TSTP Solution File: SEU310+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU310+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 : n024.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 13.86s 4.44s
% Output   : CNFRefutation 13.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  188 (  43 unt;  34 typ;   0 def)
%            Number of atoms       :  504 (  87 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  654 ( 304   ~; 333   |;  10   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   41 (  31   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   3 con; 0-3 aty)
%            Number of variables   :  138 (; 135   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ 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 > set_difference > #nlpp > the_carrier > powerset > cast_as_carrier_subset > #skF_13 > #skF_7 > #skF_11 > #skF_4 > #skF_8 > #skF_12 > #skF_5 > #skF_2 > #skF_10 > #skF_1 > #skF_3 > #skF_9 > #skF_6

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_13',type,
    '#skF_13': ( $i * $i * $i ) > $i ).

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

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

tff(set_difference,type,
    set_difference: ( $i * $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_5',type,
    '#skF_5': $i ).

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

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

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

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

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

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

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

tff(f_41,negated_conjecture,
    ~ ! [A,B] :
        ( ( topological_space(A)
          & top_str(A)
          & element(B,powerset(powerset(the_carrier(A)))) )
       => ? [C] :
          ! [D] :
            ( in(D,C)
          <=> ( in(D,powerset(the_carrier(A)))
              & in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).

tff(f_306,axiom,
    ! [A,B] :
      ( ( topological_space(A)
        & top_str(A)
        & element(B,powerset(powerset(the_carrier(A)))) )
     => ( ! [C,D,E] :
            ( ( ( C = D )
              & in(set_difference(cast_as_carrier_subset(A),D),B)
              & ( C = E )
              & in(set_difference(cast_as_carrier_subset(A),E),B) )
           => ( D = E ) )
       => ? [C] :
          ! [D] :
            ( in(D,C)
          <=> ? [E] :
                ( in(E,powerset(the_carrier(A)))
                & ( E = D )
                & in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).

tff(f_261,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

tff(c_18,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | in('#skF_4'(C_4),C_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_14,plain,
    ! [C_4] :
      ( ~ in('#skF_3'(C_4),C_4)
      | in('#skF_4'(C_4),C_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_6,plain,
    topological_space('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_4,plain,
    top_str('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_2,plain,
    element('#skF_2',powerset(powerset(the_carrier('#skF_1')))),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_1415,plain,
    ! [A_299,B_300,D_301] :
      ( ( '#skF_11'(A_299,B_300) = '#skF_9'(A_299,B_300) )
      | in(set_difference(cast_as_carrier_subset(A_299),D_301),B_300)
      | ~ in(D_301,'#skF_12'(A_299,B_300))
      | ~ element(B_300,powerset(powerset(the_carrier(A_299))))
      | ~ top_str(A_299)
      | ~ topological_space(A_299) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1423,plain,
    ! [D_301] :
      ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in(set_difference(cast_as_carrier_subset('#skF_1'),D_301),'#skF_2')
      | ~ in(D_301,'#skF_12'('#skF_1','#skF_2'))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_2,c_1415]) ).

tff(c_1430,plain,
    ! [D_301] :
      ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in(set_difference(cast_as_carrier_subset('#skF_1'),D_301),'#skF_2')
      | ~ in(D_301,'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_1423]) ).

tff(c_2228,plain,
    '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2'),
    inference(splitLeft,[status(thm)],[c_1430]) ).

tff(c_1452,plain,
    ! [A_308,B_309,D_310] :
      ( ( '#skF_11'(A_308,B_309) != '#skF_10'(A_308,B_309) )
      | in(set_difference(cast_as_carrier_subset(A_308),D_310),B_309)
      | ~ in(D_310,'#skF_12'(A_308,B_309))
      | ~ element(B_309,powerset(powerset(the_carrier(A_308))))
      | ~ top_str(A_308)
      | ~ topological_space(A_308) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1460,plain,
    ! [D_310] :
      ( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
      | in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
      | ~ in(D_310,'#skF_12'('#skF_1','#skF_2'))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_2,c_1452]) ).

