TSTP Solution File: SWW620_2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW620_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : n004.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 11:07:49 EDT 2023

% Result   : Theorem 13.09s 4.14s
% Output   : CNFRefutation 13.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   81
% Syntax   : Number of formulae    :  108 (  23 unt;  77 typ;   0 def)
%            Number of atoms       :   44 (   8 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   28 (  15   ~;   6   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number arithmetic     :   75 (  19 atm;  18 fun;  20 num;  18 var)
%            Number of types       :    9 (   7 usr;   1 ari)
%            Number of type conns  :  162 (  54   >; 108   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  13 usr;   1 prp; 0-7 aty)
%            Number of functors    :   60 (  57 usr;  18 con; 0-7 aty)
%            Number of variables   :   30 (;  30   !;   0   ?;  30   :)

% Comments : 
%------------------------------------------------------------------------------
%$ exchange2 > permut_sub1 > permut3 > permut2 > map_eq_sub1 > exchange3 > array_eq_sub1 > sorted_sub4 > permut_all > array_eq > sort1 > le4 > sorted4 > set > occ1 > set2 > match_bool1 > get > mk_array1 > make1 > get2 > const > mod > mk_ref > min > max > map > length1 > elts > div > contents > #nlpp > witness1 > tb2t12 > tb2t11 > tb2t10 > tb2t > t2tb12 > t2tb11 > t2tb10 > t2tb > ref > array > abs > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > elt7 > bool > #skF_1 > #skF_4 > #skF_9 > #skF_10 > #skF_3 > #skF_11 > #skF_8 > #skF_2 > #skF_5 > #skF_13 > #skF_6 > #skF_7

%Foreground sorts:
tff(array_elt3,type,
    array_elt3: $tType ).

tff(map_int_elt3,type,
    map_int_elt3: $tType ).

tff(tuple02,type,
    tuple02: $tType ).

tff(elt6,type,
    elt6: $tType ).

tff(bool1,type,
    bool1: $tType ).

tff(ty,type,
    ty: $tType ).

tff(uni,type,
    uni: $tType ).

%Background operators:
tff('#skF_14',type,
    '#skF_14': $int ).

tff('#skE_2',type,
    '#skE_2': $int ).

tff('#skE_1',type,
    '#skE_1': $int ).

tff('#skE_4',type,
    '#skE_4': $int ).

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

tff('#skE_3',type,
    '#skE_3': $int ).

%Foreground operators:
tff(length1,type,
    length1: ( ty * uni ) > $int ).

tff(t2tb10,type,
    t2tb10: array_elt3 > uni ).

tff(t2tb11,type,
    t2tb11: elt6 > uni ).

tff(get2,type,
    get2: ( ty * uni * $int ) > uni ).

tff('#skF_1',type,
    '#skF_1': ( array_elt3 * $int * $int ) > $int ).

tff('#skF_4',type,
    '#skF_4': array_elt3 > $int ).

tff(true1,type,
    true1: bool1 ).

tff(tb2t12,type,
    tb2t12: uni > map_int_elt3 ).

tff(const,type,
    const: ( ty * ty * uni ) > uni ).

tff(occ1,type,
    occ1: ( ty * uni * uni * $int * $int ) > $int ).

tff(elts,type,
    elts: ( ty * uni ) > uni ).

tff(div,type,
    div: ( $int * $int ) > $int ).

tff(int,type,
    int: ty ).

tff(false1,type,
    false1: bool1 ).

tff(map_eq_sub1,type,
    map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).

tff(tb2t,type,
    tb2t: uni > $int ).

tff(abs,type,
    abs: $int > $int ).

tff(sort1,type,
    sort1: ( ty * uni ) > $o ).

tff(contents,type,
    contents: ( ty * uni ) > uni ).

tff('#skF_9',type,
    '#skF_9': ( $int * uni * ty * uni * $int * $int ) > $int ).

tff(t2tb,type,
    t2tb: $int > uni ).

tff(exchange3,type,
    exchange3: ( ty * uni * uni * $int * $int ) > $o ).

