :
      ( in(B_2222,powerset(the_carrier('#skF_1')))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | ~ element(B_2222,'#skF_9'('#skF_1','#skF_2'))
      | empty('#skF_9'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_2,c_108793]) ).

tff(c_108919,plain,
    ! [B_2222] :
      ( in(B_2222,powerset(the_carrier('#skF_1')))
      | ~ element(B_2222,'#skF_9'('#skF_1','#skF_2'))
      | empty('#skF_9'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_108870]) ).

tff(c_109187,plain,
    ! [B_2234] :
      ( in(B_2234,powerset(the_carrier('#skF_1')))
      | ~ element(B_2234,'#skF_9'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_106006,c_108919]) ).

tff(c_174,plain,
    ! [A_94,B_95] :
      ( ~ in('#skF_12'(A_94,B_95),B_95)
      | element(A_94,powerset(B_95)) ),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_173320,plain,
    ! [A_2835] :
      ( element(A_2835,powerset(powerset(the_carrier('#skF_1'))))
      | ~ element('#skF_12'(A_2835,powerset(the_carrier('#skF_1'))),'#skF_9'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_109187,c_174]) ).

tff(c_173330,plain,
    ( empty('#skF_9'('#skF_1','#skF_2'))
    | element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_2228,c_173320]) ).

tff(c_173338,plain,
    element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))),
    inference(negUnitSimplification,[status(thm)],[c_106006,c_173330]) ).

tff(c_16,plain,
    ! [C_12] :
      ( in('#skF_3'(C_12),C_12)
      | subset('#skF_2','#skF_3'(C_12))
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_173511,plain,
    ( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
    | subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) ),
    inference(resolution,[status(thm)],[c_173338,c_16]) ).

tff(c_173516,plain,
    subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),
    inference(splitLeft,[status(thm)],[c_173511]) ).

tff(c_173515,plain,
    ( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
    | ( '#skF_4'('#skF_9'('#skF_1','#skF_2')) = '#skF_3'('#skF_9'('#skF_1','#skF_2')) ) ),
    inference(resolution,[status(thm)],[c_173338,c_24]) ).

tff(c_173552,plain,
    '#skF_4'('#skF_9'('#skF_1','#skF_2')) = '#skF_3'('#skF_9'('#skF_1','#skF_2')),
    inference(splitLeft,[status(thm)],[c_173515]) ).

tff(c_20,plain,
    ! [C_12] :
      ( in('#skF_3'(C_12),C_12)
      | closed_subset('#skF_4'(C_12),'#skF_1')
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_173514,plain,
    ( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
    | closed_subset('#skF_4'('#skF_9'('#skF_1','#skF_2')),'#skF_1') ),
    inference(resolution,[status(thm)],[c_173338,c_20]) ).

tff(c_173546,plain,
    closed_subset('#skF_4'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
    inference(splitLeft,[status(thm)],[c_173514]) ).

tff(c_173553,plain,
    closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_173552,c_173546]) ).

tff(c_28,plain,
    ! [C_12] :
      ( in('#skF_3'(C_12),C_12)
      | element('#skF_4'(C_12),powerset(the_carrier('#skF_1')))
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_8,plain,
    ! [C_12] :
      ( element('#skF_3'(C_12),powerset(the_carrier('#skF_1')))
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_746,plain,
    ! [C_182] :
      ( ~ subset('#skF_2','#skF_3'(C_182))
      | ~ closed_subset('#skF_3'(C_182),'#skF_1')
      | ~ element('#skF_3'(C_182),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_3'(C_182),C_182)
      | ~ element(C_182,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_65665,plain,
    ! [C_1470] :
      ( ~ subset('#skF_2','#skF_3'(C_1470))
      | ~ closed_subset('#skF_3'(C_1470),'#skF_1')
      | ~ in('#skF_3'(C_1470),C_1470)
      | ~ element(C_1470,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_8,c_746]) ).

tff(c_65681,plain,
    ! [C_12] :
      ( ~ subset('#skF_2','#skF_3'(C_12))
      | ~ closed_subset('#skF_3'(C_12),'#skF_1')
      | element('#skF_4'(C_12),powerset(the_carrier('#skF_1')))
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_28,c_65665]) ).

