TSTP Solution File: SET681+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET681+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n032.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 10:56:52 EDT 2023

% Result   : Theorem 12.23s 4.15s
% Output   : CNFRefutation 12.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  138 (  40 unt;  34 typ;   0 def)
%            Number of atoms       :  251 (   8 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  271 ( 124   ~; 100   |;   9   &)
%                                         (   5 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  26   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   30 (  30 usr;   8 con; 0-3 aty)
%            Number of variables   :  136 (; 134   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ member > ilf_type > relation_like > empty > range > domain > unordered_pair > relation_type > ordered_pair > cross_product > #nlpp > subset_type > singleton > range_of > power_set > member_type > domain_of > set_type > binary_relation_type > #skF_4 > #skF_15 > #skF_16 > #skF_14 > #skF_5 > #skF_13 > #skF_10 > #skF_8 > #skF_3 > #skF_11 > #skF_2 > #skF_7 > #skF_1 > #skF_9 > #skF_6 > #skF_12

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(relation_type,type,
    relation_type: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_375,negated_conjecture,
    ~ ! [B] :
        ( ( ~ empty(B)
          & ilf_type(B,set_type) )
       => ! [C] :
            ( ( ~ empty(C)
              & ilf_type(C,set_type) )
           => ! [D] :
                ( ilf_type(D,relation_type(C,B))
               => ! [E] :
                    ( ilf_type(E,member_type(B))
                   => ( member(E,range(C,B,D))
                    <=> ? [F] :
                          ( ilf_type(F,member_type(C))
                          & member(ordered_pair(F,E),D) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).

tff(f_349,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).

tff(f_335,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ( range(B,C,D) = range_of(D) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).

tff(f_258,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( member(B,power_set(C))
          <=> ! [D] :
                ( ilf_type(D,set_type)
               => ( member(D,B)
                 => member(D,C) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).

tff(f_119,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ! [D] :
                ( ilf_type(D,subset_type(cross_product(B,C)))
               => ilf_type(D,relation_type(B,C)) )
            & ! [E] :
                ( ilf_type(E,relation_type(B,C))
               => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).

tff(f_302,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,subset_type(cross_product(B,C)))
             => relation_like(D) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).

tff(f_209,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ilf_type(B,binary_relation_type)
      <=> ( relation_like(B)
          & ilf_type(B,set_type) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).

tff(f_55,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,binary_relation_type)
             => ( member(ordered_pair(B,C),D)
               => ( member(B,domain_of(D))
                  & member(C,range_of(D)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

tff(f_40,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,binary_relation_type)
         => ( member(B,range_of(C))
          <=> ? [D] :
                ( ilf_type(D,set_type)
                & member(ordered_pair(D,B),C) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

tff(f_76,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ! [E] :
                  ( ilf_type(E,set_type)
                 => ! [F] :
                      ( ilf_type(F,relation_type(B,C))
                     => ( member(ordered_pair(D,E),F)
                       => ( member(D,B)
                          & member(E,C) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

tff(f_141,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ( ~ empty(C)
            & ilf_type(C,set_type) )
         => ( ilf_type(B,member_type(C))
          <=> member(B,C) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).

tff(c_120,plain,
    ilf_type('#skF_14',relation_type('#skF_13','#skF_12')),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_116,plain,
    ! [B_210] : ilf_type(B_210,set_type),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_112,plain,
    ! [B_196,C_200,D_202] :
      ( ( range(B_196,C_200,D_202) = range_of(D_202) )
      | ~ ilf_type(D_202,relation_type(B_196,C_200))
      | ~ ilf_type(C_200,set_type)
      | ~ ilf_type(B_196,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_335]) ).

tff(c_8124,plain,
    ! [B_983,C_984,D_985] :
      ( ( range(B_983,C_984,D_985) = range_of(D_985) )
      | ~ ilf_type(D_985,relation_type(B_983,C_984)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_112]) ).

tff(c_8132,plain,
    range('#skF_13','#skF_12','#skF_14') = range_of('#skF_14'),
    inference(resolution,[status(thm)],[c_120,c_8124]) ).

