TSTP Solution File: SEU293+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU293+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/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 : n001.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 10:58:18 EDT 2023

% Result   : Theorem 11.64s 3.84s
% Output   : CNFRefutation 11.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  282 ( 122 unt;  43 typ;   0 def)
%            Number of atoms       :  432 (  66 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives :  368 ( 175   ~; 153   |;  17   &)
%                                         (   7 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  26   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   32 (  32 usr;  17 con; 0-3 aty)
%            Number of variables   :  233 (; 229   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_dom_as_subset > relation_inverse_image > cartesian_product2 > apply > #nlpp > relation_dom > powerset > empty_set > #skF_1 > #skF_20 > #skF_4 > #skF_18 > #skF_17 > #skF_11 > #skF_25 > #skF_19 > #skF_3 > #skF_13 > #skF_16 > #skF_15 > #skF_14 > #skF_10 > #skF_6 > #skF_2 > #skF_21 > #skF_9 > #skF_8 > #skF_22 > #skF_24 > #skF_23 > #skF_7 > #skF_5 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_182,axiom,
    ? [A] :
      ( relation(A)
      & empty(A)
      & function(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

tff(f_276,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_199,axiom,
    ! [A] :
    ? [B] :
      ( element(B,powerset(A))
      & empty(B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

tff(f_272,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

tff(f_140,axiom,
    ! [A] :
      ( empty(A)
     => ( empty(relation_dom(A))
        & relation(relation_dom(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

tff(f_161,axiom,
    ? [A] :
      ( relation(A)
      & function(A)
      & one_to_one(A)
      & empty(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).

tff(f_238,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

tff(f_259,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( function(D)
          & quasi_total(D,A,B)
          & relation_of2_as_subset(D,A,B) )
       => ( ( B != empty_set )
         => ! [E] :
              ( in(E,relation_inverse_image(D,C))
            <=> ( in(E,A)
                & in(apply(D,E),C) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).

tff(f_96,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
     => element(C,powerset(cartesian_product2(A,B))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

tff(f_43,axiom,
    ! [A,B,C] :
      ( element(C,powerset(cartesian_product2(A,B)))
     => relation(C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

tff(f_69,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B,C] :
          ( ( C = relation_inverse_image(A,B) )
        <=> ! [D] :
              ( in(D,C)
            <=> ( in(D,relation_dom(A))
                & in(apply(A,D),B) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).

tff(f_226,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
    <=> relation_of2(C,A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

tff(f_222,axiom,
    ! [A,B,C] :
      ( relation_of2(C,A,B)
     => ( relation_dom_as_subset(A,B,C) = relation_dom(C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).

tff(f_92,axiom,
    ! [A,B,C] :
      ( relation_of2(C,A,B)
     => element(relation_dom_as_subset(A,B,C),powerset(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).

tff(f_265,axiom,
    ! [A,B,C] :
      ( ( in(A,B)
        & element(B,powerset(C)) )
     => element(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

tff(f_102,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

tff(f_134,axiom,
    ! [A] :
      ( ( ~ empty(A)
        & relation(A) )
     => ~ empty(relation_dom(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

tff(f_242,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

tff(f_87,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
     => ( ( ( ( B = empty_set )
           => ( A = empty_set ) )
         => ( quasi_total(C,A,B)
          <=> ( A = relation_dom_as_subset(A,B,C) ) ) )
        & ( ( B = empty_set )
         => ( ( A = empty_set )
            | ( quasi_total(C,A,B)
            <=> ( C = empty_set ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).

tff(c_126,plain,
    empty('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_217,plain,
    ! [A_88] :
      ( ( empty_set = A_88 )
      | ~ empty(A_88) ),
    inference(cnfTransformation,[status(thm)],[f_276]) ).

tff(c_240,plain,
    empty_set = '#skF_12',
    inference(resolution,[status(thm)],[c_126,c_217]) ).

tff(c_140,plain,
    ! [A_51] : empty('#skF_15'(A_51)),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_236,plain,
    ! [A_51] : ( '#skF_15'(A_51) = empty_set ),
    inference(resolution,[status(thm)],[c_140,c_217]) ).

tff(c_4404,plain,
    ! [A_51] : ( '#skF_15'(A_51) = '#skF_12' ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_236]) ).

tff(c_142,plain,
    ! [A_51] : element('#skF_15'(A_51),powerset(A_51)),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_4431,plain,
    ! [A_51] : element('#skF_12',powerset(A_51)),
    inference(demodulation,[status(thm),theory(equality)],[c_4404,c_142]) ).

tff(c_5371,plain,
    ! [C_988,B_989,A_990] :
      ( ~ empty(C_988)
      | ~ element(B_989,powerset(C_988))
      | ~ in(A_990,B_989) ),
    inference(cnfTransformation,[status(thm)],[f_272]) ).

tff(c_5383,plain,
    ! [A_51,A_990] :
      ( ~ empty(A_51)
      | ~ in(A_990,'#skF_12') ),
    inference(resolution,[status(thm)],[c_4431,c_5371]) ).

tff(c_5391,plain,
    ! [A_990] : ~ in(A_990,'#skF_12'),
    inference(splitLeft,[status(thm)],[c_5383]) ).

tff(c_128,plain,
    relation('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_124,plain,
    function('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_4425,plain,
    ! [A_795] :
      ( empty(relation_dom(A_795))
      | ~ empty(A_795) ),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_106,plain,
    empty('#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_237,plain,
    empty_set = '#skF_8',
    inference(resolution,[status(thm)],[c_106,c_217]) ).