tff(le4,type,
    le4: ( elt6 * elt6 ) > $o ).

tff(tb2t11,type,
    tb2t11: uni > elt6 ).

tff('#skF_10',type,
    '#skF_10': ( $int * ty * uni * $int * uni ) > $int ).

tff(witness1,type,
    witness1: ty > uni ).

tff(permut2,type,
    permut2: ( ty * uni * uni * $int * $int ) > $o ).

tff(permut_all,type,
    permut_all: ( ty * uni * uni ) > $o ).

tff('#skF_3',type,
    '#skF_3': array_elt3 > $int ).

tff(real,type,
    real: ty ).

tff('#skF_11',type,
    '#skF_11': ( $int * uni * uni * $int * ty * $int * $int ) > $int ).

tff(elt7,type,
    elt7: ty ).

tff(set,type,
    set: ( ty * ty * uni * uni * uni ) > uni ).

tff(sorted4,type,
    sorted4: array_elt3 > $o ).

tff(match_bool1,type,
    match_bool1: ( ty * bool1 * uni * uni ) > uni ).

tff(array,type,
    array: ty > ty ).

tff(mod,type,
    mod: ( $int * $int ) > $int ).

tff(max,type,
    max: ( $int * $int ) > $int ).

tff('#skF_8',type,
    '#skF_8': ( uni * $int * $int * uni * ty ) > uni ).

tff(array_eq,type,
    array_eq: ( ty * uni * uni ) > $o ).

tff(make1,type,
    make1: ( ty * $int * uni ) > uni ).

tff(exchange2,type,
    exchange2: ( ty * uni * uni * $int * $int * $int * $int ) > $o ).

tff(array_eq_sub1,type,
    array_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).

tff('#skF_2',type,
    '#skF_2': ( array_elt3 * $int * $int ) > $int ).

tff(tuple0,type,
    tuple0: ty ).

tff(qtmark,type,
    qtmark: ty ).

tff(bool,type,
    bool: ty ).

tff(permut_sub1,type,
    permut_sub1: ( ty * uni * uni * $int * $int ) > $o ).

tff(get,type,
    get: ( ty * ty * uni * uni ) > uni ).

tff('#skF_5',type,
    '#skF_5': ( $int * ty * uni * uni * $int ) > $int ).

tff(tuple03,type,
    tuple03: tuple02 ).

tff(map,type,
    map: ( ty * ty ) > ty ).

tff(permut3,type,
    permut3: ( ty * uni * uni * $int * $int ) > $o ).

tff(set2,type,
    set2: ( ty * uni * $int * uni ) > uni ).

tff(ref,type,
    ref: ty > ty ).

tff(mk_array1,type,
    mk_array1: ( ty * $int * uni ) > uni ).

tff(t2tb12,type,
    t2tb12: map_int_elt3 > uni ).

tff('#skF_13',type,
    '#skF_13': map_int_elt3 ).

tff('#skF_6',type,
    '#skF_6': ( uni * $int * ty * uni * $int ) > $int ).

tff(min,type,
    min: ( $int * $int ) > $int ).

tff('#skF_7',type,
    '#skF_7': ( $int * ty * $int * uni * uni * uni ) > $int ).

tff(mk_ref,type,
    mk_ref: ( ty * uni ) > uni ).

tff(sorted_sub4,type,
    sorted_sub4: ( array_elt3 * $int * $int ) > $o ).

tff(tb2t10,type,
    tb2t10: uni > array_elt3 ).

tff(f_112,axiom,
    ! [X: elt6] : le4(X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl4) ).

tff(f_147,axiom,
    ! [A: array_elt3,La: $int,Ua: $int] :
      ( sorted_sub4(A,La,Ua)
    <=> ! [I1a: $int,I2a: $int] :
          ( ( $lesseq(La,I1a)
            & $lesseq(I1a,I2a)
            & $less(I2a,Ua) )
         => le4(tb2t11(get2(elt7,t2tb10(A),I1a)),tb2t11(get2(elt7,t2tb10(A),I2a))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sorted_sub_def3) ).

