TSTP Solution File: SET682+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET682+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n025.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 6.22s 2.49s
% Output   : CNFRefutation 6.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  130 (  34 unt;  30 typ;   0 def)
%            Number of atoms       :  247 (  13 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  255 ( 108   ~;  92   |;  10   &)
%                                         (   6 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  23   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;   7 con; 0-3 aty)
%            Number of variables   :  137 (; 133   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ member > ilf_type > relation_like > empty > range > domain > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > domain_of > set_type > binary_relation_type > #skF_4 > #skF_11 > #skF_14 > #skF_5 > #skF_10 > #skF_13 > #skF_8 > #skF_3 > #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('#skF_11',type,
    '#skF_11': $i ).

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

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

tff('#skF_13',type,
    '#skF_13': $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(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_284,negated_conjecture,
    ~ ! [B] :
        ( ( ~ empty(B)
          & ilf_type(B,set_type) )
       => ! [C] :
            ( ( ~ empty(C)
              & ilf_type(C,set_type) )
           => ! [D] :
                ( ilf_type(D,relation_type(B,C))
               => ! [E] :
                    ( ilf_type(E,member_type(B))
                   => ( member(E,domain(B,C,D))
                     => ? [F] :
                          ( ilf_type(F,member_type(C))
                          & member(F,range(B,C,D)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_49) ).

tff(f_258,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).

tff(f_56,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/sandbox/benchmark/theBenchmark.p',p2) ).

tff(f_203,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/sandbox/benchmark/theBenchmark.p',p18) ).

tff(f_125,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ilf_type(B,binary_relation_type)
      <=> ( relation_like(B)
          & ilf_type(B,set_type) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).

tff(f_244,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/sandbox/benchmark/theBenchmark.p',p22) ).

tff(f_167,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ~ empty(power_set(B))
        & ilf_type(power_set(B),set_type) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).

tff(f_138,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ilf_type(C,subset_type(B))
          <=> ilf_type(C,member_type(power_set(B))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).

tff(f_78,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/sandbox/benchmark/theBenchmark.p',p4) ).

tff(f_185,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( relation_like(B)
      <=> ! [C] :
            ( ilf_type(C,set_type)
           => ( member(C,B)
             => ? [D] :
                  ( ilf_type(D,set_type)
                  & ? [E] :
                      ( ilf_type(E,set_type)
                      & ( C = ordered_pair(D,E) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).

tff(f_159,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/sandbox/benchmark/theBenchmark.p',p14) ).

tff(f_255,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ilf_type(range(B,C,D),subset_type(C)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).

tff(f_98,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( empty(B)
      <=> ! [C] :
            ( ilf_type(C,set_type)
           => ~ member(C,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).

tff(f_222,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ( domain(B,C,D) = domain_of(D) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).

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

tff(c_90,plain,
    ilf_type('#skF_13',relation_type('#skF_11','#skF_12')),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_82,plain,
    ! [B_120] : ilf_type(B_120,set_type),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_6,plain,
    ! [E_17,B_7,C_13] :
      ( ilf_type(E_17,subset_type(cross_product(B_7,C_13)))
      | ~ ilf_type(E_17,relation_type(B_7,C_13))
      | ~ ilf_type(C_13,set_type)
      | ~ ilf_type(B_7,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_1725,plain,
    ! [E_357,B_358,C_359] :
      ( ilf_type(E_357,subset_type(cross_product(B_358,C_359)))
      | ~ ilf_type(E_357,relation_type(B_358,C_359)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_6]) ).

tff(c_70,plain,
    ! [D_88,B_82,C_86] :
      ( relation_like(D_88)
      | ~ ilf_type(D_88,subset_type(cross_product(B_82,C_86)))
      | ~ ilf_type(C_86,set_type)
      | ~ ilf_type(B_82,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_112,plain,
    ! [D_88,B_82,C_86] :
      ( relation_like(D_88)
      | ~ ilf_type(D_88,subset_type(cross_product(B_82,C_86))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_70]) ).

tff(c_1736,plain,
    ! [E_362,B_363,C_364] :
      ( relation_like(E_362)
      | ~ ilf_type(E_362,relation_type(B_363,C_364)) ),
    inference(resolution,[status(thm)],[c_1725,c_112]) ).

tff(c_1744,plain,
    relation_like('#skF_13'),
    inference(resolution,[status(thm)],[c_90,c_1736]) ).