tff(c_1467,plain,
    ! [D_310] :
      ( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
      | in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
      | ~ in(D_310,'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_1460]) ).

tff(c_2243,plain,
    ! [D_310] :
      ( ( '#skF_10'('#skF_1','#skF_2') != '#skF_9'('#skF_1','#skF_2') )
      | in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
      | ~ in(D_310,'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2228,c_1467]) ).

tff(c_2244,plain,
    '#skF_10'('#skF_1','#skF_2') != '#skF_9'('#skF_1','#skF_2'),
    inference(splitLeft,[status(thm)],[c_2243]) ).

tff(c_16,plain,
    ! [C_4] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
      | in('#skF_4'(C_4),C_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_2699,plain,
    ! [A_438,B_439,E_440] :
      ( ( '#skF_10'(A_438,B_439) = '#skF_9'(A_438,B_439) )
      | in(E_440,'#skF_12'(A_438,B_439))
      | ~ in(set_difference(cast_as_carrier_subset(A_438),E_440),B_439)
      | ~ in(E_440,powerset(the_carrier(A_438)))
      | ~ element(B_439,powerset(powerset(the_carrier(A_438))))
      | ~ top_str(A_438)
      | ~ topological_space(A_438) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_2741,plain,
    ! [C_4] :
      ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | in('#skF_4'(C_4),C_4) ),
    inference(resolution,[status(thm)],[c_16,c_2699]) ).

tff(c_2785,plain,
    ! [C_4] :
      ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | in('#skF_4'(C_4),C_4) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_2741]) ).

tff(c_2788,plain,
    ! [C_441] :
      ( in('#skF_3'(C_441),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_441),powerset(the_carrier('#skF_1')))
      | in('#skF_4'(C_441),C_441) ),
    inference(negUnitSimplification,[status(thm)],[c_2244,c_2785]) ).

tff(c_2807,plain,
    ! [C_442] :
      ( in('#skF_3'(C_442),'#skF_12'('#skF_1','#skF_2'))
      | in('#skF_4'(C_442),C_442) ),
    inference(resolution,[status(thm)],[c_18,c_2788]) ).

tff(c_190,plain,
    ! [A_63,B_64,D_84] :
      ( ( '#skF_10'(A_63,B_64) = '#skF_9'(A_63,B_64) )
      | ( '#skF_13'(A_63,B_64,D_84) = D_84 )
      | ~ in(D_84,'#skF_12'(A_63,B_64))
      | ~ element(B_64,powerset(powerset(the_carrier(A_63))))
      | ~ top_str(A_63)
      | ~ topological_space(A_63) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_3675,plain,
    ! [A_521,B_522] :
      ( ( '#skF_10'(A_521,B_522) = '#skF_9'(A_521,B_522) )
      | ( '#skF_13'(A_521,B_522,'#skF_4'('#skF_12'(A_521,B_522))) = '#skF_4'('#skF_12'(A_521,B_522)) )
      | ~ element(B_522,powerset(powerset(the_carrier(A_521))))
      | ~ top_str(A_521)
      | ~ topological_space(A_521)
      | in('#skF_3'('#skF_12'(A_521,B_522)),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_2807,c_190]) ).

tff(c_1271,plain,
    ! [A_266,B_267,D_268] :
      ( ( '#skF_10'(A_266,B_267) = '#skF_9'(A_266,B_267) )
      | ( '#skF_13'(A_266,B_267,D_268) = D_268 )
      | ~ in(D_268,'#skF_12'(A_266,B_267))
      | ~ element(B_267,powerset(powerset(the_carrier(A_266))))
      | ~ top_str(A_266)
      | ~ topological_space(A_266) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1283,plain,
    ! [A_266,B_267] :
      ( ( '#skF_10'(A_266,B_267) = '#skF_9'(A_266,B_267) )
      | ( '#skF_13'(A_266,B_267,'#skF_4'('#skF_12'(A_266,B_267))) = '#skF_4'('#skF_12'(A_266,B_267)) )
      | ~ element(B_267,powerset(powerset(the_carrier(A_266))))
      | ~ top_str(A_266)
      | ~ topological_space(A_266)
      | ~ in('#skF_3'('#skF_12'(A_266,B_267)),'#skF_12'(A_266,B_267)) ),
    inference(resolution,[status(thm)],[c_14,c_1271]) ).

