TSTP Solution File: SEU391+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU391+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 10:58:36 EDT 2023

% Result   : Theorem 101.76s 81.08s
% Output   : CNFRefutation 101.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   91
% Syntax   : Number of formulae    :  214 (  62 unt;  88 typ;   0 def)
%            Number of atoms       :  341 (  42 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  339 ( 124   ~; 198   |;  10   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   92 (  68   >;  24   *;   0   +;   0  <<)
%            Number of predicates  :   40 (  38 usr;   1 prp; 0-3 aty)
%            Number of functors    :   50 (  50 usr;  20 con; 0-3 aty)
%            Number of variables   :   57 (;  56   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > is_eventually_in > upper_relstr_subset > subset > net_str > lower_relstr_subset > in > filtered_subset > element > directed_subset > with_suprema_relstr > with_infima_relstr > v1_yellow_3 > upper_bounded_relstr > up_complete_relstr > trivial_carrier > transitive_relstr > strict_rel_str > relation_empty_yielding > relation > rel_str > reflexive_relstr > one_sorted_str > lower_bounded_relstr > join_complete_relstr > heyting_relstr > finite > empty_carrier > empty > distributive_relstr > directed_relstr > connected_relstr > complete_relstr > complemented_relstr > bounded_relstr > boolean_relstr > antisymmetric_relstr > rel_str_of > filter_of_net_str > cartesian_product2 > a_2_1_yellow19 > #nlpp > the_carrier > the_InternalRel > powerset > cast_as_carrier_subset > boole_POSet > empty_set > #skF_9 > #skF_25 > #skF_5 > #skF_21 > #skF_16 > #skF_6 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_31 > #skF_22 > #skF_38 > #skF_36 > #skF_8 > #skF_19 > #skF_37 > #skF_10 > #skF_34 > #skF_29 > #skF_15 > #skF_26 > #skF_32 > #skF_14 > #skF_28 > #skF_13 > #skF_2 > #skF_1 > #skF_7 > #skF_23 > #skF_33 > #skF_30 > #skF_3 > #skF_35 > #skF_24 > #skF_27 > #skF_40 > #skF_12 > #skF_4 > #skF_39

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_31',type,
    '#skF_31': $i > $i ).

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

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

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

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

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

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

tff('#skF_38',type,
    '#skF_38': $i ).

tff('#skF_36',type,
    '#skF_36': $i ).

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

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

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

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

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

tff('#skF_37',type,
    '#skF_37': $i ).

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

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

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

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

tff('#skF_34',type,
    '#skF_34': $i > $i ).

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

tff('#skF_29',type,
    '#skF_29': $i > $i ).

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

tff('#skF_26',type,
    '#skF_26': $i ).

tff('#skF_32',type,
    '#skF_32': $i > $i ).

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

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

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

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

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

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

tff('#skF_28',type,
    '#skF_28': $i > $i ).

tff(a_2_1_yellow19,type,
    a_2_1_yellow19: ( $i * $i ) > $i ).

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

tff(v1_yellow_3,type,
    v1_yellow_3: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_33',type,
    '#skF_33': $i > $i ).

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

tff('#skF_30',type,
    '#skF_30': $i ).

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

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

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

tff('#skF_35',type,
    '#skF_35': $i ).

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

tff('#skF_27',type,
    '#skF_27': $i ).

tff('#skF_40',type,
    '#skF_40': ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

tff('#skF_39',type,
    '#skF_39': ( $i * $i ) > $i ).

