TSTP Solution File: SEU173+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU173+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 : 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 10:57:54 EDT 2023

% Result   : Theorem 21.72s 8.83s
% Output   : CNFRefutation 21.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   61
% Syntax   : Number of formulae    :   74 (   6 unt;  56 typ;   0 def)
%            Number of atoms       :   39 (   1 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   33 (  12   ~;  10   |;   1   &)
%                                         (   5 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  109 (  51   >;  58   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   49 (  49 usr;   5 con; 0-4 aty)
%            Number of variables   :   27 (;  27   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > empty > unordered_pair > subset_complement > set_union2 > set_intersection2 > set_difference > ordered_pair > cartesian_product2 > #nlpp > union > singleton > powerset > empty_set > #skF_13 > #skF_25 > #skF_24 > #skF_35 > #skF_17 > #skF_6 > #skF_31 > #skF_18 > #skF_20 > #skF_37 > #skF_22 > #skF_12 > #skF_38 > #skF_34 > #skF_15 > #skF_26 > #skF_32 > #skF_23 > #skF_19 > #skF_28 > #skF_33 > #skF_11 > #skF_36 > #skF_7 > #skF_9 > #skF_3 > #skF_29 > #skF_2 > #skF_27 > #skF_8 > #skF_14 > #skF_1 > #skF_16 > #skF_21 > #skF_5 > #skF_30 > #skF_4 > #skF_10

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_118,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_264,negated_conjecture,
    ~ ! [A,B] :
        ( ! [C] :
            ( in(C,A)
           => in(C,B) )
       => element(A,powerset(B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).

tff(f_175,axiom,
    ! [A] : ~ empty(powerset(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

tff(f_68,axiom,
    ! [A,B] :
      ( ( B = powerset(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> subset(C,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

tff(f_81,axiom,
    ! [A,B] :
      ( ( ~ empty(A)
       => ( element(B,A)
        <=> in(B,A) ) )
      & ( empty(A)
       => ( element(B,A)
        <=> empty(B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).

tff(c_4881,plain,
    ! [A_682,B_683] :
      ( in('#skF_16'(A_682,B_683),A_682)
      | subset(A_682,B_683) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_268,plain,
    ! [C_165] :
      ( in(C_165,'#skF_27')
      | ~ in(C_165,'#skF_26') ),
    inference(cnfTransformation,[status(thm)],[f_264]) ).

tff(c_5024,plain,
    ! [B_690] :
      ( in('#skF_16'('#skF_26',B_690),'#skF_27')
      | subset('#skF_26',B_690) ),
    inference(resolution,[status(thm)],[c_4881,c_268]) ).

tff(c_116,plain,
    ! [A_75,B_76] :
      ( ~ in('#skF_16'(A_75,B_76),B_76)
      | subset(A_75,B_76) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_5040,plain,
    subset('#skF_26','#skF_27'),
    inference(resolution,[status(thm)],[c_5024,c_116]) ).

tff(c_214,plain,
    ! [A_123] : ~ empty(powerset(A_123)),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_36,plain,
    ! [C_26,A_22] :
      ( in(C_26,powerset(A_22))
      | ~ subset(C_26,A_22) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_4389,plain,
    ! [B_660,A_661] :
      ( element(B_660,A_661)
      | ~ in(B_660,A_661)
      | empty(A_661) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_4407,plain,
    ! [C_26,A_22] :
      ( element(C_26,powerset(A_22))
      | empty(powerset(A_22))
      | ~ subset(C_26,A_22) ),
    inference(resolution,[status(thm)],[c_36,c_4389]) ).

tff(c_42703,plain,
    ! [C_137687,A_137688] :
      ( element(C_137687,powerset(A_137688))
      | ~ subset(C_137687,A_137688) ),
    inference(negUnitSimplification,[status(thm)],[c_214,c_4407]) ).

tff(c_266,plain,
    ~ element('#skF_26',powerset('#skF_27')),
    inference(cnfTransformation,[status(thm)],[f_264]) ).

tff(c_42751,plain,
    ~ subset('#skF_26','#skF_27'),
    inference(resolution,[status(thm)],[c_42703,c_266]) ).

tff(c_42774,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5040,c_42751]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU173+2 : 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
% 0.17/0.34  % Computer : n025.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit : 300
% 0.17/0.34  % WCLimit  : 300
% 0.17/0.34  % DateTime : Thu Aug  3 12:09:49 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 21.72/8.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.72/8.83  
% 21.72/8.83  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.84/8.86  
% 21.84/8.86  Inference rules
% 21.84/8.86  ----------------------
% 21.84/8.86  #Ref     : 5
% 21.84/8.86  #Sup     : 9256
% 21.84/8.86  #Fact    : 4
% 21.84/8.86  #Define  : 0
% 21.84/8.86  #Split   : 8
% 21.84/8.86  #Chain   : 0
% 21.84/8.86  #Close   : 0
% 21.84/8.86  
% 21.84/8.86  Ordering : KBO
% 21.84/8.86  
% 21.84/8.86  Simplification rules
% 21.84/8.86  ----------------------
% 21.84/8.86  #Subsume      : 3446
% 21.84/8.86  #Demod        : 1846
% 21.84/8.86  #Tautology    : 1941
% 21.84/8.86  #SimpNegUnit  : 312
% 21.84/8.86  #BackRed      : 79
% 21.84/8.86  
% 21.84/8.86  #Partial instantiations: 69580
% 21.84/8.86  #Strategies tried      : 1
% 21.84/8.86  
% 21.84/8.86  Timing (in seconds)
% 21.84/8.86  ----------------------
% 21.84/8.87  Preprocessing        : 0.83
% 21.84/8.87  Parsing              : 0.39
% 21.84/8.87  CNF conversion       : 0.09
% 21.84/8.87  Main loop            : 6.96
% 21.84/8.87  Inferencing          : 1.91
% 21.84/8.87  Reduction            : 2.73
% 21.84/8.87  Demodulation         : 1.80
% 21.84/8.87  BG Simplification    : 0.12
% 21.84/8.87  Subsumption          : 1.77
% 21.84/8.87  Abstraction          : 0.10
% 21.84/8.87  MUC search           : 0.00
% 21.84/8.87  Cooper               : 0.00
% 21.84/8.87  Total                : 7.84
% 21.84/8.87  Index Insertion      : 0.00
% 21.84/8.87  Index Deletion       : 0.00
% 21.84/8.87  Index Matching       : 0.00
% 21.84/8.87  BG Taut test         : 0.00
%------------------------------------------------------------------------------