tff(c_3740,plain,
    ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) )
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_3675,c_1283]) ).

tff(c_3800,plain,
    ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_3740]) ).

tff(c_3801,plain,
    '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')),
    inference(negUnitSimplification,[status(thm)],[c_2244,c_3800]) ).

tff(c_2076,plain,
    ! [A_381,B_382,D_383] :
      ( ( '#skF_10'(A_381,B_382) = '#skF_9'(A_381,B_382) )
      | in('#skF_13'(A_381,B_382,D_383),powerset(the_carrier(A_381)))
      | ~ in(D_383,'#skF_12'(A_381,B_382))
      | ~ element(B_382,powerset(powerset(the_carrier(A_381))))
      | ~ top_str(A_381)
      | ~ topological_space(A_381) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_154,plain,
    ! [B_58,A_57] :
      ( ~ in(B_58,A_57)
      | ~ in(A_57,B_58) ),
    inference(cnfTransformation,[status(thm)],[f_261]) ).

tff(c_2097,plain,
    ! [A_381,B_382,D_383] :
      ( ~ in(powerset(the_carrier(A_381)),'#skF_13'(A_381,B_382,D_383))
      | ( '#skF_10'(A_381,B_382) = '#skF_9'(A_381,B_382) )
      | ~ in(D_383,'#skF_12'(A_381,B_382))
      | ~ element(B_382,powerset(powerset(the_carrier(A_381))))
      | ~ top_str(A_381)
      | ~ topological_space(A_381) ),
    inference(resolution,[status(thm)],[c_2076,c_154]) ).

tff(c_3836,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_3801,c_2097]) ).

tff(c_3878,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_3836]) ).

tff(c_3879,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_2244,c_3878]) ).

tff(c_3896,plain,
    ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(splitLeft,[status(thm)],[c_3879]) ).

tff(c_3929,plain,
    ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_14,c_3896]) ).

tff(c_2806,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | in('#skF_4'(C_4),C_4) ),
    inference(resolution,[status(thm)],[c_18,c_2788]) ).

tff(c_3928,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_2806,c_3896]) ).

tff(c_3938,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3929,c_3928]) ).

tff(c_3940,plain,
    in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_3879]) ).

tff(c_1493,plain,
    ! [A_314,B_315,D_316] :
      ( ( '#skF_10'(A_314,B_315) = '#skF_9'(A_314,B_315) )
      | in(set_difference(cast_as_carrier_subset(A_314),D_316),B_315)
      | ~ in(D_316,'#skF_12'(A_314,B_315))
      | ~ element(B_315,powerset(powerset(the_carrier(A_314))))
      | ~ top_str(A_314)
      | ~ topological_space(A_314) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1501,plain,
    ! [D_316] :
      ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in(set_difference(cast_as_carrier_subset('#skF_1'),D_316),'#skF_2')
      | ~ in(D_316,'#skF_12'('#skF_1','#skF_2'))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_2,c_1493]) ).

tff(c_1508,plain,
    ! [D_316] :
      ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in(set_difference(cast_as_carrier_subset('#skF_1'),D_316),'#skF_2')
      | ~ in(D_316,'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_1501]) ).

tff(c_2290,plain,
    ! [D_316] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),D_316),'#skF_2')
      | ~ in(D_316,'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_2244,c_1508]) ).

tff(c_200,plain,
    ! [A_63,B_64,D_84] :
      ( ( '#skF_10'(A_63,B_64) = '#skF_9'(A_63,B_64) )
      | in('#skF_13'(A_63,B_64,D_84),powerset(the_carrier(A_63)))
      | ~ in(D_84,'#skF_12'(A_63,B_64))
      | ~ element(B_64,powerset(powerset(the_carrier(A_63))))
      | ~ top_str(A_63)
      | ~ topological_space(A_63) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_3854,plain,
    ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_3801,c_200]) ).