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

tff(f_1035,negated_conjecture,
    ~ ! [A] :
        ( ( ~ empty_carrier(A)
          & one_sorted_str(A) )
       => ! [B] :
            ( ( ~ empty_carrier(B)
              & net_str(B,A) )
           => ! [C] :
                ( in(C,filter_of_net_str(A,B))
              <=> ( is_eventually_in(A,B,C)
                  & element(C,powerset(the_carrier(A))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_yellow19) ).

tff(f_294,axiom,
    ! [A] :
      ( ( ~ empty_carrier(A)
        & one_sorted_str(A) )
     => ! [B] :
          ( ( ~ empty_carrier(B)
            & net_str(B,A) )
         => ( filter_of_net_str(A,B) = a_2_1_yellow19(A,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).

tff(f_629,axiom,
    ! [A,B,C] :
      ( ( ~ empty_carrier(B)
        & one_sorted_str(B)
        & ~ empty_carrier(C)
        & net_str(C,B) )
     => ( in(A,a_2_1_yellow19(B,C))
      <=> ? [D] :
            ( element(D,powerset(the_carrier(B)))
            & ( A = D )
            & is_eventually_in(B,C,D) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).

tff(c_630,plain,
    ~ empty_carrier('#skF_36'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_628,plain,
    net_str('#skF_36','#skF_35'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_634,plain,
    ~ empty_carrier('#skF_35'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_636,plain,
    ( ~ in('#skF_37',filter_of_net_str('#skF_35','#skF_36'))
    | ~ element('#skF_38',powerset(the_carrier('#skF_35')))
    | ~ is_eventually_in('#skF_35','#skF_36','#skF_38') ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_722,plain,
    ~ is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitLeft,[status(thm)],[c_636]) ).

tff(c_632,plain,
    one_sorted_str('#skF_35'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_6408,plain,
    ! [A_947,B_948] :
      ( ( filter_of_net_str(A_947,B_948) = a_2_1_yellow19(A_947,B_948) )
      | ~ net_str(B_948,A_947)
      | empty_carrier(B_948)
      | ~ one_sorted_str(A_947)
      | empty_carrier(A_947) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_6414,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_628,c_6408]) ).

tff(c_6418,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_6414]) ).

tff(c_6419,plain,
    filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36'),
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_6418]) ).

tff(c_644,plain,
    ( element('#skF_37',powerset(the_carrier('#skF_35')))
    | in('#skF_38',filter_of_net_str('#skF_35','#skF_36')) ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_720,plain,
    in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitLeft,[status(thm)],[c_644]) ).

tff(c_6438,plain,
    in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36')),
    inference(demodulation,[status(thm),theory(equality)],[c_6419,c_720]) ).

tff(c_8258,plain,
    ! [A_1041,B_1042,C_1043] :
      ( ( '#skF_7'(A_1041,B_1042,C_1043) = A_1041 )
      | ~ in(A_1041,a_2_1_yellow19(B_1042,C_1043))
      | ~ net_str(C_1043,B_1042)
      | empty_carrier(C_1043)
      | ~ one_sorted_str(B_1042)
      | empty_carrier(B_1042) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_8261,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_6438,c_8258]) ).

tff(c_8292,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_8261]) ).

tff(c_8293,plain,
    '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38',
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_8292]) ).

tff(c_8475,plain,
    ! [B_1053,C_1054,A_1055] :
      ( is_eventually_in(B_1053,C_1054,'#skF_7'(A_1055,B_1053,C_1054))
      | ~ in(A_1055,a_2_1_yellow19(B_1053,C_1054))
      | ~ net_str(C_1054,B_1053)
      | empty_carrier(C_1054)
      | ~ one_sorted_str(B_1053)
      | empty_carrier(B_1053) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_8478,plain,
    ( is_eventually_in('#skF_35','#skF_36','#skF_38')
    | ~ in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36'))
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(superposition,[status(thm),theory(equality)],[c_8293,c_8475]) ).

tff(c_8480,plain,
    ( is_eventually_in('#skF_35','#skF_36','#skF_38')
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_6438,c_8478]) ).

tff(c_8482,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_722,c_8480]) ).

tff(c_8484,plain,
    is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitRight,[status(thm)],[c_636]) ).

tff(c_640,plain,
    ( is_eventually_in('#skF_35','#skF_36','#skF_37')
    | ~ element('#skF_38',powerset(the_carrier('#skF_35')))
    | ~ is_eventually_in('#skF_35','#skF_36','#skF_38') ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_721,plain,
    ~ is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitLeft,[status(thm)],[c_640]) ).