tff(f_559,negated_conjecture,
    ~ ! [Aa: $int,A1: map_int_elt3,Loa: $int] :
        ( ( $lesseq(0,Aa)
          & $lesseq(0,Loa)
          & $less(Loa,Aa) )
       => sorted_sub4(tb2t10(mk_array1(elt7,Aa,t2tb12(A1))),Loa,$sum(Loa,1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_find_run) ).

tff(f_128,axiom,
    ! [J: uni] : ( t2tb10(tb2t10(J)) = J ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR10) ).

tff(c_58,plain,
    ! [X_82: elt6] : le4(X_82,X_82),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_2474,plain,
    ! [A_762: array_elt3,L_763a: $int,U_764a: $int] :
      ( $less('#skF_2'(A_762,L_763a,U_764a),U_764a)
      | sorted_sub4(A_762,L_763a,U_764a) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_332,plain,
    ~ sorted_sub4(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum('#skF_14',1)),
    inference(cnfTransformation,[status(thm)],[f_559]) ).

tff(c_368,plain,
    ~ sorted_sub4(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_332]) ).

tff(c_2481,plain,
    $less('#skF_2'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')),$sum(1,'#skF_14')),
    inference(resolution,[status(thm)],[c_2474,c_368]) ).

tff(c_2888,plain,
    '#skF_2'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_2481]) ).

tff(c_85,plain,
    ! [L_95a: $int,A_94: array_elt3,U_96a: $int] :
      ( $lesseq(L_95a,'#skF_1'(A_94,L_95a,U_96a))
      | sorted_sub4(A_94,L_95a,U_96a) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_2595,plain,
    ! [A_906: array_elt3,L_907a: $int,U_908a: $int] :
      ( ~ $less('#skF_1'(A_906,L_907a,U_908a),L_907a)
      | sorted_sub4(A_906,L_907a,U_908a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_85]) ).

tff(c_2602,plain,
    ~ $less('#skF_1'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')),'#skF_14'),
    inference(resolution,[status(thm)],[c_2595,c_368]) ).

tff(c_3009,plain,
    '#skF_1'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')) = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_2602]) ).

tff(c_68,plain,
    ! [J_90: uni] : ( t2tb10(tb2t10(J_90)) = J_90 ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_12280,plain,
    ! [A_1880: array_elt3,L_1881a: $int,U_1882a: $int] :
      ( ~ le4(tb2t11(get2(elt7,t2tb10(A_1880),'#skF_1'(A_1880,L_1881a,U_1882a))),tb2t11(get2(elt7,t2tb10(A_1880),'#skF_2'(A_1880,L_1881a,U_1882a))))
      | sorted_sub4(A_1880,L_1881a,U_1882a) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_12284,plain,
    ~ le4(tb2t11(get2(elt7,t2tb10(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13')))),'#skF_1'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')))),tb2t11(get2(elt7,t2tb10(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13')))),'#skF_2'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14'))))),
    inference(resolution,[status(thm)],[c_12280,c_368]) ).

tff(c_12840,plain,
    ~ le4(tb2t11(get2(elt7,mk_array1(elt7,'#skF_12',t2tb12('#skF_13')),'#skE_3')),tb2t11(get2(elt7,mk_array1(elt7,'#skF_12',t2tb12('#skF_13')),'#skE_2'))),
    inference(demodulation,[status(thm),theory(equality)],[c_2888,c_3009,c_68,c_68,c_12284]) ).

tff(c_12875,plain,
    '#skE_3' != '#skE_2',
    inference(resolution,[status(thm)],[c_58,c_12840]) ).

tff(c_12877,plain,
    '#skE_3' != '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12875]) ).