tff(c_3891,plain,
    ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_3854]) ).

tff(c_3892,plain,
    ( in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_2244,c_3891]) ).

tff(c_4048,plain,
    in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_3940,c_3892]) ).

tff(c_2291,plain,
    ! [D_406] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),D_406),'#skF_2')
      | ~ in(D_406,'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_2244,c_1508]) ).

tff(c_12,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'(C_4)),'#skF_2')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1'))) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_2301,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_2291,c_12]) ).

tff(c_4057,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_4048,c_2301]) ).

tff(c_4068,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_3940,c_4057]) ).

tff(c_10,plain,
    ! [C_4] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
      | ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'(C_4)),'#skF_2')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1'))) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_2300,plain,
    ! [C_4] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_2291,c_10]) ).

tff(c_2715,plain,
    ! [C_4] :
      ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_2300,c_2699]) ).

tff(c_2757,plain,
    ! [C_4] :
      ( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_2715]) ).

tff(c_2758,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_2244,c_2757]) ).

tff(c_4051,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_4048,c_2758]) ).

tff(c_4062,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3940,c_4051]) ).

tff(c_4093,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_4068,c_4062]) ).

tff(c_8,plain,
    ! [C_4] :
      ( ~ in('#skF_3'(C_4),C_4)
      | ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'(C_4)),'#skF_2')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1'))) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_4117,plain,
    ( ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2')
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
    inference(resolution,[status(thm)],[c_4093,c_8]) ).

tff(c_4149,plain,
    ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_4048,c_4117]) ).

tff(c_4153,plain,
    ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_2290,c_4149]) ).

tff(c_4163,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3940,c_4153]) ).

tff(c_4165,plain,
    '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2'),
    inference(splitRight,[status(thm)],[c_2243]) ).

tff(c_4417,plain,
    ! [A_548,B_549,E_550] :
      ( ( '#skF_11'(A_548,B_549) != '#skF_10'(A_548,B_549) )
      | in(E_550,'#skF_12'(A_548,B_549))
      | ~ in(set_difference(cast_as_carrier_subset(A_548),E_550),B_549)
      | ~ in(E_550,powerset(the_carrier(A_548)))
      | ~ element(B_549,powerset(powerset(the_carrier(A_548))))
      | ~ top_str(A_548)
      | ~ topological_space(A_548) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_4455,plain,
    ! [C_4] :
      ( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | in('#skF_4'(C_4),C_4) ),
    inference(resolution,[status(thm)],[c_16,c_4417]) ).

tff(c_4490,plain,
    ! [C_551] :
      ( in('#skF_3'(C_551),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_551),powerset(the_carrier('#skF_1')))
      | in('#skF_4'(C_551),C_551) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_4455]) ).

tff(c_4509,plain,
    ! [C_552] :
      ( in('#skF_3'(C_552),'#skF_12'('#skF_1','#skF_2'))
      | in('#skF_4'(C_552),C_552) ),
    inference(resolution,[status(thm)],[c_18,c_4490]) ).

tff(c_182,plain,
    ! [A_63,B_64,D_84] :
      ( ( '#skF_11'(A_63,B_64) != '#skF_10'(A_63,B_64) )
      | ( '#skF_13'(A_63,B_64,D_84) = D_84 )
      | ~ in(D_84,'#skF_12'(A_63,B_64))
      | ~ element(B_64,powerset(powerset(the_carrier(A_63))))
      | ~ top_str(A_63)
      | ~ topological_space(A_63) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_5648,plain,
    ! [A_651,B_652] :
      ( ( '#skF_11'(A_651,B_652) != '#skF_10'(A_651,B_652) )
      | ( '#skF_13'(A_651,B_652,'#skF_4'('#skF_12'(A_651,B_652))) = '#skF_4'('#skF_12'(A_651,B_652)) )
      | ~ element(B_652,powerset(powerset(the_carrier(A_651))))
      | ~ top_str(A_651)
      | ~ topological_space(A_651)
      | in('#skF_3'('#skF_12'(A_651,B_652)),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_4509,c_182]) ).