tff(c_1777,plain,
    ! [B_475,C_476,D_477] :
      ( ( range(B_475,C_476,D_477) = range_of(D_477) )
      | ~ ilf_type(D_477,relation_type(B_475,C_476)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_112]) ).

tff(c_1785,plain,
    range('#skF_13','#skF_12','#skF_14') = range_of('#skF_14'),
    inference(resolution,[status(thm)],[c_120,c_1777]) ).

tff(c_84,plain,
    ! [B_137,C_143] :
      ( member('#skF_8'(B_137,C_143),B_137)
      | member(B_137,power_set(C_143))
      | ~ ilf_type(C_143,set_type)
      | ~ ilf_type(B_137,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_174,plain,
    ! [B_137,C_143] :
      ( member('#skF_8'(B_137,C_143),B_137)
      | member(B_137,power_set(C_143)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_84]) ).

tff(c_82,plain,
    ! [B_137,C_143] :
      ( ~ member('#skF_8'(B_137,C_143),C_143)
      | member(B_137,power_set(C_143))
      | ~ ilf_type(C_143,set_type)
      | ~ ilf_type(B_137,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_409,plain,
    ! [B_294,C_295] :
      ( ~ member('#skF_8'(B_294,C_295),C_295)
      | member(B_294,power_set(C_295)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_82]) ).

tff(c_423,plain,
    ! [B_137] : member(B_137,power_set(B_137)),
    inference(resolution,[status(thm)],[c_174,c_409]) ).

tff(c_140,plain,
    ( member('#skF_15',range('#skF_13','#skF_12','#skF_14'))
    | ilf_type('#skF_16',member_type('#skF_13')) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_304,plain,
    ilf_type('#skF_16',member_type('#skF_13')),
    inference(splitLeft,[status(thm)],[c_140]) ).

tff(c_136,plain,
    ( member('#skF_15',range('#skF_13','#skF_12','#skF_14'))
    | member(ordered_pair('#skF_16','#skF_15'),'#skF_14') ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_370,plain,
    member(ordered_pair('#skF_16','#skF_15'),'#skF_14'),
    inference(splitLeft,[status(thm)],[c_136]) ).

tff(c_80,plain,
    ! [D_146,C_143,B_137] :
      ( member(D_146,C_143)
      | ~ member(D_146,B_137)
      | ~ ilf_type(D_146,set_type)
      | ~ member(B_137,power_set(C_143))
      | ~ ilf_type(C_143,set_type)
      | ~ ilf_type(B_137,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_487,plain,
    ! [D_304,C_305,B_306] :
      ( member(D_304,C_305)
      | ~ member(D_304,B_306)
      | ~ member(B_306,power_set(C_305)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_116,c_80]) ).

tff(c_512,plain,
    ! [C_305] :
      ( member(ordered_pair('#skF_16','#skF_15'),C_305)
      | ~ member('#skF_14',power_set(C_305)) ),
    inference(resolution,[status(thm)],[c_370,c_487]) ).

tff(c_22,plain,
    ! [E_93,B_83,C_89] :
      ( ilf_type(E_93,subset_type(cross_product(B_83,C_89)))
      | ~ ilf_type(E_93,relation_type(B_83,C_89))
      | ~ ilf_type(C_89,set_type)
      | ~ ilf_type(B_83,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_931,plain,
    ! [E_361,B_362,C_363] :
      ( ilf_type(E_361,subset_type(cross_product(B_362,C_363)))
      | ~ ilf_type(E_361,relation_type(B_362,C_363)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_22]) ).

tff(c_106,plain,
    ! [D_181,B_175,C_179] :
      ( relation_like(D_181)
      | ~ ilf_type(D_181,subset_type(cross_product(B_175,C_179)))
      | ~ ilf_type(C_179,set_type)
      | ~ ilf_type(B_175,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_152,plain,
    ! [D_181,B_175,C_179] :
      ( relation_like(D_181)
      | ~ ilf_type(D_181,subset_type(cross_product(B_175,C_179))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_106]) ).