tff(c_30,plain,
    ! [B_38] :
      ( ilf_type(B_38,binary_relation_type)
      | ~ relation_like(B_38)
      | ~ ilf_type(B_38,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_148,plain,
    ! [B_38] :
      ( ilf_type(B_38,binary_relation_type)
      | ~ relation_like(B_38) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_30]) ).

tff(c_78,plain,
    ! [B_106,C_110,D_112] :
      ( ( range(B_106,C_110,D_112) = range_of(D_112) )
      | ~ ilf_type(D_112,relation_type(B_106,C_110))
      | ~ ilf_type(C_110,set_type)
      | ~ ilf_type(B_106,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_244]) ).

tff(c_1809,plain,
    ! [B_374,C_375,D_376] :
      ( ( range(B_374,C_375,D_376) = range_of(D_376) )
      | ~ ilf_type(D_376,relation_type(B_374,C_375)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_78]) ).

tff(c_1817,plain,
    range('#skF_11','#skF_12','#skF_13') = range_of('#skF_13'),
    inference(resolution,[status(thm)],[c_90,c_1809]) ).

tff(c_509,plain,
    ! [E_212,B_213,C_214] :
      ( ilf_type(E_212,subset_type(cross_product(B_213,C_214)))
      | ~ ilf_type(E_212,relation_type(B_213,C_214)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_6]) ).

tff(c_524,plain,
    ! [E_215,B_216,C_217] :
      ( relation_like(E_215)
      | ~ ilf_type(E_215,relation_type(B_216,C_217)) ),
    inference(resolution,[status(thm)],[c_509,c_112]) ).

tff(c_532,plain,
    relation_like('#skF_13'),
    inference(resolution,[status(thm)],[c_90,c_524]) ).

tff(c_54,plain,
    ! [B_54] :
      ( ~ empty(power_set(B_54))
      | ~ ilf_type(B_54,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_167]) ).

tff(c_128,plain,
    ! [B_54] : ~ empty(power_set(B_54)),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_54]) ).

tff(c_40,plain,
    ! [C_41,B_39] :
      ( ilf_type(C_41,member_type(power_set(B_39)))
      | ~ ilf_type(C_41,subset_type(B_39))
      | ~ ilf_type(C_41,set_type)
      | ~ ilf_type(B_39,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_138]) ).

tff(c_265,plain,
    ! [C_177,B_178] :
      ( ilf_type(C_177,member_type(power_set(B_178)))
      | ~ ilf_type(C_177,subset_type(B_178)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_40]) ).

tff(c_14,plain,
    ! [B_24,C_26] :
      ( member(B_24,C_26)
      | ~ ilf_type(B_24,member_type(C_26))
      | ~ ilf_type(C_26,set_type)
      | empty(C_26)
      | ~ ilf_type(B_24,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_162,plain,
    ! [B_24,C_26] :
      ( member(B_24,C_26)
      | ~ ilf_type(B_24,member_type(C_26))
      | empty(C_26) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_14]) ).

tff(c_268,plain,
    ! [C_177,B_178] :
      ( member(C_177,power_set(B_178))
      | empty(power_set(B_178))
      | ~ ilf_type(C_177,subset_type(B_178)) ),
    inference(resolution,[status(thm)],[c_265,c_162]) ).

tff(c_271,plain,
    ! [C_177,B_178] :
      ( member(C_177,power_set(B_178))
      | ~ ilf_type(C_177,subset_type(B_178)) ),
    inference(negUnitSimplification,[status(thm)],[c_128,c_268]) ).

tff(c_58,plain,
    ! [B_55] :
      ( member('#skF_10'(B_55),B_55)
      | relation_like(B_55)
      | ~ ilf_type(B_55,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_124,plain,
    ! [B_55] :
      ( member('#skF_10'(B_55),B_55)
      | relation_like(B_55) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_58]) ).

tff(c_44,plain,
    ! [D_53,C_50,B_44] :
      ( member(D_53,C_50)
      | ~ member(D_53,B_44)
      | ~ ilf_type(D_53,set_type)
      | ~ member(B_44,power_set(C_50))
      | ~ ilf_type(C_50,set_type)
      | ~ ilf_type(B_44,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_393,plain,
    ! [D_199,C_200,B_201] :
      ( member(D_199,C_200)
      | ~ member(D_199,B_201)
      | ~ member(B_201,power_set(C_200)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_82,c_44]) ).

tff(c_418,plain,
    ! [B_55,C_200] :
      ( member('#skF_10'(B_55),C_200)
      | ~ member(B_55,power_set(C_200))
      | relation_like(B_55) ),
    inference(resolution,[status(thm)],[c_124,c_393]) ).