tff(c_8492,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8484,c_721]) ).

tff(c_8493,plain,
    ( ~ element('#skF_38',powerset(the_carrier('#skF_35')))
    | is_eventually_in('#skF_35','#skF_36','#skF_37') ),
    inference(splitRight,[status(thm)],[c_640]) ).

tff(c_8608,plain,
    ~ element('#skF_38',powerset(the_carrier('#skF_35'))),
    inference(splitLeft,[status(thm)],[c_8493]) ).

tff(c_13473,plain,
    ! [A_1803,B_1804] :
      ( ( filter_of_net_str(A_1803,B_1804) = a_2_1_yellow19(A_1803,B_1804) )
      | ~ net_str(B_1804,A_1803)
      | empty_carrier(B_1804)
      | ~ one_sorted_str(A_1803)
      | empty_carrier(A_1803) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_13479,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_628,c_13473]) ).

tff(c_13483,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_13479]) ).

tff(c_13484,plain,
    filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36'),
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_13483]) ).

tff(c_13499,plain,
    in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36')),
    inference(demodulation,[status(thm),theory(equality)],[c_13484,c_720]) ).

tff(c_14726,plain,
    ! [A_1881,B_1882,C_1883] :
      ( ( '#skF_7'(A_1881,B_1882,C_1883) = A_1881 )
      | ~ in(A_1881,a_2_1_yellow19(B_1882,C_1883))
      | ~ net_str(C_1883,B_1882)
      | empty_carrier(C_1883)
      | ~ one_sorted_str(B_1882)
      | empty_carrier(B_1882) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_14729,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_13499,c_14726]) ).

tff(c_14760,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_14729]) ).

tff(c_14761,plain,
    '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38',
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_14760]) ).

tff(c_15224,plain,
    ! [A_1905,B_1906,C_1907] :
      ( element('#skF_7'(A_1905,B_1906,C_1907),powerset(the_carrier(B_1906)))
      | ~ in(A_1905,a_2_1_yellow19(B_1906,C_1907))
      | ~ net_str(C_1907,B_1906)
      | empty_carrier(C_1907)
      | ~ one_sorted_str(B_1906)
      | empty_carrier(B_1906) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_15239,plain,
    ( element('#skF_38',powerset(the_carrier('#skF_35')))
    | ~ in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36'))
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(superposition,[status(thm),theory(equality)],[c_14761,c_15224]) ).

tff(c_15248,plain,
    ( element('#skF_38',powerset(the_carrier('#skF_35')))
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_13499,c_15239]) ).

tff(c_15250,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_8608,c_15248]) ).

tff(c_15251,plain,
    is_eventually_in('#skF_35','#skF_36','#skF_37'),
    inference(splitRight,[status(thm)],[c_8493]) ).

tff(c_8494,plain,
    is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitRight,[status(thm)],[c_640]) ).

tff(c_638,plain,
    ( element('#skF_37',powerset(the_carrier('#skF_35')))
    | ~ element('#skF_38',powerset(the_carrier('#skF_35')))
    | ~ is_eventually_in('#skF_35','#skF_36','#skF_38') ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_8509,plain,
    ~ is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitLeft,[status(thm)],[c_638]) ).

tff(c_8511,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8494,c_8509]) ).

tff(c_8512,plain,
    ( ~ element('#skF_38',powerset(the_carrier('#skF_35')))
    | element('#skF_37',powerset(the_carrier('#skF_35'))) ),
    inference(splitRight,[status(thm)],[c_638]) ).

tff(c_15265,plain,
    ~ element('#skF_38',powerset(the_carrier('#skF_35'))),
    inference(splitLeft,[status(thm)],[c_8512]) ).

tff(c_15252,plain,
    element('#skF_38',powerset(the_carrier('#skF_35'))),
    inference(splitRight,[status(thm)],[c_8493]) ).