tff(c_964,plain,
    ! [E_364,B_365,C_366] :
      ( relation_like(E_364)
      | ~ ilf_type(E_364,relation_type(B_365,C_366)) ),
    inference(resolution,[status(thm)],[c_931,c_152]) ).

tff(c_986,plain,
    relation_like('#skF_14'),
    inference(resolution,[status(thm)],[c_120,c_964]) ).

tff(c_52,plain,
    ! [B_121] :
      ( ilf_type(B_121,binary_relation_type)
      | ~ relation_like(B_121)
      | ~ ilf_type(B_121,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_194,plain,
    ! [B_121] :
      ( ilf_type(B_121,binary_relation_type)
      | ~ relation_like(B_121) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_52]) ).

tff(c_607,plain,
    ! [B_318,C_319,D_320] :
      ( ( range(B_318,C_319,D_320) = range_of(D_320) )
      | ~ ilf_type(D_320,relation_type(B_318,C_319)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_112]) ).

tff(c_615,plain,
    range('#skF_13','#skF_12','#skF_14') = range_of('#skF_14'),
    inference(resolution,[status(thm)],[c_120,c_607]) ).

tff(c_130,plain,
    ! [F_252] :
      ( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
      | ~ ilf_type(F_252,member_type('#skF_13'))
      | ~ member('#skF_15',range('#skF_13','#skF_12','#skF_14')) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_671,plain,
    ! [F_252] :
      ( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
      | ~ ilf_type(F_252,member_type('#skF_13'))
      | ~ member('#skF_15',range_of('#skF_14')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_615,c_130]) ).

tff(c_672,plain,
    ~ member('#skF_15',range_of('#skF_14')),
    inference(splitLeft,[status(thm)],[c_671]) ).

tff(c_8,plain,
    ! [C_15,D_17,B_11] :
      ( member(C_15,range_of(D_17))
      | ~ member(ordered_pair(B_11,C_15),D_17)
      | ~ ilf_type(D_17,binary_relation_type)
      | ~ ilf_type(C_15,set_type)
      | ~ ilf_type(B_11,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_1283,plain,
    ! [C_407,D_408,B_409] :
      ( member(C_407,range_of(D_408))
      | ~ member(ordered_pair(B_409,C_407),D_408)
      | ~ ilf_type(D_408,binary_relation_type) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_8]) ).

tff(c_1301,plain,
    ( member('#skF_15',range_of('#skF_14'))
    | ~ ilf_type('#skF_14',binary_relation_type) ),
    inference(resolution,[status(thm)],[c_370,c_1283]) ).

tff(c_1308,plain,
    ~ ilf_type('#skF_14',binary_relation_type),
    inference(negUnitSimplification,[status(thm)],[c_672,c_1301]) ).

tff(c_1311,plain,
    ~ relation_like('#skF_14'),
    inference(resolution,[status(thm)],[c_194,c_1308]) ).

tff(c_1315,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_986,c_1311]) ).

tff(c_1436,plain,
    ! [F_425] :
      ( ~ member(ordered_pair(F_425,'#skF_15'),'#skF_14')
      | ~ ilf_type(F_425,member_type('#skF_13')) ),
    inference(splitRight,[status(thm)],[c_671]) ).

tff(c_1440,plain,
    ( ~ ilf_type('#skF_16',member_type('#skF_13'))
    | ~ member('#skF_14',power_set('#skF_14')) ),
    inference(resolution,[status(thm)],[c_512,c_1436]) ).

tff(c_1447,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_423,c_304,c_1440]) ).

tff(c_1448,plain,
    member('#skF_15',range('#skF_13','#skF_12','#skF_14')),
    inference(splitRight,[status(thm)],[c_136]) ).

tff(c_1787,plain,
    member('#skF_15',range_of('#skF_14')),
    inference(demodulation,[status(thm),theory(equality)],[c_1785,c_1448]) ).

tff(c_1670,plain,
    ! [E_460,B_461,C_462] :
      ( ilf_type(E_460,subset_type(cross_product(B_461,C_462)))
      | ~ ilf_type(E_460,relation_type(B_461,C_462)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_22]) ).