tff(c_82,plain,
    ! [A_94: array_elt3,L_95a: $int,U_96a: $int] :
      ( $lesseq('#skF_1'(A_94,L_95a,U_96a),'#skF_2'(A_94,L_95a,U_96a))
      | sorted_sub4(A_94,L_95a,U_96a) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_4509,plain,
    ! [A_1362: array_elt3,L_1363a: $int,U_1364a: $int] :
      ( ~ $less('#skF_2'(A_1362,L_1363a,U_1364a),'#skF_1'(A_1362,L_1363a,U_1364a))
      | sorted_sub4(A_1362,L_1363a,U_1364a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_82]) ).

tff(c_4513,plain,
    ~ $less('#skF_2'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')),'#skF_1'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14'))),
    inference(resolution,[status(thm)],[c_4509,c_368]) ).

tff(c_4516,plain,
    ~ $less('#skE_2','#skE_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_2888,c_3009,c_4513]) ).

tff(c_2654,plain,
    '#skF_1'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')) = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_2602]) ).

tff(c_2653,plain,
    ~ $less('#skF_1'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')),'#skF_14'),
    inference(resolution,[status(thm)],[c_2595,c_368]) ).

tff(c_2661,plain,
    ~ $less('#skE_3','#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_2654,c_2653]) ).

tff(c_2547,plain,
    '#skF_2'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_2481]) ).

tff(c_2546,plain,
    $less('#skF_2'(tb2t10(mk_array1(elt7,'#skF_12',t2tb12('#skF_13'))),'#skF_14',$sum(1,'#skF_14')),$sum(1,'#skF_14')),
    inference(resolution,[status(thm)],[c_2474,c_368]) ).

tff(c_2554,plain,
    $less('#skE_2',$sum(1,'#skF_14')),
    inference(demodulation,[status(thm),theory(equality)],[c_2547,c_2546]) ).

tff(c_12878,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_12877,c_4516,c_2661,c_2554]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW620_2 : TPTP v8.1.2. Released v6.1.0.
% 0.13/0.13  % 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
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 19:26:26 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 13.09/4.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.09/4.14  
% 13.09/4.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.09/4.18  
% 13.09/4.18  Inference rules
% 13.09/4.18  ----------------------
% 13.09/4.18  #Ref     : 1
% 13.09/4.18  #Sup     : 2167
% 13.09/4.18  #Fact    : 13
% 13.09/4.18  #Define  : 4
% 13.80/4.18  #Split   : 0
% 13.80/4.18  #Chain   : 0
% 13.80/4.18  #Close   : 1
% 13.80/4.18  
% 13.80/4.18  Ordering : LPO
% 13.80/4.18  
% 13.80/4.18  Simplification rules
% 13.80/4.18  ----------------------
% 13.80/4.18  #Subsume      : 146
% 13.80/4.18  #Demod        : 659
% 13.80/4.18  #Tautology    : 1381
% 13.80/4.18  #SimpNegUnit  : 0
% 13.80/4.18  #BackRed      : 4
% 13.80/4.18  
% 13.80/4.18  #Partial instantiations: 254
% 13.80/4.18  #Strategies tried      : 1
% 13.80/4.18  
% 13.80/4.18  Timing (in seconds)
% 13.80/4.18  ----------------------
% 13.80/4.18  Preprocessing        : 1.04
% 13.80/4.18  Parsing              : 0.52
% 13.80/4.18  CNF conversion       : 0.08
% 13.80/4.18  Main loop            : 2.06
% 13.80/4.18  Inferencing          : 0.63
% 13.80/4.18  Reduction            : 0.63
% 13.80/4.18  Demodulation         : 0.48
% 13.80/4.18  BG Simplification    : 0.25
% 13.80/4.18  Subsumption          : 0.44
% 13.80/4.18  Abstraction          : 0.07
% 13.80/4.18  MUC search           : 0.01
% 13.80/4.18  Cooper               : 0.04
% 13.80/4.18  Total                : 3.16
% 13.80/4.18  Index Insertion      : 0.00
% 13.80/4.18  Index Deletion       : 0.00
% 13.80/4.18  Index Matching       : 0.00
% 13.80/4.18  BG Taut test         : 0.00
%------------------------------------------------------------------------------