tff(c_264,plain,
    '#skF_8' = '#skF_12',
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_237]) ).

tff(c_202,plain,
    ! [A_74] :
      ( ( empty_set = A_74 )
      | ~ empty(A_74) ),
    inference(cnfTransformation,[status(thm)],[f_276]) ).

tff(c_243,plain,
    ! [A_74] :
      ( ( A_74 = '#skF_8' )
      | ~ empty(A_74) ),
    inference(demodulation,[status(thm),theory(equality)],[c_237,c_202]) ).

tff(c_4417,plain,
    ! [A_74] :
      ( ( A_74 = '#skF_12' )
      | ~ empty(A_74) ),
    inference(demodulation,[status(thm),theory(equality)],[c_264,c_243]) ).

tff(c_4454,plain,
    ! [A_802] :
      ( ( relation_dom(A_802) = '#skF_12' )
      | ~ empty(A_802) ),
    inference(resolution,[status(thm)],[c_4425,c_4417]) ).

tff(c_4462,plain,
    relation_dom('#skF_12') = '#skF_12',
    inference(resolution,[status(thm)],[c_126,c_4454]) ).

tff(c_4669,plain,
    ! [A_846,B_847] :
      ( in(A_846,B_847)
      | empty(B_847)
      | ~ element(A_846,B_847) ),
    inference(cnfTransformation,[status(thm)],[f_238]) ).

tff(c_190,plain,
    ( in('#skF_24','#skF_20')
    | ~ in(apply('#skF_23','#skF_25'),'#skF_22')
    | ~ in('#skF_25','#skF_20') ),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_4438,plain,
    ~ in('#skF_25','#skF_20'),
    inference(splitLeft,[status(thm)],[c_190]) ).

tff(c_4691,plain,
    ( empty('#skF_20')
    | ~ element('#skF_25','#skF_20') ),
    inference(resolution,[status(thm)],[c_4669,c_4438]) ).

tff(c_4693,plain,
    ~ element('#skF_25','#skF_20'),
    inference(splitLeft,[status(thm)],[c_4691]) ).

tff(c_180,plain,
    relation_of2_as_subset('#skF_23','#skF_20','#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_4793,plain,
    ! [C_872,A_873,B_874] :
      ( element(C_872,powerset(cartesian_product2(A_873,B_874)))
      | ~ relation_of2_as_subset(C_872,A_873,B_874) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_8,plain,
    ! [C_7,A_5,B_6] :
      ( relation(C_7)
      | ~ element(C_7,powerset(cartesian_product2(A_5,B_6))) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_4808,plain,
    ! [C_875,A_876,B_877] :
      ( relation(C_875)
      | ~ relation_of2_as_subset(C_875,A_876,B_877) ),
    inference(resolution,[status(thm)],[c_4793,c_8]) ).

tff(c_4820,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_180,c_4808]) ).

tff(c_184,plain,
    function('#skF_23'),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_194,plain,
    ( in(apply('#skF_23','#skF_24'),'#skF_22')
    | in('#skF_25',relation_inverse_image('#skF_23','#skF_22')) ),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_4414,plain,
    in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitLeft,[status(thm)],[c_194]) ).

tff(c_5268,plain,
    ! [D_985,A_986,B_987] :
      ( in(D_985,relation_dom(A_986))
      | ~ in(D_985,relation_inverse_image(A_986,B_987))
      | ~ function(A_986)
      | ~ relation(A_986) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_5278,plain,
    ( in('#skF_25',relation_dom('#skF_23'))
    | ~ function('#skF_23')
    | ~ relation('#skF_23') ),
    inference(resolution,[status(thm)],[c_4414,c_5268]) ).

tff(c_5285,plain,
    in('#skF_25',relation_dom('#skF_23')),
    inference(demodulation,[status(thm),theory(equality)],[c_4820,c_184,c_5278]) ).

tff(c_4566,plain,
    ! [C_827,A_828,B_829] :
      ( relation_of2(C_827,A_828,B_829)
      | ~ relation_of2_as_subset(C_827,A_828,B_829) ),
    inference(cnfTransformation,[status(thm)],[f_226]) ).

tff(c_4574,plain,
    relation_of2('#skF_23','#skF_20','#skF_21'),
    inference(resolution,[status(thm)],[c_180,c_4566]) ).

tff(c_4822,plain,
    ! [A_880,B_881,C_882] :
      ( ( relation_dom_as_subset(A_880,B_881,C_882) = relation_dom(C_882) )
      | ~ relation_of2(C_882,A_880,B_881) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_4839,plain,
    relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
    inference(resolution,[status(thm)],[c_4574,c_4822]) ).

tff(c_4959,plain,
    ! [A_909,B_910,C_911] :
      ( element(relation_dom_as_subset(A_909,B_910,C_911),powerset(A_909))
      | ~ relation_of2(C_911,A_909,B_910) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_4973,plain,
    ( element(relation_dom('#skF_23'),powerset('#skF_20'))
    | ~ relation_of2('#skF_23','#skF_20','#skF_21') ),
    inference(superposition,[status(thm),theory(equality)],[c_4839,c_4959]) ).

tff(c_4979,plain,
    element(relation_dom('#skF_23'),powerset('#skF_20')),
    inference(demodulation,[status(thm),theory(equality)],[c_4574,c_4973]) ).

tff(c_198,plain,
    ! [A_68,C_70,B_69] :
      ( element(A_68,C_70)
      | ~ element(B_69,powerset(C_70))
      | ~ in(A_68,B_69) ),
    inference(cnfTransformation,[status(thm)],[f_265]) ).