tff(c_173619,plain,
    ( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
    | ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
    | element('#skF_3'('#skF_9'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
    inference(superposition,[status(thm),theory(equality)],[c_173552,c_65681]) ).

tff(c_173694,plain,
    ( ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
    | element('#skF_3'('#skF_9'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173516,c_173619]) ).

tff(c_173704,plain,
    element('#skF_3'('#skF_9'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_173553,c_173694]) ).

tff(c_109933,plain,
    ! [B_2252,A_2253,B_2254] :
      ( in(B_2252,'#skF_9'(A_2253,B_2254))
      | ~ subset(B_2254,B_2252)
      | ~ closed_subset(B_2252,A_2253)
      | ~ element(B_2254,powerset(the_carrier(A_2253)))
      | ~ top_str(A_2253)
      | ~ topological_space(A_2253)
      | ~ element(B_2252,powerset(the_carrier(A_2253))) ),
    inference(negUnitSimplification,[status(thm)],[c_146,c_3327]) ).

tff(c_110015,plain,
    ! [B_2252] :
      ( in(B_2252,'#skF_9'('#skF_1','#skF_2'))
      | ~ subset('#skF_2',B_2252)
      | ~ closed_subset(B_2252,'#skF_1')
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | ~ element(B_2252,powerset(the_carrier('#skF_1'))) ),
    inference(resolution,[status(thm)],[c_2,c_109933]) ).

tff(c_110068,plain,
    ! [B_2252] :
      ( in(B_2252,'#skF_9'('#skF_1','#skF_2'))
      | ~ subset('#skF_2',B_2252)
      | ~ closed_subset(B_2252,'#skF_1')
      | ~ element(B_2252,powerset(the_carrier('#skF_1'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_110015]) ).

tff(c_173712,plain,
    ( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
    | ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
    | ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1') ),
    inference(resolution,[status(thm)],[c_173704,c_110068]) ).

tff(c_173826,plain,
    in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_173553,c_173516,c_173712]) ).

tff(c_749,plain,
    ! [C_12] :
      ( ~ subset('#skF_2','#skF_3'(C_12))
      | ~ closed_subset('#skF_3'(C_12),'#skF_1')
      | ~ in('#skF_3'(C_12),C_12)
      | ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_8,c_746]) ).

tff(c_173907,plain,
    ( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
    | ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
    | ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_173826,c_749]) ).

tff(c_173975,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173553,c_173516,c_173907]) ).

tff(c_173976,plain,
    in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_173515]) ).

tff(c_174009,plain,
    ( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
    | ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
    | ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_173976,c_749]) ).

tff(c_174076,plain,
    ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173516,c_174009]) ).

tff(c_154,plain,
    ! [A_68,B_69,D_86] :
      ( ( '#skF_10'(A_68,B_69,D_86) = D_86 )
      | ~ in(D_86,'#skF_9'(A_68,B_69))
      | ~ element(B_69,powerset(the_carrier(A_68)))
      | ~ top_str(A_68)
      | ~ topological_space(A_68) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_174018,plain,
    ( ( '#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')) )
    | ~ element('#skF_2',powerset(the_carrier('#skF_1')))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_173976,c_154]) ).

tff(c_174086,plain,
    '#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_174018]) ).

tff(c_152,plain,
    ! [A_68,B_69,D_86] :
      ( closed_subset('#skF_10'(A_68,B_69,D_86),A_68)
      | ~ in(D_86,'#skF_9'(A_68,B_69))
      | ~ element(B_69,powerset(the_carrier(A_68)))
      | ~ top_str(A_68)
      | ~ topological_space(A_68) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_174011,plain,
    ( closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1')
    | ~ element('#skF_2',powerset(the_carrier('#skF_1')))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_173976,c_152]) ).

tff(c_174079,plain,
    closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_174011]) ).

tff(c_175454,plain,
    closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_174086,c_174079]) ).

tff(c_175456,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_174076,c_175454]) ).

tff(c_175457,plain,
    in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_173514]) ).

tff(c_177140,plain,
    ( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
    | ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
    | ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
    inference(resolution,[status(thm)],[c_175457,c_749]) ).

tff(c_177207,plain,
    ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173516,c_177140]) ).

tff(c_177149,plain,
    ( ( '#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')) )
    | ~ element('#skF_2',powerset(the_carrier('#skF_1')))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_175457,c_154]) ).

