TSTP Solution File: NUM394+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n010.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 10:51:35 EDT 2023

% Result   : Theorem 4.79s 2.13s
% Output   : CNFRefutation 4.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   87 (  16 unt;  30 typ;   0 def)
%            Number of atoms       :  143 (   5 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  157 (  71   ~;  64   |;  10   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  16   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;  14 con; 0-1 aty)
%            Number of variables   :   67 (;  66   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > ordinal_subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_187,negated_conjecture,
    ~ ! [A] :
        ( ordinal(A)
       => ! [B] :
            ( ordinal(B)
           => ( ordinal_subset(A,B)
              | in(B,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_ordinal1) ).

tff(f_156,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ordinal_subset(A,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).

tff(f_100,axiom,
    ? [A] :
      ( epsilon_transitive(A)
      & epsilon_connected(A)
      & ordinal(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).

tff(f_71,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
        | ordinal_subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).

tff(f_150,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
      <=> subset(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

tff(f_177,axiom,
    ! [A] :
      ( ordinal(A)
     => ! [B] :
          ( ordinal(B)
         => ~ ( ~ in(A,B)
              & ( A != B )
              & ~ in(B,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).

tff(f_197,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

tff(f_210,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

tff(f_203,axiom,
    ! [A,B,C] :
      ( ( in(A,B)
        & element(B,powerset(C)) )
     => element(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

tff(f_193,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(f_31,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

tff(c_110,plain,
    ordinal('#skF_14'),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_96,plain,
    ! [A_18,B_19] :
      ( ordinal_subset(A_18,A_18)
      | ~ ordinal(B_19)
      | ~ ordinal(A_18) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_249,plain,
    ! [B_19] : ~ ordinal(B_19),
    inference(splitLeft,[status(thm)],[c_96]) ).

tff(c_46,plain,
    ordinal('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_254,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_249,c_46]) ).

tff(c_255,plain,
    ! [A_18] :
      ( ordinal_subset(A_18,A_18)
      | ~ ordinal(A_18) ),
    inference(splitRight,[status(thm)],[c_96]) ).

tff(c_108,plain,
    ordinal('#skF_15'),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_20,plain,
    ! [B_9,A_8] :
      ( ordinal_subset(B_9,A_8)
      | ordinal_subset(A_8,B_9)
      | ~ ordinal(B_9)
      | ~ ordinal(A_8) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_94,plain,
    ! [A_16,B_17] :
      ( subset(A_16,B_17)
      | ~ ordinal_subset(A_16,B_17)
      | ~ ordinal(B_17)
      | ~ ordinal(A_16) ),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_525,plain,
    ! [B_109,A_110] :
      ( in(B_109,A_110)
      | ( B_109 = A_110 )
      | in(A_110,B_109)
      | ~ ordinal(B_109)
      | ~ ordinal(A_110) ),
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_104,plain,
    ~ in('#skF_15','#skF_14'),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_553,plain,
    ( ( '#skF_15' = '#skF_14' )
    | in('#skF_14','#skF_15')
    | ~ ordinal('#skF_15')
    | ~ ordinal('#skF_14') ),
    inference(resolution,[status(thm)],[c_525,c_104]) ).

tff(c_592,plain,
    ( ( '#skF_15' = '#skF_14' )
    | in('#skF_14','#skF_15') ),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_108,c_553]) ).

tff(c_604,plain,
    in('#skF_14','#skF_15'),
    inference(splitLeft,[status(thm)],[c_592]) ).

tff(c_116,plain,
    ! [A_30,B_31] :
      ( element(A_30,powerset(B_31))
      | ~ subset(A_30,B_31) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_349,plain,
    ! [C_76,B_77,A_78] :
      ( ~ empty(C_76)
      | ~ element(B_77,powerset(C_76))
      | ~ in(A_78,B_77) ),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_358,plain,
    ! [B_31,A_78,A_30] :
      ( ~ empty(B_31)
      | ~ in(A_78,A_30)
      | ~ subset(A_30,B_31) ),
    inference(resolution,[status(thm)],[c_116,c_349]) ).

tff(c_670,plain,
    ! [B_113] :
      ( ~ empty(B_113)
      | ~ subset('#skF_15',B_113) ),
    inference(resolution,[status(thm)],[c_604,c_358]) ).

tff(c_674,plain,
    ! [B_17] :
      ( ~ empty(B_17)
      | ~ ordinal_subset('#skF_15',B_17)
      | ~ ordinal(B_17)
      | ~ ordinal('#skF_15') ),
    inference(resolution,[status(thm)],[c_94,c_670]) ).

tff(c_707,plain,
    ! [B_115] :
      ( ~ empty(B_115)
      | ~ ordinal_subset('#skF_15',B_115)
      | ~ ordinal(B_115) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_674]) ).

tff(c_711,plain,
    ! [A_8] :
      ( ~ empty(A_8)
      | ordinal_subset(A_8,'#skF_15')
      | ~ ordinal('#skF_15')
      | ~ ordinal(A_8) ),
    inference(resolution,[status(thm)],[c_20,c_707]) ).

tff(c_756,plain,
    ! [A_117] :
      ( ~ empty(A_117)
      | ordinal_subset(A_117,'#skF_15')
      | ~ ordinal(A_117) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_711]) ).

tff(c_106,plain,
    ~ ordinal_subset('#skF_14','#skF_15'),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_763,plain,
    ( ~ empty('#skF_14')
    | ~ ordinal('#skF_14') ),
    inference(resolution,[status(thm)],[c_756,c_106]) ).

tff(c_769,plain,
    ~ empty('#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_763]) ).

