TSTP Solution File: SEU186+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU186+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 : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:57:56 EDT 2023

% Result   : Theorem 19.73s 5.92s
% Output   : CNFRefutation 19.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  101
% Syntax   : Number of formulae    :  117 (   8 unt;  96 typ;   0 def)
%            Number of atoms       :   39 (  14 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   37 (  19   ~;  11   |;   2   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  192 (  90   >; 102   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   88 (  88 usr;   6 con; 0-5 aty)
%            Number of variables   :   22 (;  21   !;   1   ?;   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_12 > #skF_53 > #skF_48 > #skF_45 > #skF_10 > #skF_35 > #skF_19 > #skF_66 > #skF_42 > #skF_8 > #skF_36 > #skF_57 > #skF_59 > #skF_20 > #skF_64 > #skF_28 > #skF_34 > #skF_15 > #skF_23 > #skF_14 > #skF_54 > #skF_52 > #skF_50 > #skF_46 > #skF_2 > #skF_21 > #skF_40 > #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_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('#skF_66',type,
    '#skF_66': ( $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_64',type,
    '#skF_64': $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_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(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_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_434,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_835,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_806,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( ! [B,C] : ~ in(ordered_pair(B,C),A)
         => ( A = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).

tff(f_94,axiom,
    ! [A] :
      ( ( A = empty_set )
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

tff(f_62,axiom,
    ! [A] :
      ( relation(A)
    <=> ! [B] :
          ~ ( in(B,A)
            & ! [C,D] : ( B != ordered_pair(C,D) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).

tff(c_412,plain,
    empty('#skF_53'),
    inference(cnfTransformation,[status(thm)],[f_434]) ).

tff(c_696,plain,
    ! [A_692] :
      ( ( empty_set = A_692 )
      | ~ empty(A_692) ),
    inference(cnfTransformation,[status(thm)],[f_835]) ).

tff(c_711,plain,
    empty_set = '#skF_53',
    inference(resolution,[status(thm)],[c_412,c_696]) ).

tff(c_594,plain,
    empty_set != '#skF_64',
    inference(cnfTransformation,[status(thm)],[f_806]) ).

tff(c_729,plain,
    '#skF_53' != '#skF_64',
    inference(demodulation,[status(thm),theory(equality)],[c_711,c_594]) ).

tff(c_598,plain,
    relation('#skF_64'),
    inference(cnfTransformation,[status(thm)],[f_806]) ).

tff(c_62,plain,
    ! [A_56] :
      ( ( empty_set = A_56 )
      | in('#skF_10'(A_56),A_56) ),
    inference(cnfTransformation,[status(thm)],[f_94]) ).

tff(c_1003,plain,
    ! [A_56] :
      ( ( A_56 = '#skF_53' )
      | in('#skF_10'(A_56),A_56) ),
    inference(demodulation,[status(thm),theory(equality)],[c_711,c_62]) ).

tff(c_23671,plain,
    ! [A_84124,B_84125] :
      ( ( ordered_pair('#skF_2'(A_84124,B_84125),'#skF_3'(A_84124,B_84125)) = B_84125 )
      | ~ in(B_84125,A_84124)
      | ~ relation(A_84124) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_596,plain,
    ! [B_601,C_602] : ~ in(ordered_pair(B_601,C_602),'#skF_64'),
    inference(cnfTransformation,[status(thm)],[f_806]) ).

tff(c_24402,plain,
    ! [B_85568,A_85569] :
      ( ~ in(B_85568,'#skF_64')
      | ~ in(B_85568,A_85569)
      | ~ relation(A_85569) ),
    inference(superposition,[status(thm),theory(equality)],[c_23671,c_596]) ).

tff(c_24436,plain,
    ! [A_85569] :
      ( ~ in('#skF_10'('#skF_64'),A_85569)
      | ~ relation(A_85569)
      | ( '#skF_53' = '#skF_64' ) ),
    inference(resolution,[status(thm)],[c_1003,c_24402]) ).

tff(c_24451,plain,
    ! [A_85748] :
      ( ~ in('#skF_10'('#skF_64'),A_85748)
      | ~ relation(A_85748) ),
    inference(negUnitSimplification,[status(thm)],[c_729,c_24436]) ).

tff(c_24511,plain,
    ( ~ relation('#skF_64')
    | ( '#skF_53' = '#skF_64' ) ),
    inference(resolution,[status(thm)],[c_1003,c_24451]) ).

tff(c_24548,plain,
    '#skF_53' = '#skF_64',
    inference(demodulation,[status(thm),theory(equality)],[c_598,c_24511]) ).

tff(c_24550,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_729,c_24548]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU186+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
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 12:23:53 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 19.73/5.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.73/5.92  
% 19.73/5.92  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.73/5.95  
% 19.73/5.95  Inference rules
% 19.73/5.95  ----------------------
% 19.73/5.95  #Ref     : 5
% 19.73/5.95  #Sup     : 4797
% 19.73/5.95  #Fact    : 0
% 19.73/5.95  #Define  : 0
% 19.73/5.95  #Split   : 2
% 19.73/5.95  #Chain   : 0
% 19.73/5.95  #Close   : 0
% 19.73/5.95  
% 19.73/5.95  Ordering : KBO
% 19.73/5.95  
% 19.73/5.95  Simplification rules
% 19.73/5.95  ----------------------
% 19.73/5.95  #Subsume      : 1576
% 19.73/5.95  #Demod        : 1093
% 19.73/5.95  #Tautology    : 1266
% 19.73/5.95  #SimpNegUnit  : 133
% 19.73/5.95  #BackRed      : 24
% 19.73/5.95  
% 19.73/5.95  #Partial instantiations: 41624
% 19.73/5.95  #Strategies tried      : 1
% 19.73/5.95  
% 19.73/5.95  Timing (in seconds)
% 19.73/5.95  ----------------------
% 19.73/5.95  Preprocessing        : 0.94
% 19.73/5.95  Parsing              : 0.44
% 19.73/5.95  CNF conversion       : 0.10
% 19.73/5.95  Main loop            : 3.93
% 19.73/5.95  Inferencing          : 1.23
% 19.73/5.95  Reduction            : 1.43
% 19.73/5.95  Demodulation         : 0.96
% 19.73/5.95  BG Simplification    : 0.11
% 19.73/5.95  Subsumption          : 0.91
% 19.73/5.95  Abstraction          : 0.08
% 19.73/5.95  MUC search           : 0.00
% 19.73/5.95  Cooper               : 0.00
% 19.73/5.95  Total                : 4.92
% 19.73/5.95  Index Insertion      : 0.00
% 19.73/5.95  Index Deletion       : 0.00
% 19.73/5.95  Index Matching       : 0.00
% 19.73/5.95  BG Taut test         : 0.00
%------------------------------------------------------------------------------