TSTP Solution File: SEU189+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU189+2 : 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 10:57:57 EDT 2023

% Result   : Theorem 10.19s 3.35s
% Output   : CNFRefutation 10.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  104
% Syntax   : Number of formulae    :  151 (  38 unt;  98 typ;   0 def)
%            Number of atoms       :   75 (  57 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   45 (  23   ~;  15   |;   2   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  194 (  92   >; 102   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   90 (  90 usr;   6 con; 0-5 aty)
%            Number of variables   :   11 (;   9   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > relation > empty > subset_difference > unordered_pair > union_of_subsets > subset_complement > set_union2 > set_intersection2 > set_difference > relation_composition > ordered_pair > meet_of_subsets > complements_of_subsets > cartesian_product2 > #nlpp > union > singleton > set_meet > relation_rng > relation_inverse > relation_field > relation_dom > powerset > cast_to_subset > empty_set > #skF_13 > #skF_49 > #skF_24 > #skF_37 > #skF_62 > #skF_11 > #skF_41 > #skF_44 > #skF_6 > #skF_17 > #skF_33 > #skF_26 > #skF_30 > #skF_1 > #skF_18 > #skF_47 > #skF_55 > #skF_63 > #skF_32 > #skF_56 > #skF_60 > #skF_31 > #skF_38 > #skF_4 > #skF_3 > #skF_39 > #skF_29 > #skF_64 > #skF_12 > #skF_53 > #skF_48 > #skF_45 > #skF_10 > #skF_35 > #skF_19 > #skF_42 > #skF_8 > #skF_36 > #skF_57 > #skF_59 > #skF_20 > #skF_28 > #skF_34 > #skF_15 > #skF_23 > #skF_14 > #skF_67 > #skF_54 > #skF_52 > #skF_50 > #skF_46 > #skF_2 > #skF_21 > #skF_66 > #skF_40 > #skF_68 > #skF_25 > #skF_43 > #skF_7 > #skF_27 > #skF_61 > #skF_9 > #skF_5 > #skF_22 > #skF_58 > #skF_65 > #skF_16 > #skF_51

%Foreground sorts:

%Background operators:

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

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

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

tff('#skF_49',type,
    '#skF_49': ( $i * $i * $i ) > $i ).

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

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

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

tff('#skF_62',type,
    '#skF_62': ( $i * $i ) > $i ).

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

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

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

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

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

tff('#skF_41',type,
    '#skF_41': ( $i * $i ) > $i ).

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

tff('#skF_44',type,
    '#skF_44': ( $i * $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

tff('#skF_47',type,
    '#skF_47': ( $i * $i * $i ) > $i ).

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

tff('#skF_55',type,
    '#skF_55': $i ).

tff('#skF_63',type,
    '#skF_63': ( $i * $i ) > $i ).

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

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

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

tff('#skF_56',type,
    '#skF_56': $i ).

tff('#skF_60',type,
    '#skF_60': ( $i * $i ) > $i ).

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

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

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

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

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

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

tff('#skF_64',type,
    '#skF_64': $i > $i ).

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

tff('#skF_53',type,
    '#skF_53': $i ).

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

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

tff('#skF_48',type,
    '#skF_48': ( $i * $i * $i ) > $i ).

tff('#skF_45',type,
    '#skF_45': ( $i * $i * $i ) > $i ).

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

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

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

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

tff(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

tff('#skF_42',type,
    '#skF_42': ( $i * $i ) > $i ).

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

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

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

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

tff('#skF_57',type,
    '#skF_57': $i > $i ).

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

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

tff('#skF_59',type,
    '#skF_59': $i > $i ).

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

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

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

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

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

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

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

tff('#skF_67',type,
    '#skF_67': $i > $i ).

tff('#skF_54',type,
    '#skF_54': $i > $i ).

tff('#skF_52',type,
    '#skF_52': ( $i * $i ) > $i ).

tff('#skF_50',type,
    '#skF_50': ( $i * $i * $i ) > $i ).

tff('#skF_46',type,
    '#skF_46': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_66',type,
    '#skF_66': $i ).

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

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

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

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

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

tff('#skF_68',type,
    '#skF_68': ( $i * $i ) > $i ).

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

tff('#skF_43',type,
    '#skF_43': ( $i * $i ) > $i ).

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

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

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

tff('#skF_61',type,
    '#skF_61': ( $i * $i ) > $i ).

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

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

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

tff('#skF_58',type,
    '#skF_58': $i ).

tff('#skF_65',type,
    '#skF_65': $i > $i ).