tff(c_4987,plain,
    ! [A_68] :
      ( element(A_68,'#skF_20')
      | ~ in(A_68,relation_dom('#skF_23')) ),
    inference(resolution,[status(thm)],[c_4979,c_198]) ).

tff(c_5317,plain,
    element('#skF_25','#skF_20'),
    inference(resolution,[status(thm)],[c_5285,c_4987]) ).

tff(c_5336,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4693,c_5317]) ).

tff(c_5337,plain,
    empty('#skF_20'),
    inference(splitRight,[status(thm)],[c_4691]) ).

tff(c_5352,plain,
    '#skF_20' = '#skF_12',
    inference(resolution,[status(thm)],[c_5337,c_4417]) ).

tff(c_5356,plain,
    relation_of2_as_subset('#skF_23','#skF_12','#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_5352,c_180]) ).

tff(c_5554,plain,
    ! [C_1029,A_1030,B_1031] :
      ( element(C_1029,powerset(cartesian_product2(A_1030,B_1031)))
      | ~ relation_of2_as_subset(C_1029,A_1030,B_1031) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_5569,plain,
    ! [C_1032,A_1033,B_1034] :
      ( relation(C_1032)
      | ~ relation_of2_as_subset(C_1032,A_1033,B_1034) ),
    inference(resolution,[status(thm)],[c_5554,c_8]) ).

tff(c_5579,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_5356,c_5569]) ).

tff(c_68,plain,
    ! [A_33] : element('#skF_4'(A_33),A_33),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_172,plain,
    ! [A_63,B_64] :
      ( in(A_63,B_64)
      | empty(B_64)
      | ~ element(A_63,B_64) ),
    inference(cnfTransformation,[status(thm)],[f_238]) ).

tff(c_5354,plain,
    relation_of2('#skF_23','#skF_12','#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_5352,c_4574]) ).

tff(c_5461,plain,
    ! [A_1008,B_1009,C_1010] :
      ( ( relation_dom_as_subset(A_1008,B_1009,C_1010) = relation_dom(C_1010) )
      | ~ relation_of2(C_1010,A_1008,B_1009) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_5477,plain,
    relation_dom_as_subset('#skF_12','#skF_21','#skF_23') = relation_dom('#skF_23'),
    inference(resolution,[status(thm)],[c_5354,c_5461]) ).

tff(c_5609,plain,
    ! [A_1042,B_1043,C_1044] :
      ( element(relation_dom_as_subset(A_1042,B_1043,C_1044),powerset(A_1042))
      | ~ relation_of2(C_1044,A_1042,B_1043) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_5623,plain,
    ( element(relation_dom('#skF_23'),powerset('#skF_12'))
    | ~ relation_of2('#skF_23','#skF_12','#skF_21') ),
    inference(superposition,[status(thm),theory(equality)],[c_5477,c_5609]) ).

tff(c_5629,plain,
    element(relation_dom('#skF_23'),powerset('#skF_12')),
    inference(demodulation,[status(thm),theory(equality)],[c_5354,c_5623]) ).

tff(c_200,plain,
    ! [C_73,B_72,A_71] :
      ( ~ empty(C_73)
      | ~ element(B_72,powerset(C_73))
      | ~ in(A_71,B_72) ),
    inference(cnfTransformation,[status(thm)],[f_272]) ).

tff(c_5633,plain,
    ! [A_71] :
      ( ~ empty('#skF_12')
      | ~ in(A_71,relation_dom('#skF_23')) ),
    inference(resolution,[status(thm)],[c_5629,c_200]) ).

tff(c_5642,plain,
    ! [A_1045] : ~ in(A_1045,relation_dom('#skF_23')),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_5633]) ).

tff(c_5647,plain,
    ! [A_63] :
      ( empty(relation_dom('#skF_23'))
      | ~ element(A_63,relation_dom('#skF_23')) ),
    inference(resolution,[status(thm)],[c_172,c_5642]) ).

tff(c_5649,plain,
    ! [A_1046] : ~ element(A_1046,relation_dom('#skF_23')),
    inference(splitLeft,[status(thm)],[c_5647]) ).

tff(c_5654,plain,
    $false,
    inference(resolution,[status(thm)],[c_68,c_5649]) ).

tff(c_5655,plain,
    empty(relation_dom('#skF_23')),
    inference(splitRight,[status(thm)],[c_5647]) ).

tff(c_88,plain,
    ! [A_41] :
      ( ~ empty(relation_dom(A_41))
      | ~ relation(A_41)
      | empty(A_41) ),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_5662,plain,
    ( ~ relation('#skF_23')
    | empty('#skF_23') ),
    inference(resolution,[status(thm)],[c_5655,c_88]) ).

tff(c_5675,plain,
    empty('#skF_23'),
    inference(demodulation,[status(thm),theory(equality)],[c_5579,c_5662]) ).

tff(c_5695,plain,
    '#skF_23' = '#skF_12',
    inference(resolution,[status(thm)],[c_5675,c_4417]) ).

tff(c_192,plain,
    ( ~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
    | in('#skF_25',relation_inverse_image('#skF_23','#skF_22')) ),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_295,plain,
    ~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitLeft,[status(thm)],[c_192]) ).

tff(c_3227,plain,
    ! [C_614,A_615,B_616] :
      ( element(C_614,powerset(cartesian_product2(A_615,B_616)))
      | ~ relation_of2_as_subset(C_614,A_615,B_616) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_3239,plain,
    ! [C_617,A_618,B_619] :
      ( relation(C_617)
      | ~ relation_of2_as_subset(C_617,A_618,B_619) ),
    inference(resolution,[status(thm)],[c_3227,c_8]) ).