tff(c_177217,plain,
    '#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_177149]) ).

tff(c_177142,plain,
    ( closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1')
    | ~ element('#skF_2',powerset(the_carrier('#skF_1')))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_175457,c_152]) ).

tff(c_177210,plain,
    closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_177142]) ).

tff(c_178350,plain,
    closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_177217,c_177210]) ).

tff(c_178352,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_177207,c_178350]) ).

tff(c_178354,plain,
    ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),
    inference(splitRight,[status(thm)],[c_173511]) ).

tff(c_178353,plain,
    in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_173511]) ).

tff(c_150,plain,
    ! [B_69,D_86,A_68] :
      ( subset(B_69,D_86)
      | ~ in(D_86,'#skF_9'(A_68,B_69))
      | ~ element(B_69,powerset(the_carrier(A_68)))
      | ~ top_str(A_68)
      | ~ topological_space(A_68) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_178402,plain,
    ( subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
    | ~ element('#skF_2',powerset(the_carrier('#skF_1')))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_178353,c_150]) ).

tff(c_178471,plain,
    subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_178402]) ).

tff(c_178473,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_178354,c_178471]) ).

tff(c_178474,plain,
    in('#skF_3'('#skF_13'),'#skF_13'),
    inference(splitRight,[status(thm)],[c_290]) ).

tff(c_178480,plain,
    ~ empty('#skF_13'),
    inference(resolution,[status(thm)],[c_178474,c_184]) ).

tff(c_178485,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_178480]) ).

tff(c_178486,plain,
    in('#skF_3'('#skF_13'),'#skF_13'),
    inference(splitRight,[status(thm)],[c_382]) ).

tff(c_178528,plain,
    ~ empty('#skF_13'),
    inference(resolution,[status(thm)],[c_178486,c_184]) ).

tff(c_178533,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_178528]) ).

tff(c_178534,plain,
    in('#skF_3'('#skF_13'),'#skF_13'),
    inference(splitRight,[status(thm)],[c_300]) ).

tff(c_178540,plain,
    ~ empty('#skF_13'),
    inference(resolution,[status(thm)],[c_178534,c_184]) ).

tff(c_178545,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_178540]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 11:39:36 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 39.47/25.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.56/25.30  
% 39.56/25.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.56/25.34  
% 39.56/25.34  Inference rules
% 39.56/25.34  ----------------------
% 39.56/25.34  #Ref     : 0
% 39.56/25.34  #Sup     : 45082
% 39.56/25.34  #Fact    : 0
% 39.56/25.34  #Define  : 0
% 39.56/25.34  #Split   : 125
% 39.56/25.34  #Chain   : 0
% 39.56/25.34  #Close   : 0
% 39.56/25.34  
% 39.56/25.34  Ordering : KBO
% 39.56/25.34  
% 39.56/25.34  Simplification rules
% 39.56/25.34  ----------------------
% 39.56/25.34  #Subsume      : 25094
% 39.56/25.34  #Demod        : 14962
% 39.56/25.34  #Tautology    : 4254
% 39.56/25.34  #SimpNegUnit  : 5172
% 39.56/25.34  #BackRed      : 20
% 39.56/25.34  
% 39.56/25.34  #Partial instantiations: 0
% 39.56/25.34  #Strategies tried      : 1
% 39.56/25.34  
% 39.56/25.34  Timing (in seconds)
% 39.56/25.34  ----------------------
% 39.56/25.34  Preprocessing        : 0.63
% 39.56/25.34  Parsing              : 0.31
% 39.56/25.34  CNF conversion       : 0.06
% 39.56/25.34  Main loop            : 23.62
% 39.56/25.34  Inferencing          : 4.96
% 39.56/25.34  Reduction            : 7.69
% 39.56/25.34  Demodulation         : 5.33
% 39.56/25.34  BG Simplification    : 0.19
% 39.56/25.34  Subsumption          : 9.39
% 39.56/25.34  Abstraction          : 0.35
% 39.56/25.34  MUC search           : 0.00
% 39.56/25.34  Cooper               : 0.00
% 39.56/25.34  Total                : 24.32
% 39.56/25.34  Index Insertion      : 0.00
% 39.56/25.34  Index Deletion       : 0.00
% 39.56/25.34  Index Matching       : 0.00
% 39.56/25.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------