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

tff('#skF_51',type,
    '#skF_51': $i > $i ).

tff(f_462,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_880,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_473,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_869,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( ( relation_dom(A) = empty_set )
        <=> ( relation_rng(A) = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).

tff(f_862,lemma,
    ! [A] :
      ( relation(A)
     => ( ( ( relation_dom(A) = empty_set )
          | ( relation_rng(A) = empty_set ) )
       => ( A = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).

tff(f_843,lemma,
    ( ( relation_dom(empty_set) = empty_set )
    & ( relation_rng(empty_set) = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).

tff(c_424,plain,
    empty('#skF_53'),
    inference(cnfTransformation,[status(thm)],[f_462]) ).

tff(c_3165,plain,
    ! [A_898] :
      ( ( empty_set = A_898 )
      | ~ empty(A_898) ),
    inference(cnfTransformation,[status(thm)],[f_880]) ).

tff(c_3180,plain,
    empty_set = '#skF_53',
    inference(resolution,[status(thm)],[c_424,c_3165]) ).

tff(c_430,plain,
    empty('#skF_55'),
    inference(cnfTransformation,[status(thm)],[f_473]) ).

tff(c_3179,plain,
    empty_set = '#skF_55',
    inference(resolution,[status(thm)],[c_430,c_3165]) ).

tff(c_3203,plain,
    '#skF_55' = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_3180,c_3179]) ).

tff(c_624,plain,
    ( ( relation_rng('#skF_66') != empty_set )
    | ( relation_dom('#skF_66') != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_683,plain,
    relation_dom('#skF_66') != empty_set,
    inference(splitLeft,[status(thm)],[c_624]) ).

tff(c_748,plain,
    ! [A_701] :
      ( ( empty_set = A_701 )
      | ~ empty(A_701) ),
    inference(cnfTransformation,[status(thm)],[f_880]) ).

tff(c_763,plain,
    empty_set = '#skF_53',
    inference(resolution,[status(thm)],[c_424,c_748]) ).

tff(c_762,plain,
    empty_set = '#skF_55',
    inference(resolution,[status(thm)],[c_430,c_748]) ).

tff(c_785,plain,
    '#skF_55' = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_763,c_762]) ).

tff(c_630,plain,
    ( ( relation_dom('#skF_66') = empty_set )
    | ( relation_rng('#skF_66') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_699,plain,
    relation_rng('#skF_66') = empty_set,
    inference(splitLeft,[status(thm)],[c_630]) ).

tff(c_771,plain,
    relation_rng('#skF_66') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_762,c_699]) ).

tff(c_794,plain,
    relation_rng('#skF_66') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_785,c_771]) ).

tff(c_622,plain,
    relation('#skF_66'),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_618,plain,
    ! [A_614] :
      ( ( relation_rng(A_614) != empty_set )
      | ( empty_set = A_614 )
      | ~ relation(A_614) ),
    inference(cnfTransformation,[status(thm)],[f_862]) ).

tff(c_2854,plain,
    ! [A_870] :
      ( ( relation_rng(A_870) != '#skF_53' )
      | ( A_870 = '#skF_53' )
      | ~ relation(A_870) ),
    inference(demodulation,[status(thm),theory(equality)],[c_763,c_763,c_618]) ).

tff(c_2875,plain,
    ( ( relation_rng('#skF_66') != '#skF_53' )
    | ( '#skF_53' = '#skF_66' ) ),
    inference(resolution,[status(thm)],[c_622,c_2854]) ).

tff(c_2887,plain,
    '#skF_53' = '#skF_66',
    inference(demodulation,[status(thm),theory(equality)],[c_794,c_2875]) ).

tff(c_770,plain,
    relation_dom('#skF_66') != '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_762,c_683]) ).

tff(c_831,plain,
    relation_dom('#skF_66') != '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_785,c_770]) ).

tff(c_2930,plain,
    relation_dom('#skF_66') != '#skF_66',
    inference(demodulation,[status(thm),theory(equality)],[c_2887,c_831]) ).

tff(c_612,plain,
    relation_dom(empty_set) = empty_set,
    inference(cnfTransformation,[status(thm)],[f_843]) ).

tff(c_772,plain,
    relation_dom('#skF_55') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_762,c_762,c_612]) ).

tff(c_815,plain,
    relation_dom('#skF_53') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_785,c_785,c_772]) ).

tff(c_2935,plain,
    relation_dom('#skF_66') = '#skF_66',
    inference(demodulation,[status(thm),theory(equality)],[c_2887,c_2887,c_815]) ).

tff(c_3040,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2930,c_2935]) ).

tff(c_3041,plain,
    relation_dom('#skF_66') = empty_set,
    inference(splitRight,[status(thm)],[c_630]) ).

