TSTP Solution File: SEU152+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU152+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 : n023.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 10:57:48 EDT 2023

% Result   : Theorem 22.45s 8.92s
% Output   : CNFRefutation 22.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   51 (   9 unt;  34 typ;   0 def)
%            Number of atoms       :   25 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   17 (   9   ~;   5   |;   0   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   62 (  29   >;  33   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   29 (  29 usr;   5 con; 0-3 aty)
%            Number of variables   :   24 (;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > #nlpp > singleton > powerset > empty_set > #skF_13 > #skF_22 > #skF_18 > #skF_17 > #skF_6 > #skF_15 > #skF_20 > #skF_12 > #skF_16 > #skF_19 > #skF_10 > #skF_11 > #skF_7 > #skF_9 > #skF_14 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_21 > #skF_5 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_10',type,
    '#skF_10': ( $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_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_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(f_152,negated_conjecture,
    ~ ! [A,B] :
        ( in(A,B)
       => ( set_union2(singleton(A),B) = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).

tff(f_156,lemma,
    ! [A,B] :
      ( subset(singleton(A),B)
    <=> in(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).

tff(f_244,lemma,
    ! [A,B] : ( set_union2(A,set_difference(B,A)) = set_union2(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).

tff(f_274,lemma,
    ! [A,B] :
      ( subset(A,B)
     => ( B = set_union2(A,set_difference(B,A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).

tff(f_40,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(c_164,plain,
    in('#skF_15','#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_2032,plain,
    ! [A_309,B_310] :
      ( subset(singleton(A_309),B_310)
      | ~ in(A_309,B_310) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_228,plain,
    ! [A_116,B_117] : ( set_union2(A_116,set_difference(B_117,A_116)) = set_union2(A_116,B_117) ),
    inference(cnfTransformation,[status(thm)],[f_244]) ).

tff(c_242,plain,
    ! [A_127,B_128] :
      ( ( set_union2(A_127,set_difference(B_128,A_127)) = B_128 )
      | ~ subset(A_127,B_128) ),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_277,plain,
    ! [A_127,B_128] :
      ( ( set_union2(A_127,B_128) = B_128 )
      | ~ subset(A_127,B_128) ),
    inference(demodulation,[status(thm),theory(equality)],[c_228,c_242]) ).

tff(c_29953,plain,
    ! [A_53776,B_53777] :
      ( ( set_union2(singleton(A_53776),B_53777) = B_53777 )
      | ~ in(A_53776,B_53777) ),
    inference(resolution,[status(thm)],[c_2032,c_277]) ).

tff(c_8,plain,
    ! [B_8,A_7] : ( set_union2(B_8,A_7) = set_union2(A_7,B_8) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_52713,plain,
    ! [B_77472,A_77473] :
      ( ( set_union2(B_77472,singleton(A_77473)) = B_77472 )
      | ~ in(A_77473,B_77472) ),
    inference(superposition,[status(thm),theory(equality)],[c_29953,c_8]) ).

tff(c_162,plain,
    set_union2(singleton('#skF_15'),'#skF_16') != '#skF_16',
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_282,plain,
    set_union2('#skF_16',singleton('#skF_15')) != '#skF_16',
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_162]) ).

tff(c_53366,plain,
    ~ in('#skF_15','#skF_16'),
    inference(superposition,[status(thm),theory(equality)],[c_52713,c_282]) ).

tff(c_53462,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_164,c_53366]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU152+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % 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
% 0.12/0.35  % Computer : n023.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Thu Aug  3 12:06:37 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 22.45/8.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.45/8.92  
% 22.45/8.92  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.45/8.95  
% 22.45/8.95  Inference rules
% 22.45/8.95  ----------------------
% 22.45/8.95  #Ref     : 6
% 22.45/8.95  #Sup     : 12657
% 22.45/8.95  #Fact    : 6
% 22.45/8.95  #Define  : 0
% 22.45/8.95  #Split   : 10
% 22.45/8.95  #Chain   : 0
% 22.45/8.95  #Close   : 0
% 22.45/8.95  
% 22.45/8.95  Ordering : KBO
% 22.45/8.95  
% 22.45/8.95  Simplification rules
% 22.45/8.95  ----------------------
% 22.45/8.95  #Subsume      : 6132
% 22.45/8.95  #Demod        : 2790
% 22.45/8.95  #Tautology    : 2342
% 22.45/8.95  #SimpNegUnit  : 179
% 22.45/8.95  #BackRed      : 12
% 22.45/8.95  
% 22.45/8.95  #Partial instantiations: 41528
% 22.45/8.95  #Strategies tried      : 1
% 22.45/8.95  
% 22.45/8.95  Timing (in seconds)
% 22.45/8.95  ----------------------
% 22.45/8.95  Preprocessing        : 0.71
% 22.45/8.95  Parsing              : 0.35
% 22.45/8.95  CNF conversion       : 0.07
% 22.45/8.96  Main loop            : 7.18
% 22.45/8.96  Inferencing          : 1.69
% 22.45/8.96  Reduction            : 2.90
% 22.45/8.96  Demodulation         : 1.93
% 22.45/8.96  BG Simplification    : 0.10
% 22.45/8.96  Subsumption          : 1.98
% 22.45/8.96  Abstraction          : 0.12
% 22.45/8.96  MUC search           : 0.00
% 22.45/8.96  Cooper               : 0.00
% 22.45/8.96  Total                : 7.94
% 22.45/8.96  Index Insertion      : 0.00
% 22.45/8.96  Index Deletion       : 0.00
% 22.45/8.96  Index Matching       : 0.00
% 22.45/8.96  BG Taut test         : 0.00
%------------------------------------------------------------------------------