tff(c_1685,plain,
    ! [E_463,B_464,C_465] :
      ( relation_like(E_463)
      | ~ ilf_type(E_463,relation_type(B_464,C_465)) ),
    inference(resolution,[status(thm)],[c_1670,c_152]) ).

tff(c_1693,plain,
    relation_like('#skF_14'),
    inference(resolution,[status(thm)],[c_120,c_1685]) ).

tff(c_4,plain,
    ! [B_1,C_7] :
      ( member(ordered_pair('#skF_1'(B_1,C_7),B_1),C_7)
      | ~ member(B_1,range_of(C_7))
      | ~ ilf_type(C_7,binary_relation_type)
      | ~ ilf_type(B_1,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_3732,plain,
    ! [B_711,C_712] :
      ( member(ordered_pair('#skF_1'(B_711,C_712),B_711),C_712)
      | ~ member(B_711,range_of(C_712))
      | ~ ilf_type(C_712,binary_relation_type) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_4]) ).

tff(c_1449,plain,
    ~ member(ordered_pair('#skF_16','#skF_15'),'#skF_14'),
    inference(splitRight,[status(thm)],[c_136]) ).

tff(c_134,plain,
    ! [F_252] :
      ( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
      | ~ ilf_type(F_252,member_type('#skF_13'))
      | member(ordered_pair('#skF_16','#skF_15'),'#skF_14') ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_1609,plain,
    ! [F_252] :
      ( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
      | ~ ilf_type(F_252,member_type('#skF_13')) ),
    inference(negUnitSimplification,[status(thm)],[c_1449,c_134]) ).

tff(c_3758,plain,
    ( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
    | ~ member('#skF_15',range_of('#skF_14'))
    | ~ ilf_type('#skF_14',binary_relation_type) ),
    inference(resolution,[status(thm)],[c_3732,c_1609]) ).

tff(c_3777,plain,
    ( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
    | ~ ilf_type('#skF_14',binary_relation_type) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1787,c_3758]) ).

tff(c_3802,plain,
    ~ ilf_type('#skF_14',binary_relation_type),
    inference(splitLeft,[status(thm)],[c_3777]) ).

tff(c_3805,plain,
    ~ relation_like('#skF_14'),
    inference(resolution,[status(thm)],[c_194,c_3802]) ).

tff(c_3809,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1693,c_3805]) ).

tff(c_3811,plain,
    ilf_type('#skF_14',binary_relation_type),
    inference(splitRight,[status(thm)],[c_3777]) ).

tff(c_14,plain,
    ! [C_34,E_46,F_48,D_42,B_18] :
      ( member(D_42,B_18)
      | ~ member(ordered_pair(D_42,E_46),F_48)
      | ~ ilf_type(F_48,relation_type(B_18,C_34))
      | ~ ilf_type(E_46,set_type)
      | ~ ilf_type(D_42,set_type)
      | ~ ilf_type(C_34,set_type)
      | ~ ilf_type(B_18,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_230,plain,
    ! [C_34,E_46,F_48,D_42,B_18] :
      ( member(D_42,B_18)
      | ~ member(ordered_pair(D_42,E_46),F_48)
      | ~ ilf_type(F_48,relation_type(B_18,C_34)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_116,c_116,c_14]) ).

tff(c_7763,plain,
    ! [B_928,C_929,B_930,C_931] :
      ( member('#skF_1'(B_928,C_929),B_930)
      | ~ ilf_type(C_929,relation_type(B_930,C_931))
      | ~ member(B_928,range_of(C_929))
      | ~ ilf_type(C_929,binary_relation_type) ),
    inference(resolution,[status(thm)],[c_3732,c_230]) ).

tff(c_7789,plain,
    ! [B_928] :
      ( member('#skF_1'(B_928,'#skF_14'),'#skF_13')
      | ~ member(B_928,range_of('#skF_14'))
      | ~ ilf_type('#skF_14',binary_relation_type) ),
    inference(resolution,[status(thm)],[c_120,c_7763]) ).