tff(c_3057,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_683,c_3041]) ).

tff(c_3059,plain,
    relation_dom('#skF_66') = empty_set,
    inference(splitRight,[status(thm)],[c_624]) ).

tff(c_3194,plain,
    relation_dom('#skF_66') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_3179,c_3059]) ).

tff(c_3219,plain,
    relation_dom('#skF_66') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_3203,c_3194]) ).

tff(c_620,plain,
    ! [A_614] :
      ( ( relation_dom(A_614) != empty_set )
      | ( empty_set = A_614 )
      | ~ relation(A_614) ),
    inference(cnfTransformation,[status(thm)],[f_862]) ).

tff(c_7028,plain,
    ! [A_1139] :
      ( ( relation_dom(A_1139) != '#skF_53' )
      | ( A_1139 = '#skF_53' )
      | ~ relation(A_1139) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3180,c_3180,c_620]) ).

tff(c_7049,plain,
    ( ( relation_dom('#skF_66') != '#skF_53' )
    | ( '#skF_53' = '#skF_66' ) ),
    inference(resolution,[status(thm)],[c_622,c_7028]) ).

tff(c_7061,plain,
    '#skF_53' = '#skF_66',
    inference(demodulation,[status(thm),theory(equality)],[c_3219,c_7049]) ).

tff(c_3058,plain,
    relation_rng('#skF_66') != empty_set,
    inference(splitRight,[status(thm)],[c_624]) ).

tff(c_3190,plain,
    relation_rng('#skF_66') != '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_3179,c_3058]) ).

tff(c_3209,plain,
    relation_rng('#skF_66') != '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_3203,c_3190]) ).

tff(c_7116,plain,
    relation_rng('#skF_66') != '#skF_66',
    inference(demodulation,[status(thm),theory(equality)],[c_7061,c_3209]) ).

tff(c_610,plain,
    relation_rng(empty_set) = empty_set,
    inference(cnfTransformation,[status(thm)],[f_843]) ).

tff(c_3188,plain,
    relation_rng('#skF_55') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_3179,c_3179,c_610]) ).

tff(c_3245,plain,
    relation_rng('#skF_53') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_3203,c_3203,c_3188]) ).

tff(c_7113,plain,
    relation_rng('#skF_66') = '#skF_66',
    inference(demodulation,[status(thm),theory(equality)],[c_7061,c_7061,c_3245]) ).

tff(c_7204,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7116,c_7113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU189+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % 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
% 0.15/0.36  % Computer : n001.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 12:17:09 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 10.19/3.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.19/3.35  
% 10.19/3.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.31/3.39  
% 10.31/3.39  Inference rules
% 10.31/3.39  ----------------------
% 10.31/3.39  #Ref     : 1
% 10.31/3.39  #Sup     : 1530
% 10.31/3.39  #Fact    : 0
% 10.31/3.39  #Define  : 0
% 10.31/3.39  #Split   : 3
% 10.31/3.39  #Chain   : 0
% 10.31/3.39  #Close   : 0
% 10.31/3.39  
% 10.31/3.39  Ordering : KBO
% 10.31/3.39  
% 10.31/3.39  Simplification rules
% 10.31/3.39  ----------------------
% 10.31/3.39  #Subsume      : 301
% 10.31/3.39  #Demod        : 834
% 10.31/3.39  #Tautology    : 925
% 10.31/3.39  #SimpNegUnit  : 22
% 10.31/3.39  #BackRed      : 155
% 10.31/3.39  
% 10.31/3.39  #Partial instantiations: 0
% 10.31/3.39  #Strategies tried      : 1
% 10.31/3.39  
% 10.31/3.39  Timing (in seconds)
% 10.31/3.39  ----------------------
% 10.31/3.39  Preprocessing        : 0.95
% 10.31/3.39  Parsing              : 0.45
% 10.31/3.39  CNF conversion       : 0.10
% 10.31/3.39  Main loop            : 1.36
% 10.31/3.39  Inferencing          : 0.39
% 10.31/3.39  Reduction            : 0.51
% 10.31/3.39  Demodulation         : 0.35
% 10.31/3.39  BG Simplification    : 0.08
% 10.31/3.39  Subsumption          : 0.26
% 10.31/3.39  Abstraction          : 0.05
% 10.31/3.39  MUC search           : 0.00
% 10.31/3.39  Cooper               : 0.00
% 10.31/3.39  Total                : 2.36
% 10.31/3.39  Index Insertion      : 0.00
% 10.31/3.39  Index Deletion       : 0.00
% 10.31/3.39  Index Matching       : 0.00
% 10.31/3.39  BG Taut test         : 0.00
%------------------------------------------------------------------------------