tff(c_3251,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_180,c_3239]) ).

tff(c_2175,plain,
    ! [C_419,A_420,B_421] :
      ( element(C_419,powerset(cartesian_product2(A_420,B_421)))
      | ~ relation_of2_as_subset(C_419,A_420,B_421) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_2218,plain,
    ! [C_427,A_428,B_429] :
      ( relation(C_427)
      | ~ relation_of2_as_subset(C_427,A_428,B_429) ),
    inference(resolution,[status(thm)],[c_2175,c_8]) ).

tff(c_2230,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_180,c_2218]) ).

tff(c_196,plain,
    ( in('#skF_24','#skF_20')
    | in('#skF_25',relation_inverse_image('#skF_23','#skF_22')) ),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_254,plain,
    in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitLeft,[status(thm)],[c_196]) ).

tff(c_2803,plain,
    ! [A_560,D_561,B_562] :
      ( in(apply(A_560,D_561),B_562)
      | ~ in(D_561,relation_inverse_image(A_560,B_562))
      | ~ function(A_560)
      | ~ relation(A_560) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_296,plain,
    ! [A_51] : ( '#skF_15'(A_51) = '#skF_12' ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_236]) ).

tff(c_308,plain,
    ! [A_51] : element('#skF_12',powerset(A_51)),
    inference(demodulation,[status(thm),theory(equality)],[c_296,c_142]) ).

tff(c_1178,plain,
    ! [C_255,B_256,A_257] :
      ( ~ empty(C_255)
      | ~ element(B_256,powerset(C_255))
      | ~ in(A_257,B_256) ),
    inference(cnfTransformation,[status(thm)],[f_272]) ).

tff(c_1190,plain,
    ! [A_51,A_257] :
      ( ~ empty(A_51)
      | ~ in(A_257,'#skF_12') ),
    inference(resolution,[status(thm)],[c_308,c_1178]) ).

tff(c_1192,plain,
    ! [A_257] : ~ in(A_257,'#skF_12'),
    inference(splitLeft,[status(thm)],[c_1190]) ).

tff(c_318,plain,
    ! [A_98] :
      ( empty(relation_dom(A_98))
      | ~ empty(A_98) ),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_310,plain,
    ! [A_74] :
      ( ( A_74 = '#skF_12' )
      | ~ empty(A_74) ),
    inference(demodulation,[status(thm),theory(equality)],[c_264,c_243]) ).

tff(c_331,plain,
    ! [A_102] :
      ( ( relation_dom(A_102) = '#skF_12' )
      | ~ empty(A_102) ),
    inference(resolution,[status(thm)],[c_318,c_310]) ).

tff(c_339,plain,
    relation_dom('#skF_12') = '#skF_12',
    inference(resolution,[status(thm)],[c_126,c_331]) ).

tff(c_514,plain,
    ! [A_151,B_152] :
      ( in(A_151,B_152)
      | empty(B_152)
      | ~ element(A_151,B_152) ),
    inference(cnfTransformation,[status(thm)],[f_238]) ).

tff(c_359,plain,
    ~ in('#skF_25','#skF_20'),
    inference(splitLeft,[status(thm)],[c_190]) ).

tff(c_534,plain,
    ( empty('#skF_20')
    | ~ element('#skF_25','#skF_20') ),
    inference(resolution,[status(thm)],[c_514,c_359]) ).

tff(c_540,plain,
    ~ element('#skF_25','#skF_20'),
    inference(splitLeft,[status(thm)],[c_534]) ).

tff(c_498,plain,
    ! [C_141,A_142,B_143] :
      ( relation_of2(C_141,A_142,B_143)
      | ~ relation_of2_as_subset(C_141,A_142,B_143) ),
    inference(cnfTransformation,[status(thm)],[f_226]) ).

tff(c_506,plain,
    relation_of2('#skF_23','#skF_20','#skF_21'),
    inference(resolution,[status(thm)],[c_180,c_498]) ).

tff(c_644,plain,
    ! [A_165,B_166,C_167] :
      ( ( relation_dom_as_subset(A_165,B_166,C_167) = relation_dom(C_167) )
      | ~ relation_of2(C_167,A_165,B_166) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_661,plain,
    relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
    inference(resolution,[status(thm)],[c_506,c_644]) ).

tff(c_850,plain,
    ! [A_216,B_217,C_218] :
      ( element(relation_dom_as_subset(A_216,B_217,C_218),powerset(A_216))
      | ~ relation_of2(C_218,A_216,B_217) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_873,plain,
    ( element(relation_dom('#skF_23'),powerset('#skF_20'))
    | ~ relation_of2('#skF_23','#skF_20','#skF_21') ),
    inference(superposition,[status(thm),theory(equality)],[c_661,c_850]) ).

tff(c_885,plain,
    element(relation_dom('#skF_23'),powerset('#skF_20')),
    inference(demodulation,[status(thm),theory(equality)],[c_506,c_873]) ).

tff(c_174,plain,
    ! [A_65,B_66] :
      ( subset(A_65,B_66)
      | ~ element(A_65,powerset(B_66)) ),
    inference(cnfTransformation,[status(thm)],[f_242]) ).

tff(c_895,plain,
    subset(relation_dom('#skF_23'),'#skF_20'),
    inference(resolution,[status(thm)],[c_885,c_174]) ).