tff(c_460,plain,
    ! [A_99,C_100,B_101] :
      ( element(A_99,C_100)
      | ~ element(B_101,powerset(C_100))
      | ~ in(A_99,B_101) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_469,plain,
    ! [A_99,B_31,A_30] :
      ( element(A_99,B_31)
      | ~ in(A_99,A_30)
      | ~ subset(A_30,B_31) ),
    inference(resolution,[status(thm)],[c_116,c_460]) ).

tff(c_688,plain,
    ! [B_114] :
      ( element('#skF_14',B_114)
      | ~ subset('#skF_15',B_114) ),
    inference(resolution,[status(thm)],[c_604,c_469]) ).

tff(c_692,plain,
    ! [B_17] :
      ( element('#skF_14',B_17)
      | ~ ordinal_subset('#skF_15',B_17)
      | ~ ordinal(B_17)
      | ~ ordinal('#skF_15') ),
    inference(resolution,[status(thm)],[c_94,c_688]) ).

tff(c_770,plain,
    ! [B_118] :
      ( element('#skF_14',B_118)
      | ~ ordinal_subset('#skF_15',B_118)
      | ~ ordinal(B_118) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_692]) ).

tff(c_778,plain,
    ! [A_8] :
      ( element('#skF_14',A_8)
      | ordinal_subset(A_8,'#skF_15')
      | ~ ordinal('#skF_15')
      | ~ ordinal(A_8) ),
    inference(resolution,[status(thm)],[c_20,c_770]) ).

tff(c_799,plain,
    ! [A_119] :
      ( element('#skF_14',A_119)
      | ordinal_subset(A_119,'#skF_15')
      | ~ ordinal(A_119) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_778]) ).

tff(c_810,plain,
    ( element('#skF_14','#skF_14')
    | ~ ordinal('#skF_14') ),
    inference(resolution,[status(thm)],[c_799,c_106]) ).

tff(c_819,plain,
    element('#skF_14','#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_810]) ).

tff(c_112,plain,
    ! [A_28,B_29] :
      ( in(A_28,B_29)
      | empty(B_29)
      | ~ element(A_28,B_29) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_283,plain,
    ! [A_73,B_74] :
      ( in(A_73,B_74)
      | empty(B_74)
      | ~ element(A_73,B_74) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_2,plain,
    ! [B_2,A_1] :
      ( ~ in(B_2,A_1)
      | ~ in(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_399,plain,
    ! [B_87,A_88] :
      ( ~ in(B_87,A_88)
      | empty(B_87)
      | ~ element(A_88,B_87) ),
    inference(resolution,[status(thm)],[c_283,c_2]) ).

tff(c_882,plain,
    ! [A_127,B_128] :
      ( empty(A_127)
      | ~ element(B_128,A_127)
      | empty(B_128)
      | ~ element(A_127,B_128) ),
    inference(resolution,[status(thm)],[c_112,c_399]) ).

tff(c_886,plain,
    ( empty('#skF_14')
    | ~ element('#skF_14','#skF_14') ),
    inference(resolution,[status(thm)],[c_819,c_882]) ).

tff(c_900,plain,
    empty('#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_819,c_886]) ).

tff(c_902,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_769,c_900]) ).

tff(c_903,plain,
    '#skF_15' = '#skF_14',
    inference(splitRight,[status(thm)],[c_592]) ).

tff(c_908,plain,
    ~ ordinal_subset('#skF_14','#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_903,c_106]) ).

tff(c_929,plain,
    ~ ordinal('#skF_14'),
    inference(resolution,[status(thm)],[c_255,c_908]) ).

tff(c_933,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_929]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 15:06:14 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 4.79/2.13  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.79/2.14  
% 4.79/2.14  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.79/2.17  
% 4.79/2.17  Inference rules
% 4.79/2.17  ----------------------
% 4.79/2.17  #Ref     : 0
% 4.79/2.17  #Sup     : 154
% 4.79/2.17  #Fact    : 4
% 4.79/2.17  #Define  : 0
% 4.79/2.17  #Split   : 6
% 4.79/2.17  #Chain   : 0
% 4.79/2.17  #Close   : 0
% 4.79/2.17  
% 4.79/2.17  Ordering : KBO
% 4.79/2.17  
% 4.79/2.17  Simplification rules
% 4.79/2.17  ----------------------
% 4.79/2.17  #Subsume      : 36
% 4.79/2.17  #Demod        : 71
% 4.79/2.17  #Tautology    : 45
% 4.79/2.17  #SimpNegUnit  : 5
% 4.79/2.17  #BackRed      : 21
% 4.79/2.17  
% 4.79/2.17  #Partial instantiations: 0
% 4.79/2.17  #Strategies tried      : 1
% 4.79/2.17  
% 4.79/2.17  Timing (in seconds)
% 4.79/2.17  ----------------------
% 4.79/2.18  Preprocessing        : 0.54
% 4.79/2.18  Parsing              : 0.29
% 4.79/2.18  CNF conversion       : 0.05
% 4.79/2.18  Main loop            : 0.55
% 4.79/2.18  Inferencing          : 0.21
% 4.79/2.18  Reduction            : 0.15
% 4.79/2.18  Demodulation         : 0.10
% 4.79/2.18  BG Simplification    : 0.03
% 4.79/2.18  Subsumption          : 0.11
% 4.79/2.18  Abstraction          : 0.02
% 4.79/2.18  MUC search           : 0.00
% 4.79/2.18  Cooper               : 0.00
% 4.79/2.18  Total                : 1.15
% 4.79/2.18  Index Insertion      : 0.00
% 4.79/2.18  Index Deletion       : 0.00
% 4.79/2.18  Index Matching       : 0.00
% 4.79/2.18  BG Taut test         : 0.00
%------------------------------------------------------------------------------