tff(c_15288,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_15265,c_15252]) ).

tff(c_15289,plain,
    element('#skF_37',powerset(the_carrier('#skF_35'))),
    inference(splitRight,[status(thm)],[c_8512]) ).

tff(c_23713,plain,
    ! [D_2742,B_2743,C_2744] :
      ( in(D_2742,a_2_1_yellow19(B_2743,C_2744))
      | ~ is_eventually_in(B_2743,C_2744,D_2742)
      | ~ element(D_2742,powerset(the_carrier(B_2743)))
      | ~ net_str(C_2744,B_2743)
      | empty_carrier(C_2744)
      | ~ one_sorted_str(B_2743)
      | empty_carrier(B_2743) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_23801,plain,
    ! [C_2744] :
      ( in('#skF_37',a_2_1_yellow19('#skF_35',C_2744))
      | ~ is_eventually_in('#skF_35',C_2744,'#skF_37')
      | ~ net_str(C_2744,'#skF_35')
      | empty_carrier(C_2744)
      | ~ one_sorted_str('#skF_35')
      | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_15289,c_23713]) ).

tff(c_23855,plain,
    ! [C_2744] :
      ( in('#skF_37',a_2_1_yellow19('#skF_35',C_2744))
      | ~ is_eventually_in('#skF_35',C_2744,'#skF_37')
      | ~ net_str(C_2744,'#skF_35')
      | empty_carrier(C_2744)
      | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_23801]) ).

tff(c_23923,plain,
    ! [C_2747] :
      ( in('#skF_37',a_2_1_yellow19('#skF_35',C_2747))
      | ~ is_eventually_in('#skF_35',C_2747,'#skF_37')
      | ~ net_str(C_2747,'#skF_35')
      | empty_carrier(C_2747) ),
    inference(negUnitSimplification,[status(thm)],[c_634,c_23855]) ).

tff(c_20798,plain,
    ! [A_2605,B_2606] :
      ( ( filter_of_net_str(A_2605,B_2606) = a_2_1_yellow19(A_2605,B_2606) )
      | ~ net_str(B_2606,A_2605)
      | empty_carrier(B_2606)
      | ~ one_sorted_str(A_2605)
      | empty_carrier(A_2605) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_20804,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_628,c_20798]) ).

tff(c_20808,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_20804]) ).

tff(c_20809,plain,
    filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36'),
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_20808]) ).

tff(c_642,plain,
    ( ~ in('#skF_37',filter_of_net_str('#skF_35','#skF_36'))
    | in('#skF_38',filter_of_net_str('#skF_35','#skF_36')) ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_719,plain,
    ~ in('#skF_37',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitLeft,[status(thm)],[c_642]) ).

tff(c_20827,plain,
    ~ in('#skF_37',a_2_1_yellow19('#skF_35','#skF_36')),
    inference(demodulation,[status(thm),theory(equality)],[c_20809,c_719]) ).

tff(c_23931,plain,
    ( ~ is_eventually_in('#skF_35','#skF_36','#skF_37')
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36') ),
    inference(resolution,[status(thm)],[c_23923,c_20827]) ).

tff(c_23958,plain,
    empty_carrier('#skF_36'),
    inference(demodulation,[status(thm),theory(equality)],[c_628,c_15251,c_23931]) ).

tff(c_23960,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_630,c_23958]) ).

tff(c_23962,plain,
    ~ in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitRight,[status(thm)],[c_644]) ).

tff(c_646,plain,
    ( is_eventually_in('#skF_35','#skF_36','#skF_37')
    | in('#skF_38',filter_of_net_str('#skF_35','#skF_36')) ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_718,plain,
    in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitLeft,[status(thm)],[c_646]) ).

tff(c_24057,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_23962,c_718]) ).

tff(c_24059,plain,
    in('#skF_37',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitRight,[status(thm)],[c_642]) ).

tff(c_24061,plain,
    ~ is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitLeft,[status(thm)],[c_640]) ).