tff(c_691,plain,
    ! [C_176,A_177,B_178] :
      ( element(C_176,powerset(cartesian_product2(A_177,B_178)))
      | ~ relation_of2_as_subset(C_176,A_177,B_178) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_703,plain,
    ! [C_179,A_180,B_181] :
      ( relation(C_179)
      | ~ relation_of2_as_subset(C_179,A_180,B_181) ),
    inference(resolution,[status(thm)],[c_691,c_8]) ).

tff(c_715,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_180,c_703]) ).

tff(c_988,plain,
    ! [D_246,A_247,B_248] :
      ( in(D_246,relation_dom(A_247))
      | ~ in(D_246,relation_inverse_image(A_247,B_248))
      | ~ function(A_247)
      | ~ relation(A_247) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_995,plain,
    ( in('#skF_25',relation_dom('#skF_23'))
    | ~ function('#skF_23')
    | ~ relation('#skF_23') ),
    inference(resolution,[status(thm)],[c_254,c_988]) ).

tff(c_999,plain,
    in('#skF_25',relation_dom('#skF_23')),
    inference(demodulation,[status(thm),theory(equality)],[c_715,c_184,c_995]) ).

tff(c_176,plain,
    ! [A_65,B_66] :
      ( element(A_65,powerset(B_66))
      | ~ subset(A_65,B_66) ),
    inference(cnfTransformation,[status(thm)],[f_242]) ).

tff(c_717,plain,
    ! [A_184,C_185,B_186] :
      ( element(A_184,C_185)
      | ~ element(B_186,powerset(C_185))
      | ~ in(A_184,B_186) ),
    inference(cnfTransformation,[status(thm)],[f_265]) ).

tff(c_731,plain,
    ! [A_184,B_66,A_65] :
      ( element(A_184,B_66)
      | ~ in(A_184,A_65)
      | ~ subset(A_65,B_66) ),
    inference(resolution,[status(thm)],[c_176,c_717]) ).

tff(c_1057,plain,
    ! [B_252] :
      ( element('#skF_25',B_252)
      | ~ subset(relation_dom('#skF_23'),B_252) ),
    inference(resolution,[status(thm)],[c_999,c_731]) ).

tff(c_1060,plain,
    element('#skF_25','#skF_20'),
    inference(resolution,[status(thm)],[c_895,c_1057]) ).

tff(c_1072,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_540,c_1060]) ).

tff(c_1073,plain,
    empty('#skF_20'),
    inference(splitRight,[status(thm)],[c_534]) ).

tff(c_1088,plain,
    '#skF_20' = '#skF_12',
    inference(resolution,[status(thm)],[c_1073,c_310]) ).

tff(c_1092,plain,
    relation_of2_as_subset('#skF_23','#skF_12','#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_180]) ).

tff(c_1251,plain,
    ! [C_276,A_277,B_278] :
      ( element(C_276,powerset(cartesian_product2(A_277,B_278)))
      | ~ relation_of2_as_subset(C_276,A_277,B_278) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_1266,plain,
    ! [C_279,A_280,B_281] :
      ( relation(C_279)
      | ~ relation_of2_as_subset(C_279,A_280,B_281) ),
    inference(resolution,[status(thm)],[c_1251,c_8]) ).

tff(c_1276,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_1092,c_1266]) ).

tff(c_182,plain,
    quasi_total('#skF_23','#skF_20','#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_1093,plain,
    quasi_total('#skF_23','#skF_12','#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_182]) ).

tff(c_1090,plain,
    relation_of2('#skF_23','#skF_12','#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_506]) ).

tff(c_1306,plain,
    ! [A_289,B_290,C_291] :
      ( ( relation_dom_as_subset(A_289,B_290,C_291) = relation_dom(C_291) )
      | ~ relation_of2(C_291,A_289,B_290) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_1322,plain,
    relation_dom_as_subset('#skF_12','#skF_21','#skF_23') = relation_dom('#skF_23'),
    inference(resolution,[status(thm)],[c_1090,c_1306]) ).

tff(c_42,plain,
    ! [B_22,C_23] :
      ( ( relation_dom_as_subset(empty_set,B_22,C_23) = empty_set )
      | ~ quasi_total(C_23,empty_set,B_22)
      | ~ relation_of2_as_subset(C_23,empty_set,B_22) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_1716,plain,
    ! [B_362,C_363] :
      ( ( relation_dom_as_subset('#skF_12',B_362,C_363) = '#skF_12' )
      | ~ quasi_total(C_363,'#skF_12',B_362)
      | ~ relation_of2_as_subset(C_363,'#skF_12',B_362) ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_240,c_240,c_240,c_42]) ).

tff(c_1719,plain,
    ( ( relation_dom_as_subset('#skF_12','#skF_21','#skF_23') = '#skF_12' )
    | ~ quasi_total('#skF_23','#skF_12','#skF_21') ),
    inference(resolution,[status(thm)],[c_1092,c_1716]) ).

tff(c_1730,plain,
    relation_dom('#skF_23') = '#skF_12',
    inference(demodulation,[status(thm),theory(equality)],[c_1093,c_1322,c_1719]) ).

tff(c_1743,plain,
    ( ~ empty('#skF_12')
    | ~ relation('#skF_23')
    | empty('#skF_23') ),
    inference(superposition,[status(thm),theory(equality)],[c_1730,c_88]) ).

tff(c_1756,plain,
    empty('#skF_23'),
    inference(demodulation,[status(thm),theory(equality)],[c_1276,c_126,c_1743]) ).