tff(c_1309,plain,
    ! [A_274,B_275,D_276] :
      ( ( '#skF_11'(A_274,B_275) != '#skF_10'(A_274,B_275) )
      | ( '#skF_13'(A_274,B_275,D_276) = D_276 )
      | ~ in(D_276,'#skF_12'(A_274,B_275))
      | ~ element(B_275,powerset(powerset(the_carrier(A_274))))
      | ~ top_str(A_274)
      | ~ topological_space(A_274) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1321,plain,
    ! [A_274,B_275] :
      ( ( '#skF_11'(A_274,B_275) != '#skF_10'(A_274,B_275) )
      | ( '#skF_13'(A_274,B_275,'#skF_4'('#skF_12'(A_274,B_275))) = '#skF_4'('#skF_12'(A_274,B_275)) )
      | ~ element(B_275,powerset(powerset(the_carrier(A_274))))
      | ~ top_str(A_274)
      | ~ topological_space(A_274)
      | ~ in('#skF_3'('#skF_12'(A_274,B_275)),'#skF_12'(A_274,B_275)) ),
    inference(resolution,[status(thm)],[c_14,c_1309]) ).

tff(c_5709,plain,
    ( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
    | ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) )
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_5648,c_1321]) ).

tff(c_5768,plain,
    '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_5709]) ).

tff(c_2162,plain,
    ! [A_394,B_395,D_396] :
      ( ( '#skF_11'(A_394,B_395) != '#skF_10'(A_394,B_395) )
      | in('#skF_13'(A_394,B_395,D_396),powerset(the_carrier(A_394)))
      | ~ in(D_396,'#skF_12'(A_394,B_395))
      | ~ element(B_395,powerset(powerset(the_carrier(A_394))))
      | ~ top_str(A_394)
      | ~ topological_space(A_394) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_2183,plain,
    ! [A_394,B_395,D_396] :
      ( ~ in(powerset(the_carrier(A_394)),'#skF_13'(A_394,B_395,D_396))
      | ( '#skF_11'(A_394,B_395) != '#skF_10'(A_394,B_395) )
      | ~ in(D_396,'#skF_12'(A_394,B_395))
      | ~ element(B_395,powerset(powerset(the_carrier(A_394))))
      | ~ top_str(A_394)
      | ~ topological_space(A_394) ),
    inference(resolution,[status(thm)],[c_2162,c_154]) ).

tff(c_5803,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_5768,c_2183]) ).

tff(c_5845,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_5803]) ).

tff(c_5861,plain,
    ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(splitLeft,[status(thm)],[c_5845]) ).

tff(c_5875,plain,
    ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_14,c_5861]) ).

tff(c_4508,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | in('#skF_4'(C_4),C_4) ),
    inference(resolution,[status(thm)],[c_18,c_4490]) ).

tff(c_5874,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_4508,c_5861]) ).

tff(c_5960,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5875,c_5874]) ).

tff(c_5962,plain,
    in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_5845]) ).

tff(c_4164,plain,
    ! [D_310] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
      | ~ in(D_310,'#skF_12'('#skF_1','#skF_2')) ),
    inference(splitRight,[status(thm)],[c_2243]) ).

tff(c_192,plain,
    ! [A_63,B_64,D_84] :
      ( ( '#skF_11'(A_63,B_64) != '#skF_10'(A_63,B_64) )
      | in('#skF_13'(A_63,B_64,D_84),powerset(the_carrier(A_63)))
      | ~ in(D_84,'#skF_12'(A_63,B_64))
      | ~ element(B_64,powerset(powerset(the_carrier(A_63))))
      | ~ top_str(A_63)
      | ~ topological_space(A_63) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_5818,plain,
    ( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
    | in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_5768,c_192]) ).