tff(c_606,plain,
    ! [B_225,C_226,D_227] :
      ( ( range(B_225,C_226,D_227) = range_of(D_227) )
      | ~ ilf_type(D_227,relation_type(B_225,C_226)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_78]) ).

tff(c_614,plain,
    range('#skF_11','#skF_12','#skF_13') = range_of('#skF_13'),
    inference(resolution,[status(thm)],[c_90,c_606]) ).

tff(c_94,plain,
    ~ empty('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_12,plain,
    ! [B_24,C_26] :
      ( ilf_type(B_24,member_type(C_26))
      | ~ member(B_24,C_26)
      | ~ ilf_type(C_26,set_type)
      | empty(C_26)
      | ~ ilf_type(B_24,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_164,plain,
    ! [B_24,C_26] :
      ( ilf_type(B_24,member_type(C_26))
      | ~ member(B_24,C_26)
      | empty(C_26) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_12]) ).

tff(c_206,plain,
    ! [F_162] :
      ( ~ member(F_162,range('#skF_11','#skF_12','#skF_13'))
      | ~ ilf_type(F_162,member_type('#skF_12')) ),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_215,plain,
    ( ~ ilf_type('#skF_10'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12'))
    | relation_like(range('#skF_11','#skF_12','#skF_13')) ),
    inference(resolution,[status(thm)],[c_124,c_206]) ).

tff(c_336,plain,
    ~ ilf_type('#skF_10'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12')),
    inference(splitLeft,[status(thm)],[c_215]) ).

tff(c_470,plain,
    ( ~ member('#skF_10'(range('#skF_11','#skF_12','#skF_13')),'#skF_12')
    | empty('#skF_12') ),
    inference(resolution,[status(thm)],[c_164,c_336]) ).

tff(c_473,plain,
    ~ member('#skF_10'(range('#skF_11','#skF_12','#skF_13')),'#skF_12'),
    inference(negUnitSimplification,[status(thm)],[c_94,c_470]) ).

tff(c_617,plain,
    ~ member('#skF_10'(range_of('#skF_13')),'#skF_12'),
    inference(demodulation,[status(thm),theory(equality)],[c_614,c_473]) ).

tff(c_629,plain,
    ( ~ member(range_of('#skF_13'),power_set('#skF_12'))
    | relation_like(range_of('#skF_13')) ),
    inference(resolution,[status(thm)],[c_418,c_617]) ).

tff(c_889,plain,
    ~ member(range_of('#skF_13'),power_set('#skF_12')),
    inference(splitLeft,[status(thm)],[c_629]) ).

tff(c_896,plain,
    ~ ilf_type(range_of('#skF_13'),subset_type('#skF_12')),
    inference(resolution,[status(thm)],[c_271,c_889]) ).

tff(c_80,plain,
    ! [B_113,C_117,D_119] :
      ( ilf_type(range(B_113,C_117,D_119),subset_type(C_117))
      | ~ ilf_type(D_119,relation_type(B_113,C_117))
      | ~ ilf_type(C_117,set_type)
      | ~ ilf_type(B_113,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_965,plain,
    ! [B_265,C_266,D_267] :
      ( ilf_type(range(B_265,C_266,D_267),subset_type(C_266))
      | ~ ilf_type(D_267,relation_type(B_265,C_266)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_80]) ).

tff(c_979,plain,
    ( ilf_type(range_of('#skF_13'),subset_type('#skF_12'))
    | ~ ilf_type('#skF_13',relation_type('#skF_11','#skF_12')) ),
    inference(superposition,[status(thm),theory(equality)],[c_614,c_965]) ).

tff(c_984,plain,
    ilf_type(range_of('#skF_13'),subset_type('#skF_12')),
    inference(demodulation,[status(thm),theory(equality)],[c_90,c_979]) ).

tff(c_986,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_896,c_984]) ).

tff(c_988,plain,
    member(range_of('#skF_13'),power_set('#skF_12')),
    inference(splitRight,[status(thm)],[c_629]) ).

tff(c_20,plain,
    ! [B_29] :
      ( member('#skF_4'(B_29),B_29)
      | empty(B_29)
      | ~ ilf_type(B_29,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_156,plain,
    ! [B_29] :
      ( member('#skF_4'(B_29),B_29)
      | empty(B_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_20]) ).

tff(c_1107,plain,
    ! [B_287,C_288] :
      ( member('#skF_4'(B_287),C_288)
      | ~ member(B_287,power_set(C_288))
      | empty(B_287) ),
    inference(resolution,[status(thm)],[c_156,c_393]) ).