tff(c_1783,plain,
    '#skF_23' = '#skF_12',
    inference(resolution,[status(thm)],[c_1756,c_310]) ).

tff(c_1802,plain,
    in('#skF_25',relation_inverse_image('#skF_12','#skF_22')),
    inference(demodulation,[status(thm),theory(equality)],[c_1783,c_254]) ).

tff(c_20,plain,
    ! [D_20,A_9,B_16] :
      ( in(D_20,relation_dom(A_9))
      | ~ in(D_20,relation_inverse_image(A_9,B_16))
      | ~ function(A_9)
      | ~ relation(A_9) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_1862,plain,
    ( in('#skF_25',relation_dom('#skF_12'))
    | ~ function('#skF_12')
    | ~ relation('#skF_12') ),
    inference(resolution,[status(thm)],[c_1802,c_20]) ).

tff(c_1880,plain,
    in('#skF_25','#skF_12'),
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_124,c_339,c_1862]) ).

tff(c_1882,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1192,c_1880]) ).

tff(c_1883,plain,
    ! [A_51] : ~ empty(A_51),
    inference(splitRight,[status(thm)],[c_1190]) ).

tff(c_1892,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1883,c_126]) ).

tff(c_1894,plain,
    in('#skF_25','#skF_20'),
    inference(splitRight,[status(thm)],[c_190]) ).

tff(c_188,plain,
    ( in(apply('#skF_23','#skF_24'),'#skF_22')
    | ~ in(apply('#skF_23','#skF_25'),'#skF_22')
    | ~ in('#skF_25','#skF_20') ),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_1985,plain,
    ( in(apply('#skF_23','#skF_24'),'#skF_22')
    | ~ in(apply('#skF_23','#skF_25'),'#skF_22') ),
    inference(demodulation,[status(thm),theory(equality)],[c_1894,c_188]) ).

tff(c_1986,plain,
    ~ in(apply('#skF_23','#skF_25'),'#skF_22'),
    inference(splitLeft,[status(thm)],[c_1985]) ).

tff(c_2861,plain,
    ( ~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22'))
    | ~ function('#skF_23')
    | ~ relation('#skF_23') ),
    inference(resolution,[status(thm)],[c_2803,c_1986]) ).

tff(c_2888,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2230,c_184,c_254,c_2861]) ).

tff(c_2890,plain,
    in(apply('#skF_23','#skF_25'),'#skF_22'),
    inference(splitRight,[status(thm)],[c_1985]) ).

tff(c_1893,plain,
    ( ~ in(apply('#skF_23','#skF_25'),'#skF_22')
    | in('#skF_24','#skF_20') ),
    inference(splitRight,[status(thm)],[c_190]) ).

tff(c_2903,plain,
    ~ in(apply('#skF_23','#skF_25'),'#skF_22'),
    inference(splitLeft,[status(thm)],[c_1893]) ).

tff(c_2916,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2890,c_2903]) ).

tff(c_2917,plain,
    in('#skF_24','#skF_20'),
    inference(splitRight,[status(thm)],[c_1893]) ).

tff(c_178,plain,
    empty_set != '#skF_21',
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_245,plain,
    '#skF_21' != '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_237,c_178]) ).

tff(c_277,plain,
    '#skF_21' != '#skF_12',
    inference(demodulation,[status(thm),theory(equality)],[c_264,c_245]) ).

tff(c_3110,plain,
    ! [C_589,A_590,B_591] :
      ( relation_of2(C_589,A_590,B_591)
      | ~ relation_of2_as_subset(C_589,A_590,B_591) ),
    inference(cnfTransformation,[status(thm)],[f_226]) ).

tff(c_3122,plain,
    relation_of2('#skF_23','#skF_20','#skF_21'),
    inference(resolution,[status(thm)],[c_180,c_3110]) ).

tff(c_3306,plain,
    ! [A_633,B_634,C_635] :
      ( ( relation_dom_as_subset(A_633,B_634,C_635) = relation_dom(C_635) )
      | ~ relation_of2(C_635,A_633,B_634) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_3323,plain,
    relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
    inference(resolution,[status(thm)],[c_3122,c_3306]) ).

tff(c_44,plain,
    ! [B_22,A_21,C_23] :
      ( ( empty_set = B_22 )
      | ( relation_dom_as_subset(A_21,B_22,C_23) = A_21 )
      | ~ quasi_total(C_23,A_21,B_22)
      | ~ relation_of2_as_subset(C_23,A_21,B_22) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_4145,plain,
    ! [B_774,A_775,C_776] :
      ( ( B_774 = '#skF_12' )
      | ( relation_dom_as_subset(A_775,B_774,C_776) = A_775 )
      | ~ quasi_total(C_776,A_775,B_774)
      | ~ relation_of2_as_subset(C_776,A_775,B_774) ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_44]) ).

tff(c_4154,plain,
    ( ( '#skF_21' = '#skF_12' )
    | ( relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = '#skF_20' )
    | ~ quasi_total('#skF_23','#skF_20','#skF_21') ),
    inference(resolution,[status(thm)],[c_180,c_4145]) ).

tff(c_4160,plain,
    ( ( '#skF_21' = '#skF_12' )
    | ( relation_dom('#skF_23') = '#skF_20' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_3323,c_4154]) ).

tff(c_4161,plain,
    relation_dom('#skF_23') = '#skF_20',
    inference(negUnitSimplification,[status(thm)],[c_277,c_4160]) ).

tff(c_2889,plain,
    in(apply('#skF_23','#skF_24'),'#skF_22'),
    inference(splitRight,[status(thm)],[c_1985]) ).