tff(c_7817,plain,
    ! [B_935] :
      ( member('#skF_1'(B_935,'#skF_14'),'#skF_13')
      | ~ member(B_935,range_of('#skF_14')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3811,c_7789]) ).

tff(c_124,plain,
    ~ empty('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_28,plain,
    ! [B_100,C_102] :
      ( ilf_type(B_100,member_type(C_102))
      | ~ member(B_100,C_102)
      | ~ ilf_type(C_102,set_type)
      | empty(C_102)
      | ~ ilf_type(B_100,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_216,plain,
    ! [B_100,C_102] :
      ( ilf_type(B_100,member_type(C_102))
      | ~ member(B_100,C_102)
      | empty(C_102) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_28]) ).

tff(c_3810,plain,
    ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13')),
    inference(splitRight,[status(thm)],[c_3777]) ).

tff(c_3819,plain,
    ( ~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13')
    | empty('#skF_13') ),
    inference(resolution,[status(thm)],[c_216,c_3810]) ).

tff(c_3822,plain,
    ~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13'),
    inference(negUnitSimplification,[status(thm)],[c_124,c_3819]) ).

tff(c_7820,plain,
    ~ member('#skF_15',range_of('#skF_14')),
    inference(resolution,[status(thm)],[c_7817,c_3822]) ).

tff(c_7826,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1787,c_7820]) ).

tff(c_7827,plain,
    member('#skF_15',range('#skF_13','#skF_12','#skF_14')),
    inference(splitRight,[status(thm)],[c_140]) ).

tff(c_8134,plain,
    member('#skF_15',range_of('#skF_14')),
    inference(demodulation,[status(thm),theory(equality)],[c_8132,c_7827]) ).

tff(c_8298,plain,
    ! [E_1015,B_1016,C_1017] :
      ( ilf_type(E_1015,subset_type(cross_product(B_1016,C_1017)))
      | ~ ilf_type(E_1015,relation_type(B_1016,C_1017)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_22]) ).

tff(c_8322,plain,
    ! [E_1018,B_1019,C_1020] :
      ( relation_like(E_1018)
      | ~ ilf_type(E_1018,relation_type(B_1019,C_1020)) ),
    inference(resolution,[status(thm)],[c_8298,c_152]) ).

tff(c_8344,plain,
    relation_like('#skF_14'),
    inference(resolution,[status(thm)],[c_120,c_8322]) ).

tff(c_9652,plain,
    ! [B_1188,C_1189] :
      ( member(ordered_pair('#skF_1'(B_1188,C_1189),B_1188),C_1189)
      | ~ member(B_1188,range_of(C_1189))
      | ~ ilf_type(C_1189,binary_relation_type) ),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_4]) ).

tff(c_7828,plain,
    ~ ilf_type('#skF_16',member_type('#skF_13')),
    inference(splitRight,[status(thm)],[c_140]) ).

tff(c_138,plain,
    ! [F_252] :
      ( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
      | ~ ilf_type(F_252,member_type('#skF_13'))
      | ilf_type('#skF_16',member_type('#skF_13')) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_7945,plain,
    ! [F_252] :
      ( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
      | ~ ilf_type(F_252,member_type('#skF_13')) ),
    inference(negUnitSimplification,[status(thm)],[c_7828,c_138]) ).

tff(c_9680,plain,
    ( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
    | ~ member('#skF_15',range_of('#skF_14'))
    | ~ ilf_type('#skF_14',binary_relation_type) ),
    inference(resolution,[status(thm)],[c_9652,c_7945]) ).

tff(c_9698,plain,
    ( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
    | ~ ilf_type('#skF_14',binary_relation_type) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8134,c_9680]) ).

tff(c_9701,plain,
    ~ ilf_type('#skF_14',binary_relation_type),
    inference(splitLeft,[status(thm)],[c_9698]) ).

tff(c_9704,plain,
    ~ relation_like('#skF_14'),
    inference(resolution,[status(thm)],[c_194,c_9701]) ).

tff(c_9708,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8344,c_9704]) ).