tff(c_28758,plain,
    ! [A_3395,B_3396] :
      ( ( filter_of_net_str(A_3395,B_3396) = a_2_1_yellow19(A_3395,B_3396) )
      | ~ net_str(B_3396,A_3395)
      | empty_carrier(B_3396)
      | ~ one_sorted_str(A_3395)
      | empty_carrier(A_3395) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_28764,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_628,c_28758]) ).

tff(c_28768,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_28764]) ).

tff(c_28769,plain,
    filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36'),
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_28768]) ).

tff(c_28794,plain,
    in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36')),
    inference(demodulation,[status(thm),theory(equality)],[c_28769,c_718]) ).

tff(c_29942,plain,
    ! [A_3447,B_3448,C_3449] :
      ( ( '#skF_7'(A_3447,B_3448,C_3449) = A_3447 )
      | ~ in(A_3447,a_2_1_yellow19(B_3448,C_3449))
      | ~ net_str(C_3449,B_3448)
      | empty_carrier(C_3449)
      | ~ one_sorted_str(B_3448)
      | empty_carrier(B_3448) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_29948,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_28794,c_29942]) ).

tff(c_29983,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_29948]) ).

tff(c_29984,plain,
    '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38',
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_29983]) ).

tff(c_30013,plain,
    ! [B_3455,C_3456,A_3457] :
      ( is_eventually_in(B_3455,C_3456,'#skF_7'(A_3457,B_3455,C_3456))
      | ~ in(A_3457,a_2_1_yellow19(B_3455,C_3456))
      | ~ net_str(C_3456,B_3455)
      | empty_carrier(C_3456)
      | ~ one_sorted_str(B_3455)
      | empty_carrier(B_3455) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_30016,plain,
    ( is_eventually_in('#skF_35','#skF_36','#skF_38')
    | ~ in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36'))
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(superposition,[status(thm),theory(equality)],[c_29984,c_30013]) ).

tff(c_30021,plain,
    ( is_eventually_in('#skF_35','#skF_36','#skF_38')
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_28794,c_30016]) ).

tff(c_30023,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_24061,c_30021]) ).

tff(c_30025,plain,
    is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitRight,[status(thm)],[c_640]) ).

tff(c_30026,plain,
    ~ is_eventually_in('#skF_35','#skF_36','#skF_38'),
    inference(splitLeft,[status(thm)],[c_636]) ).

tff(c_30034,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_30025,c_30026]) ).

tff(c_30035,plain,
    ( ~ element('#skF_38',powerset(the_carrier('#skF_35')))
    | ~ in('#skF_37',filter_of_net_str('#skF_35','#skF_36')) ),
    inference(splitRight,[status(thm)],[c_636]) ).

tff(c_30166,plain,
    ~ element('#skF_38',powerset(the_carrier('#skF_35'))),
    inference(demodulation,[status(thm),theory(equality)],[c_24059,c_30035]) ).

tff(c_35080,plain,
    ! [A_4210,B_4211] :
      ( ( filter_of_net_str(A_4210,B_4211) = a_2_1_yellow19(A_4210,B_4211) )
      | ~ net_str(B_4211,A_4210)
      | empty_carrier(B_4211)
      | ~ one_sorted_str(A_4210)
      | empty_carrier(A_4210) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_35086,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_628,c_35080]) ).

tff(c_35090,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_35086]) ).

tff(c_35091,plain,
    filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36'),
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_35090]) ).

tff(c_24058,plain,
    in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitRight,[status(thm)],[c_642]) ).

tff(c_35116,plain,
    in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36')),
    inference(demodulation,[status(thm),theory(equality)],[c_35091,c_24058]) ).

tff(c_36524,plain,
    ! [A_4266,B_4267,C_4268] :
      ( ( '#skF_7'(A_4266,B_4267,C_4268) = A_4266 )
      | ~ in(A_4266,a_2_1_yellow19(B_4267,C_4268))
      | ~ net_str(C_4268,B_4267)
      | empty_carrier(C_4268)
      | ~ one_sorted_str(B_4267)
      | empty_carrier(B_4267) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_36530,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_35116,c_36524]) ).