tff(c_4378,plain,
    ! [D_785,A_786,B_787] :
      ( in(D_785,relation_inverse_image(A_786,B_787))
      | ~ in(apply(A_786,D_785),B_787)
      | ~ in(D_785,relation_dom(A_786))
      | ~ function(A_786)
      | ~ relation(A_786) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_4391,plain,
    ( in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
    | ~ in('#skF_24',relation_dom('#skF_23'))
    | ~ function('#skF_23')
    | ~ relation('#skF_23') ),
    inference(resolution,[status(thm)],[c_2889,c_4378]) ).

tff(c_4399,plain,
    in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
    inference(demodulation,[status(thm),theory(equality)],[c_3251,c_184,c_2917,c_4161,c_4391]) ).

tff(c_4401,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_295,c_4399]) ).

tff(c_4403,plain,
    in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitRight,[status(thm)],[c_192]) ).

tff(c_5715,plain,
    in('#skF_24',relation_inverse_image('#skF_12','#skF_22')),
    inference(demodulation,[status(thm),theory(equality)],[c_5695,c_4403]) ).

tff(c_5841,plain,
    ! [D_1051,A_1052,B_1053] :
      ( in(D_1051,relation_dom(A_1052))
      | ~ in(D_1051,relation_inverse_image(A_1052,B_1053))
      | ~ function(A_1052)
      | ~ relation(A_1052) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_5844,plain,
    ( in('#skF_24',relation_dom('#skF_12'))
    | ~ function('#skF_12')
    | ~ relation('#skF_12') ),
    inference(resolution,[status(thm)],[c_5715,c_5841]) ).

tff(c_5854,plain,
    in('#skF_24','#skF_12'),
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_124,c_4462,c_5844]) ).

tff(c_5856,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5391,c_5854]) ).

tff(c_5857,plain,
    ! [A_51] : ~ empty(A_51),
    inference(splitRight,[status(thm)],[c_5383]) ).

tff(c_5866,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5857,c_126]) ).

tff(c_5868,plain,
    in('#skF_25','#skF_20'),
    inference(splitRight,[status(thm)],[c_190]) ).

tff(c_186,plain,
    ( ~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
    | ~ in(apply('#skF_23','#skF_25'),'#skF_22')
    | ~ in('#skF_25','#skF_20') ),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_6851,plain,
    ~ in(apply('#skF_23','#skF_25'),'#skF_22'),
    inference(demodulation,[status(thm),theory(equality)],[c_5868,c_4403,c_186]) ).

tff(c_6258,plain,
    ! [C_1127,A_1128,B_1129] :
      ( element(C_1127,powerset(cartesian_product2(A_1128,B_1129)))
      | ~ relation_of2_as_subset(C_1127,A_1128,B_1129) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_6273,plain,
    ! [C_1130,A_1131,B_1132] :
      ( relation(C_1130)
      | ~ relation_of2_as_subset(C_1130,A_1131,B_1132) ),
    inference(resolution,[status(thm)],[c_6258,c_8]) ).

tff(c_6285,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_180,c_6273]) ).

tff(c_6765,plain,
    ! [A_1223,D_1224,B_1225] :
      ( in(apply(A_1223,D_1224),B_1225)
      | ~ in(D_1224,relation_inverse_image(A_1223,B_1225))
      | ~ function(A_1223)
      | ~ relation(A_1223) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_5874,plain,
    ( in(apply('#skF_23','#skF_24'),'#skF_22')
    | ~ in(apply('#skF_23','#skF_25'),'#skF_22') ),
    inference(demodulation,[status(thm),theory(equality)],[c_5868,c_188]) ).

tff(c_5875,plain,
    ~ in(apply('#skF_23','#skF_25'),'#skF_22'),
    inference(splitLeft,[status(thm)],[c_5874]) ).

tff(c_6820,plain,
    ( ~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22'))
    | ~ function('#skF_23')
    | ~ relation('#skF_23') ),
    inference(resolution,[status(thm)],[c_6765,c_5875]) ).

tff(c_6842,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6285,c_184,c_4414,c_6820]) ).

tff(c_6844,plain,
    in(apply('#skF_23','#skF_25'),'#skF_22'),
    inference(splitRight,[status(thm)],[c_5874]) ).

tff(c_6852,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6851,c_6844]) ).

tff(c_6854,plain,
    ~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitRight,[status(thm)],[c_194]) ).

tff(c_6879,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6854,c_254]) ).

tff(c_6881,plain,
    ~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitRight,[status(thm)],[c_196]) ).

tff(c_6889,plain,
    ~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitLeft,[status(thm)],[c_192]) ).

tff(c_7364,plain,
    ! [C_1337,A_1338,B_1339] :
      ( element(C_1337,powerset(cartesian_product2(A_1338,B_1339)))
      | ~ relation_of2_as_subset(C_1337,A_1338,B_1339) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_7376,plain,
    ! [C_1340,A_1341,B_1342] :
      ( relation(C_1340)
      | ~ relation_of2_as_subset(C_1340,A_1341,B_1342) ),
    inference(resolution,[status(thm)],[c_7364,c_8]) ).

tff(c_7388,plain,
    relation('#skF_23'),
    inference(resolution,[status(thm)],[c_180,c_7376]) ).

tff(c_6880,plain,
    in('#skF_24','#skF_20'),
    inference(splitRight,[status(thm)],[c_196]) ).

tff(c_6890,plain,
    '#skF_8' = '#skF_12',
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_237]) ).