tff(c_9710,plain,
    ilf_type('#skF_14',binary_relation_type),
    inference(splitRight,[status(thm)],[c_9698]) ).

tff(c_13362,plain,
    ! [B_1401,C_1402,B_1403,C_1404] :
      ( member('#skF_1'(B_1401,C_1402),B_1403)
      | ~ ilf_type(C_1402,relation_type(B_1403,C_1404))
      | ~ member(B_1401,range_of(C_1402))
      | ~ ilf_type(C_1402,binary_relation_type) ),
    inference(resolution,[status(thm)],[c_9652,c_230]) ).

tff(c_13400,plain,
    ! [B_1401] :
      ( member('#skF_1'(B_1401,'#skF_14'),'#skF_13')
      | ~ member(B_1401,range_of('#skF_14'))
      | ~ ilf_type('#skF_14',binary_relation_type) ),
    inference(resolution,[status(thm)],[c_120,c_13362]) ).

tff(c_13422,plain,
    ! [B_1405] :
      ( member('#skF_1'(B_1405,'#skF_14'),'#skF_13')
      | ~ member(B_1405,range_of('#skF_14')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9710,c_13400]) ).

tff(c_9709,plain,
    ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13')),
    inference(splitRight,[status(thm)],[c_9698]) ).

tff(c_9718,plain,
    ( ~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13')
    | empty('#skF_13') ),
    inference(resolution,[status(thm)],[c_216,c_9709]) ).

tff(c_9721,plain,
    ~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13'),
    inference(negUnitSimplification,[status(thm)],[c_124,c_9718]) ).

tff(c_13425,plain,
    ~ member('#skF_15',range_of('#skF_14')),
    inference(resolution,[status(thm)],[c_13422,c_9721]) ).

tff(c_13434,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8134,c_13425]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET681+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu Aug  3 16:42:51 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 12.23/4.15  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.23/4.17  
% 12.23/4.17  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.23/4.21  
% 12.23/4.21  Inference rules
% 12.23/4.21  ----------------------
% 12.23/4.21  #Ref     : 2
% 12.23/4.21  #Sup     : 3160
% 12.23/4.21  #Fact    : 12
% 12.23/4.21  #Define  : 0
% 12.23/4.21  #Split   : 18
% 12.23/4.21  #Chain   : 0
% 12.23/4.21  #Close   : 0
% 12.23/4.21  
% 12.23/4.21  Ordering : KBO
% 12.23/4.21  
% 12.23/4.21  Simplification rules
% 12.23/4.21  ----------------------
% 12.23/4.21  #Subsume      : 1081
% 12.23/4.21  #Demod        : 309
% 12.23/4.21  #Tautology    : 266
% 12.23/4.21  #SimpNegUnit  : 192
% 12.23/4.21  #BackRed      : 19
% 12.23/4.21  
% 12.23/4.21  #Partial instantiations: 0
% 12.23/4.21  #Strategies tried      : 1
% 12.23/4.21  
% 12.23/4.21  Timing (in seconds)
% 12.23/4.21  ----------------------
% 12.23/4.21  Preprocessing        : 0.67
% 12.23/4.21  Parsing              : 0.34
% 12.23/4.21  CNF conversion       : 0.06
% 12.23/4.21  Main loop            : 2.42
% 12.23/4.21  Inferencing          : 0.89
% 12.23/4.21  Reduction            : 0.74
% 12.23/4.21  Demodulation         : 0.52
% 12.23/4.21  BG Simplification    : 0.07
% 12.23/4.21  Subsumption          : 0.54
% 12.23/4.21  Abstraction          : 0.08
% 12.23/4.21  MUC search           : 0.00
% 12.23/4.21  Cooper               : 0.00
% 12.23/4.21  Total                : 3.16
% 12.23/4.21  Index Insertion      : 0.00
% 12.23/4.21  Index Deletion       : 0.00
% 12.23/4.21  Index Matching       : 0.00
% 12.23/4.21  BG Taut test         : 0.00
%------------------------------------------------------------------------------