tff(c_36565,plain,
    ( ( '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38' )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_36530]) ).

tff(c_36566,plain,
    '#skF_7'('#skF_38','#skF_35','#skF_36') = '#skF_38',
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_36565]) ).

tff(c_36763,plain,
    ! [A_4287,B_4288,C_4289] :
      ( element('#skF_7'(A_4287,B_4288,C_4289),powerset(the_carrier(B_4288)))
      | ~ in(A_4287,a_2_1_yellow19(B_4288,C_4289))
      | ~ net_str(C_4289,B_4288)
      | empty_carrier(C_4289)
      | ~ one_sorted_str(B_4288)
      | empty_carrier(B_4288) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_36778,plain,
    ( element('#skF_38',powerset(the_carrier('#skF_35')))
    | ~ in('#skF_38',a_2_1_yellow19('#skF_35','#skF_36'))
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(superposition,[status(thm),theory(equality)],[c_36566,c_36763]) ).

tff(c_36790,plain,
    ( element('#skF_38',powerset(the_carrier('#skF_35')))
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_628,c_35116,c_36778]) ).

tff(c_36792,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_30166,c_36790]) ).

tff(c_36793,plain,
    is_eventually_in('#skF_35','#skF_36','#skF_37'),
    inference(splitRight,[status(thm)],[c_646]) ).

tff(c_36794,plain,
    ~ in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitRight,[status(thm)],[c_646]) ).

tff(c_36795,plain,
    in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitLeft,[status(thm)],[c_644]) ).

tff(c_36824,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36794,c_36795]) ).

tff(c_36825,plain,
    element('#skF_37',powerset(the_carrier('#skF_35'))),
    inference(splitRight,[status(thm)],[c_644]) ).

tff(c_305324,plain,
    ! [D_246389,B_246390,C_246391] :
      ( in(D_246389,a_2_1_yellow19(B_246390,C_246391))
      | ~ is_eventually_in(B_246390,C_246391,D_246389)
      | ~ element(D_246389,powerset(the_carrier(B_246390)))
      | ~ net_str(C_246391,B_246390)
      | empty_carrier(C_246391)
      | ~ one_sorted_str(B_246390)
      | empty_carrier(B_246390) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_305415,plain,
    ! [C_246391] :
      ( in('#skF_37',a_2_1_yellow19('#skF_35',C_246391))
      | ~ is_eventually_in('#skF_35',C_246391,'#skF_37')
      | ~ net_str(C_246391,'#skF_35')
      | empty_carrier(C_246391)
      | ~ one_sorted_str('#skF_35')
      | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_36825,c_305324]) ).

tff(c_305464,plain,
    ! [C_246391] :
      ( in('#skF_37',a_2_1_yellow19('#skF_35',C_246391))
      | ~ is_eventually_in('#skF_35',C_246391,'#skF_37')
      | ~ net_str(C_246391,'#skF_35')
      | empty_carrier(C_246391)
      | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_305415]) ).

tff(c_305527,plain,
    ! [C_246394] :
      ( in('#skF_37',a_2_1_yellow19('#skF_35',C_246394))
      | ~ is_eventually_in('#skF_35',C_246394,'#skF_37')
      | ~ net_str(C_246394,'#skF_35')
      | empty_carrier(C_246394) ),
    inference(negUnitSimplification,[status(thm)],[c_634,c_305464]) ).

tff(c_42125,plain,
    ! [A_5046,B_5047] :
      ( ( filter_of_net_str(A_5046,B_5047) = a_2_1_yellow19(A_5046,B_5047) )
      | ~ net_str(B_5047,A_5046)
      | empty_carrier(B_5047)
      | ~ one_sorted_str(A_5046)
      | empty_carrier(A_5046) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_42131,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | ~ one_sorted_str('#skF_35')
    | empty_carrier('#skF_35') ),
    inference(resolution,[status(thm)],[c_628,c_42125]) ).