tff(c_6905,plain,
    '#skF_21' != '#skF_12',
    inference(demodulation,[status(thm),theory(equality)],[c_6890,c_245]) ).

tff(c_7116,plain,
    ! [C_1289,A_1290,B_1291] :
      ( relation_of2(C_1289,A_1290,B_1291)
      | ~ relation_of2_as_subset(C_1289,A_1290,B_1291) ),
    inference(cnfTransformation,[status(thm)],[f_226]) ).

tff(c_7124,plain,
    relation_of2('#skF_23','#skF_20','#skF_21'),
    inference(resolution,[status(thm)],[c_180,c_7116]) ).

tff(c_7432,plain,
    ! [A_1351,B_1352,C_1353] :
      ( ( relation_dom_as_subset(A_1351,B_1352,C_1353) = relation_dom(C_1353) )
      | ~ relation_of2(C_1353,A_1351,B_1352) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_7449,plain,
    relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
    inference(resolution,[status(thm)],[c_7124,c_7432]) ).

tff(c_8487,plain,
    ! [B_1501,A_1502,C_1503] :
      ( ( B_1501 = '#skF_12' )
      | ( relation_dom_as_subset(A_1502,B_1501,C_1503) = A_1502 )
      | ~ quasi_total(C_1503,A_1502,B_1501)
      | ~ relation_of2_as_subset(C_1503,A_1502,B_1501) ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_44]) ).

tff(c_8496,plain,
    ( ( '#skF_21' = '#skF_12' )
    | ( relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = '#skF_20' )
    | ~ quasi_total('#skF_23','#skF_20','#skF_21') ),
    inference(resolution,[status(thm)],[c_180,c_8487]) ).

tff(c_8502,plain,
    ( ( '#skF_21' = '#skF_12' )
    | ( relation_dom('#skF_23') = '#skF_20' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_7449,c_8496]) ).

tff(c_8503,plain,
    relation_dom('#skF_23') = '#skF_20',
    inference(negUnitSimplification,[status(thm)],[c_6905,c_8502]) ).

tff(c_6933,plain,
    in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitLeft,[status(thm)],[c_194]) ).

tff(c_6958,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6881,c_6933]) ).

tff(c_6959,plain,
    in(apply('#skF_23','#skF_24'),'#skF_22'),
    inference(splitRight,[status(thm)],[c_194]) ).

tff(c_8715,plain,
    ! [D_1521,A_1522,B_1523] :
      ( in(D_1521,relation_inverse_image(A_1522,B_1523))
      | ~ in(apply(A_1522,D_1521),B_1523)
      | ~ in(D_1521,relation_dom(A_1522))
      | ~ function(A_1522)
      | ~ relation(A_1522) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_8725,plain,
    ( in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
    | ~ in('#skF_24',relation_dom('#skF_23'))
    | ~ function('#skF_23')
    | ~ relation('#skF_23') ),
    inference(resolution,[status(thm)],[c_6959,c_8715]) ).

tff(c_8730,plain,
    in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
    inference(demodulation,[status(thm),theory(equality)],[c_7388,c_184,c_6880,c_8503,c_8725]) ).

tff(c_8732,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6889,c_8730]) ).

tff(c_8733,plain,
    in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
    inference(splitRight,[status(thm)],[c_192]) ).

tff(c_8789,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6881,c_8733]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n001.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
% 0.13/0.34  % DateTime : Thu Aug  3 12:45:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 11.64/3.84  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.64/3.87  
% 11.64/3.87  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.83/3.92  
% 11.83/3.92  Inference rules
% 11.83/3.92  ----------------------
% 11.83/3.92  #Ref     : 0
% 11.83/3.92  #Sup     : 1795
% 11.83/3.92  #Fact    : 0
% 11.83/3.92  #Define  : 0
% 11.83/3.92  #Split   : 77
% 11.83/3.92  #Chain   : 0
% 11.83/3.92  #Close   : 0
% 11.83/3.92  
% 11.83/3.92  Ordering : KBO
% 11.83/3.92  
% 11.83/3.92  Simplification rules
% 11.83/3.92  ----------------------
% 11.83/3.92  #Subsume      : 295
% 11.83/3.92  #Demod        : 853
% 11.83/3.92  #Tautology    : 500
% 11.83/3.92  #SimpNegUnit  : 93
% 11.83/3.92  #BackRed      : 138
% 11.83/3.92  
% 11.83/3.92  #Partial instantiations: 0
% 11.83/3.92  #Strategies tried      : 1
% 11.83/3.92  
% 11.83/3.92  Timing (in seconds)
% 11.83/3.92  ----------------------
% 11.83/3.92  Preprocessing        : 0.67
% 11.83/3.92  Parsing              : 0.33
% 11.83/3.92  CNF conversion       : 0.06
% 11.83/3.92  Main loop            : 2.06
% 11.83/3.92  Inferencing          : 0.73
% 11.83/3.92  Reduction            : 0.70
% 11.83/3.92  Demodulation         : 0.48
% 11.83/3.92  BG Simplification    : 0.06
% 11.83/3.92  Subsumption          : 0.39
% 11.83/3.92  Abstraction          : 0.05
% 11.83/3.92  MUC search           : 0.00
% 11.83/3.92  Cooper               : 0.00
% 11.83/3.92  Total                : 2.82
% 11.83/3.92  Index Insertion      : 0.00
% 11.83/3.92  Index Deletion       : 0.00
% 11.83/3.92  Index Matching       : 0.00
% 11.83/3.92  BG Taut test         : 0.00
%------------------------------------------------------------------------------