tff(c_5855,plain,
    ( in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_5818]) ).

tff(c_6011,plain,
    in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_5962,c_5855]) ).

tff(c_4231,plain,
    ! [D_534] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),D_534),'#skF_2')
      | ~ in(D_534,'#skF_12'('#skF_1','#skF_2')) ),
    inference(splitRight,[status(thm)],[c_2243]) ).

tff(c_4241,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_4231,c_12]) ).

tff(c_6020,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_6011,c_4241]) ).

tff(c_6031,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_5962,c_6020]) ).

tff(c_4240,plain,
    ! [C_4] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_4231,c_10]) ).

tff(c_4429,plain,
    ! [C_4] :
      ( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_4240,c_4417]) ).

tff(c_4465,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_4429]) ).

tff(c_6014,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_6011,c_4465]) ).

tff(c_6025,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5962,c_6014]) ).

tff(c_6114,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_6031,c_6025]) ).

tff(c_6138,plain,
    ( ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2')
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
    inference(resolution,[status(thm)],[c_6114,c_8]) ).

tff(c_6168,plain,
    ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_6011,c_6138]) ).

tff(c_6191,plain,
    ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_4164,c_6168]) ).

tff(c_6201,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5962,c_6191]) ).

tff(c_6203,plain,
    '#skF_11'('#skF_1','#skF_2') != '#skF_9'('#skF_1','#skF_2'),
    inference(splitRight,[status(thm)],[c_1430]) ).

tff(c_6899,plain,
    ! [A_717,B_718,E_719] :
      ( ( '#skF_11'(A_717,B_718) = '#skF_9'(A_717,B_718) )
      | in(E_719,'#skF_12'(A_717,B_718))
      | ~ in(set_difference(cast_as_carrier_subset(A_717),E_719),B_718)
      | ~ in(E_719,powerset(the_carrier(A_717)))
      | ~ element(B_718,powerset(powerset(the_carrier(A_717))))
      | ~ top_str(A_717)
      | ~ topological_space(A_717) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_6945,plain,
    ! [C_4] :
      ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | in('#skF_4'(C_4),C_4) ),
    inference(resolution,[status(thm)],[c_16,c_6899]) ).

tff(c_6994,plain,
    ! [C_4] :
      ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | in('#skF_4'(C_4),C_4) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_6945]) ).

tff(c_6997,plain,
    ! [C_720] :
      ( in('#skF_3'(C_720),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_720),powerset(the_carrier('#skF_1')))
      | in('#skF_4'(C_720),C_720) ),
    inference(negUnitSimplification,[status(thm)],[c_6203,c_6994]) ).

tff(c_7015,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | in('#skF_4'(C_4),C_4) ),
    inference(resolution,[status(thm)],[c_18,c_6997]) ).

tff(c_7016,plain,
    ! [C_721] :
      ( in('#skF_3'(C_721),'#skF_12'('#skF_1','#skF_2'))
      | in('#skF_4'(C_721),C_721) ),
    inference(resolution,[status(thm)],[c_18,c_6997]) ).

tff(c_186,plain,
    ! [A_63,B_64,D_84] :
      ( ( '#skF_11'(A_63,B_64) = '#skF_9'(A_63,B_64) )
      | ( '#skF_13'(A_63,B_64,D_84) = D_84 )
      | ~ in(D_84,'#skF_12'(A_63,B_64))
      | ~ element(B_64,powerset(powerset(the_carrier(A_63))))
      | ~ top_str(A_63)
      | ~ topological_space(A_63) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_7669,plain,
    ! [A_785,B_786] :
      ( ( '#skF_11'(A_785,B_786) = '#skF_9'(A_785,B_786) )
      | ( '#skF_13'(A_785,B_786,'#skF_4'('#skF_12'(A_785,B_786))) = '#skF_4'('#skF_12'(A_785,B_786)) )
      | ~ element(B_786,powerset(powerset(the_carrier(A_785))))
      | ~ top_str(A_785)
      | ~ topological_space(A_785)
      | in('#skF_3'('#skF_12'(A_785,B_786)),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_7016,c_186]) ).