tff(c_42135,plain,
    ( ( filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36') )
    | empty_carrier('#skF_36')
    | empty_carrier('#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_632,c_42131]) ).

tff(c_42136,plain,
    filter_of_net_str('#skF_35','#skF_36') = a_2_1_yellow19('#skF_35','#skF_36'),
    inference(negUnitSimplification,[status(thm)],[c_634,c_630,c_42135]) ).

tff(c_36827,plain,
    ~ in('#skF_37',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitLeft,[status(thm)],[c_642]) ).

tff(c_42139,plain,
    ~ in('#skF_37',a_2_1_yellow19('#skF_35','#skF_36')),
    inference(demodulation,[status(thm),theory(equality)],[c_42136,c_36827]) ).

tff(c_305535,plain,
    ( ~ is_eventually_in('#skF_35','#skF_36','#skF_37')
    | ~ net_str('#skF_36','#skF_35')
    | empty_carrier('#skF_36') ),
    inference(resolution,[status(thm)],[c_305527,c_42139]) ).

tff(c_305562,plain,
    empty_carrier('#skF_36'),
    inference(demodulation,[status(thm),theory(equality)],[c_628,c_36793,c_305535]) ).

tff(c_305564,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_630,c_305562]) ).

tff(c_305565,plain,
    in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitRight,[status(thm)],[c_642]) ).

tff(c_36826,plain,
    ~ in('#skF_38',filter_of_net_str('#skF_35','#skF_36')),
    inference(splitRight,[status(thm)],[c_644]) ).

tff(c_305665,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_305565,c_36826]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU391+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % 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
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu Aug  3 12:23:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 101.76/81.08  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.76/81.09  
% 101.76/81.09  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 101.88/81.13  
% 101.88/81.13  Inference rules
% 101.88/81.13  ----------------------
% 101.88/81.13  #Ref     : 20
% 101.88/81.13  #Sup     : 62190
% 101.88/81.13  #Fact    : 1
% 101.88/81.13  #Define  : 0
% 101.88/81.13  #Split   : 762
% 101.88/81.13  #Chain   : 0
% 101.88/81.13  #Close   : 0
% 101.88/81.13  
% 101.88/81.13  Ordering : KBO
% 101.88/81.13  
% 101.88/81.13  Simplification rules
% 101.88/81.13  ----------------------
% 101.88/81.13  #Subsume      : 17581
% 101.88/81.13  #Demod        : 11544
% 101.88/81.13  #Tautology    : 4918
% 101.88/81.13  #SimpNegUnit  : 6841
% 101.88/81.13  #BackRed      : 1975
% 101.88/81.13  
% 101.88/81.13  #Partial instantiations: 297500
% 101.88/81.13  #Strategies tried      : 1
% 101.88/81.13  
% 101.88/81.13  Timing (in seconds)
% 101.88/81.13  ----------------------
% 101.88/81.13  Preprocessing        : 0.79
% 101.88/81.13  Parsing              : 0.39
% 101.88/81.13  CNF conversion       : 0.08
% 101.88/81.13  Main loop            : 79.20
% 101.88/81.13  Inferencing          : 12.37
% 101.88/81.13  Reduction            : 30.02
% 101.88/81.13  Demodulation         : 22.99
% 101.88/81.13  BG Simplification    : 0.47
% 101.88/81.13  Subsumption          : 30.05
% 101.88/81.13  Abstraction          : 0.73
% 101.88/81.13  MUC search           : 0.00
% 101.88/81.13  Cooper               : 0.00
% 101.88/81.13  Total                : 80.05
% 101.88/81.13  Index Insertion      : 0.00
% 101.88/81.13  Index Deletion       : 0.00
% 101.88/81.13  Index Matching       : 0.00
% 101.88/81.13  BG Taut test         : 0.00
%------------------------------------------------------------------------------