tff(c_311,plain,
    ! [B_186,C_187] :
      ( ilf_type(B_186,member_type(C_187))
      | ~ member(B_186,C_187)
      | empty(C_187) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_12]) ).

tff(c_216,plain,
    ( ~ ilf_type('#skF_4'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12'))
    | empty(range('#skF_11','#skF_12','#skF_13')) ),
    inference(resolution,[status(thm)],[c_156,c_206]) ).

tff(c_272,plain,
    ~ ilf_type('#skF_4'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12')),
    inference(splitLeft,[status(thm)],[c_216]) ).

tff(c_318,plain,
    ( ~ member('#skF_4'(range('#skF_11','#skF_12','#skF_13')),'#skF_12')
    | empty('#skF_12') ),
    inference(resolution,[status(thm)],[c_311,c_272]) ).

tff(c_327,plain,
    ~ member('#skF_4'(range('#skF_11','#skF_12','#skF_13')),'#skF_12'),
    inference(negUnitSimplification,[status(thm)],[c_94,c_318]) ).

tff(c_619,plain,
    ~ member('#skF_4'(range_of('#skF_13')),'#skF_12'),
    inference(demodulation,[status(thm),theory(equality)],[c_614,c_327]) ).

tff(c_1118,plain,
    ( ~ member(range_of('#skF_13'),power_set('#skF_12'))
    | empty(range_of('#skF_13')) ),
    inference(resolution,[status(thm)],[c_1107,c_619]) ).

tff(c_1136,plain,
    empty(range_of('#skF_13')),
    inference(demodulation,[status(thm),theory(equality)],[c_988,c_1118]) ).

tff(c_74,plain,
    ! [B_92,C_96,D_98] :
      ( ( domain(B_92,C_96,D_98) = domain_of(D_98) )
      | ~ ilf_type(D_98,relation_type(B_92,C_96))
      | ~ ilf_type(C_96,set_type)
      | ~ ilf_type(B_92,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_672,plain,
    ! [B_230,C_231,D_232] :
      ( ( domain(B_230,C_231,D_232) = domain_of(D_232) )
      | ~ ilf_type(D_232,relation_type(B_230,C_231)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_74]) ).

tff(c_680,plain,
    domain('#skF_11','#skF_12','#skF_13') = domain_of('#skF_13'),
    inference(resolution,[status(thm)],[c_90,c_672]) ).

tff(c_86,plain,
    member('#skF_14',domain('#skF_11','#skF_12','#skF_13')),
    inference(cnfTransformation,[status(thm)],[f_284]) ).

tff(c_683,plain,
    member('#skF_14',domain_of('#skF_13')),
    inference(demodulation,[status(thm),theory(equality)],[c_680,c_86]) ).

tff(c_2,plain,
    ! [B_1,C_5] :
      ( member('#skF_1'(B_1,C_5),range_of(C_5))
      | ~ member(B_1,domain_of(C_5))
      | ~ ilf_type(C_5,binary_relation_type)
      | ~ ilf_type(B_1,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_1431,plain,
    ! [B_318,C_319] :
      ( member('#skF_1'(B_318,C_319),range_of(C_319))
      | ~ member(B_318,domain_of(C_319))
      | ~ ilf_type(C_319,binary_relation_type) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_2]) ).

tff(c_18,plain,
    ! [C_32,B_29] :
      ( ~ member(C_32,B_29)
      | ~ ilf_type(C_32,set_type)
      | ~ empty(B_29)
      | ~ ilf_type(B_29,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_158,plain,
    ! [C_32,B_29] :
      ( ~ member(C_32,B_29)
      | ~ empty(B_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_18]) ).

tff(c_1472,plain,
    ! [C_329,B_330] :
      ( ~ empty(range_of(C_329))
      | ~ member(B_330,domain_of(C_329))
      | ~ ilf_type(C_329,binary_relation_type) ),
    inference(resolution,[status(thm)],[c_1431,c_158]) ).

tff(c_1479,plain,
    ( ~ empty(range_of('#skF_13'))
    | ~ ilf_type('#skF_13',binary_relation_type) ),
    inference(resolution,[status(thm)],[c_683,c_1472]) ).

tff(c_1503,plain,
    ~ ilf_type('#skF_13',binary_relation_type),
    inference(demodulation,[status(thm),theory(equality)],[c_1136,c_1479]) ).