tff(c_1374,plain,
    ! [A_287,B_288,D_289] :
      ( ( '#skF_11'(A_287,B_288) = '#skF_9'(A_287,B_288) )
      | ( '#skF_13'(A_287,B_288,D_289) = D_289 )
      | ~ in(D_289,'#skF_12'(A_287,B_288))
      | ~ element(B_288,powerset(powerset(the_carrier(A_287))))
      | ~ top_str(A_287)
      | ~ topological_space(A_287) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1386,plain,
    ! [A_287,B_288] :
      ( ( '#skF_11'(A_287,B_288) = '#skF_9'(A_287,B_288) )
      | ( '#skF_13'(A_287,B_288,'#skF_4'('#skF_12'(A_287,B_288))) = '#skF_4'('#skF_12'(A_287,B_288)) )
      | ~ element(B_288,powerset(powerset(the_carrier(A_287))))
      | ~ top_str(A_287)
      | ~ topological_space(A_287)
      | ~ in('#skF_3'('#skF_12'(A_287,B_288)),'#skF_12'(A_287,B_288)) ),
    inference(resolution,[status(thm)],[c_14,c_1374]) ).

tff(c_7724,plain,
    ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) )
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(resolution,[status(thm)],[c_7669,c_1386]) ).

tff(c_7783,plain,
    ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_7724]) ).

tff(c_7784,plain,
    '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')),
    inference(negUnitSimplification,[status(thm)],[c_6203,c_7783]) ).

tff(c_1720,plain,
    ! [A_353,B_354,D_355] :
      ( ( '#skF_11'(A_353,B_354) = '#skF_9'(A_353,B_354) )
      | in('#skF_13'(A_353,B_354,D_355),powerset(the_carrier(A_353)))
      | ~ in(D_355,'#skF_12'(A_353,B_354))
      | ~ element(B_354,powerset(powerset(the_carrier(A_353))))
      | ~ top_str(A_353)
      | ~ topological_space(A_353) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1735,plain,
    ! [A_353,B_354,D_355] :
      ( ~ in(powerset(the_carrier(A_353)),'#skF_13'(A_353,B_354,D_355))
      | ( '#skF_11'(A_353,B_354) = '#skF_9'(A_353,B_354) )
      | ~ in(D_355,'#skF_12'(A_353,B_354))
      | ~ element(B_354,powerset(powerset(the_carrier(A_353))))
      | ~ top_str(A_353)
      | ~ topological_space(A_353) ),
    inference(resolution,[status(thm)],[c_1720,c_154]) ).

tff(c_7830,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_7784,c_1735]) ).

tff(c_7872,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_7830]) ).

tff(c_7873,plain,
    ( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_6203,c_7872]) ).

tff(c_7890,plain,
    ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(splitLeft,[status(thm)],[c_7873]) ).

tff(c_7903,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_7015,c_7890]) ).

tff(c_7904,plain,
    ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_14,c_7890]) ).

tff(c_8038,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7903,c_7904]) ).

tff(c_8040,plain,
    in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_7873]) ).

tff(c_6202,plain,
    ! [D_301] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),D_301),'#skF_2')
      | ~ in(D_301,'#skF_12'('#skF_1','#skF_2')) ),
    inference(splitRight,[status(thm)],[c_1430]) ).

tff(c_196,plain,
    ! [A_63,B_64,D_84] :
      ( ( '#skF_11'(A_63,B_64) = '#skF_9'(A_63,B_64) )
      | in('#skF_13'(A_63,B_64,D_84),powerset(the_carrier(A_63)))
      | ~ in(D_84,'#skF_12'(A_63,B_64))
      | ~ element(B_64,powerset(powerset(the_carrier(A_63))))
      | ~ top_str(A_63)
      | ~ topological_space(A_63) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_7853,plain,
    ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
    | ~ top_str('#skF_1')
    | ~ topological_space('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_7784,c_196]) ).

tff(c_7887,plain,
    ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
    | in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_7853]) ).

tff(c_7888,plain,
    ( in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_6203,c_7887]) ).

tff(c_8090,plain,
    in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_8040,c_7888]) ).

tff(c_6204,plain,
    ! [D_665] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),D_665),'#skF_2')
      | ~ in(D_665,'#skF_12'('#skF_1','#skF_2')) ),
    inference(splitRight,[status(thm)],[c_1430]) ).

tff(c_6214,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_6204,c_12]) ).

tff(c_8099,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_8090,c_6214]) ).

tff(c_8110,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
    inference(demodulation,[status(thm),theory(equality)],[c_8040,c_8099]) ).

tff(c_6213,plain,
    ! [C_4] :
      ( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_6204,c_10]) ).

tff(c_6919,plain,
    ! [C_4] :
      ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
      | ~ top_str('#skF_1')
      | ~ topological_space('#skF_1')
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_6213,c_6899]) ).

tff(c_6966,plain,
    ! [C_4] :
      ( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
      | in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_6919]) ).

tff(c_6967,plain,
    ! [C_4] :
      ( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
      | ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
      | ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_6203,c_6966]) ).

tff(c_8093,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_8090,c_6967]) ).

tff(c_8104,plain,
    ( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
    | ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8040,c_8093]) ).

tff(c_8193,plain,
    in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_8110,c_8104]) ).

tff(c_8217,plain,
    ( ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2')
    | ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
    inference(resolution,[status(thm)],[c_8193,c_8]) ).

tff(c_8249,plain,
    ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_8090,c_8217]) ).

tff(c_8272,plain,
    ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
    inference(resolution,[status(thm)],[c_6202,c_8249]) ).

tff(c_8282,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8040,c_8272]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35  % Computer : n024.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 11:28:45 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 13.86/4.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.86/4.45  
% 13.86/4.45  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.99/4.50  
% 13.99/4.50  Inference rules
% 13.99/4.50  ----------------------
% 13.99/4.50  #Ref     : 0
% 13.99/4.50  #Sup     : 1903
% 13.99/4.50  #Fact    : 4
% 13.99/4.50  #Define  : 0
% 13.99/4.50  #Split   : 26
% 13.99/4.50  #Chain   : 0
% 13.99/4.50  #Close   : 0
% 13.99/4.50  
% 13.99/4.50  Ordering : KBO
% 13.99/4.50  
% 13.99/4.50  Simplification rules
% 13.99/4.50  ----------------------
% 13.99/4.50  #Subsume      : 461
% 13.99/4.50  #Demod        : 1264
% 13.99/4.50  #Tautology    : 384
% 13.99/4.50  #SimpNegUnit  : 51
% 13.99/4.50  #BackRed      : 1
% 13.99/4.50  
% 13.99/4.50  #Partial instantiations: 0
% 13.99/4.50  #Strategies tried      : 1
% 13.99/4.50  
% 13.99/4.50  Timing (in seconds)
% 13.99/4.50  ----------------------
% 13.99/4.51  Preprocessing        : 0.69
% 13.99/4.51  Parsing              : 0.33
% 13.99/4.51  CNF conversion       : 0.06
% 13.99/4.51  Main loop            : 2.70
% 13.99/4.51  Inferencing          : 0.98
% 13.99/4.51  Reduction            : 0.76
% 13.99/4.51  Demodulation         : 0.47
% 13.99/4.51  BG Simplification    : 0.10
% 13.99/4.51  Subsumption          : 0.68
% 13.99/4.51  Abstraction          : 0.11
% 13.99/4.51  MUC search           : 0.00
% 13.99/4.51  Cooper               : 0.00
% 13.99/4.51  Total                : 3.47
% 13.99/4.51  Index Insertion      : 0.00
% 13.99/4.51  Index Deletion       : 0.00
% 13.99/4.51  Index Matching       : 0.00
% 13.99/4.51  BG Taut test         : 0.00
%------------------------------------------------------------------------------