tff(c_1511,plain,
    ~ relation_like('#skF_13'),
    inference(resolution,[status(thm)],[c_148,c_1503]) ).

tff(c_1515,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_532,c_1511]) ).

tff(c_1516,plain,
    empty(range('#skF_11','#skF_12','#skF_13')),
    inference(splitRight,[status(thm)],[c_216]) ).

tff(c_1822,plain,
    empty(range_of('#skF_13')),
    inference(demodulation,[status(thm),theory(equality)],[c_1817,c_1516]) ).

tff(c_2076,plain,
    ! [B_396,C_397,D_398] :
      ( ( domain(B_396,C_397,D_398) = domain_of(D_398) )
      | ~ ilf_type(D_398,relation_type(B_396,C_397)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_74]) ).

tff(c_2096,plain,
    domain('#skF_11','#skF_12','#skF_13') = domain_of('#skF_13'),
    inference(resolution,[status(thm)],[c_90,c_2076]) ).

tff(c_2120,plain,
    member('#skF_14',domain_of('#skF_13')),
    inference(demodulation,[status(thm),theory(equality)],[c_2096,c_86]) ).

tff(c_2373,plain,
    ! [B_428,C_429] :
      ( member('#skF_1'(B_428,C_429),range_of(C_429))
      | ~ member(B_428,domain_of(C_429))
      | ~ ilf_type(C_429,binary_relation_type) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_2]) ).

tff(c_2637,plain,
    ! [C_458,B_459] :
      ( ~ empty(range_of(C_458))
      | ~ member(B_459,domain_of(C_458))
      | ~ ilf_type(C_458,binary_relation_type) ),
    inference(resolution,[status(thm)],[c_2373,c_158]) ).

tff(c_2648,plain,
    ( ~ empty(range_of('#skF_13'))
    | ~ ilf_type('#skF_13',binary_relation_type) ),
    inference(resolution,[status(thm)],[c_2120,c_2637]) ).

tff(c_2673,plain,
    ~ ilf_type('#skF_13',binary_relation_type),
    inference(demodulation,[status(thm),theory(equality)],[c_1822,c_2648]) ).

tff(c_2681,plain,
    ~ relation_like('#skF_13'),
    inference(resolution,[status(thm)],[c_148,c_2673]) ).

tff(c_2685,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1744,c_2681]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET682+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 17:15:04 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 6.22/2.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.22/2.50  
% 6.22/2.50  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.22/2.54  
% 6.22/2.54  Inference rules
% 6.22/2.54  ----------------------
% 6.22/2.54  #Ref     : 0
% 6.22/2.54  #Sup     : 508
% 6.22/2.54  #Fact    : 0
% 6.22/2.54  #Define  : 0
% 6.22/2.54  #Split   : 6
% 6.22/2.54  #Chain   : 0
% 6.22/2.54  #Close   : 0
% 6.22/2.54  
% 6.22/2.54  Ordering : KBO
% 6.22/2.54  
% 6.22/2.54  Simplification rules
% 6.22/2.54  ----------------------
% 6.22/2.54  #Subsume      : 101
% 6.22/2.54  #Demod        : 169
% 6.22/2.54  #Tautology    : 101
% 6.22/2.54  #SimpNegUnit  : 41
% 6.22/2.54  #BackRed      : 19
% 6.22/2.54  
% 6.22/2.54  #Partial instantiations: 0
% 6.22/2.54  #Strategies tried      : 1
% 6.22/2.54  
% 6.22/2.54  Timing (in seconds)
% 6.22/2.54  ----------------------
% 6.52/2.54  Preprocessing        : 0.60
% 6.52/2.54  Parsing              : 0.32
% 6.52/2.54  CNF conversion       : 0.05
% 6.52/2.54  Main loop            : 0.85
% 6.52/2.54  Inferencing          : 0.34
% 6.52/2.54  Reduction            : 0.25
% 6.52/2.54  Demodulation         : 0.18
% 6.52/2.54  BG Simplification    : 0.04
% 6.52/2.54  Subsumption          : 0.15
% 6.52/2.54  Abstraction          : 0.03
% 6.52/2.54  MUC search           : 0.00
% 6.52/2.54  Cooper               : 0.00
% 6.52/2.54  Total                : 1.52
% 6.52/2.54  Index Insertion      : 0.00
% 6.52/2.54  Index Deletion       : 0.00
% 6.52/2.54  Index Matching       : 0.00
% 6.52/2.54  BG Taut test         : 0.00
%------------------------------------------------------------------------------