TSTP Solution File: SWV374+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV374+1 : 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 : n029.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 11:03:57 EDT 2023

% Result   : Theorem 71.86s 33.81s
% Output   : CNFRefutation 71.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   70 (  23 unt;  30 typ;   0 def)
%            Number of atoms       :   74 (  26 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   59 (  25   ~;  23   |;   6   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  24   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   21 (  21 usr;   6 con; 0-3 aty)
%            Number of variables   :   49 (;  49   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ pair_in_list > succ_cpq > strictly_less_than > less_than > contains_slb > contains_cpq > ok > isnonempty_slb > check_cpq > triple > update_slb > remove_slb > remove_pqp > remove_cpq > pair > lookup_slb > insert_slb > insert_pqp > insert_cpq > #nlpp > removemin_cpq_res > removemin_cpq_eff > findmin_pqp_res > findmin_cpq_res > findmin_cpq_eff > create_slb > bottom > bad > #skF_2 > #skF_3 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(bad,type,
    bad: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_60,axiom,
    ! [U,V] :
      ( less_than(U,V)
      | less_than(V,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).

tff(f_217,axiom,
    ! [U,V] :
      ( ok(triple(U,V,bad))
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).

tff(f_293,negated_conjecture,
    ~ ! [U,V,W] :
        ( ok(findmin_cpq_eff(triple(U,V,W)))
       => ( ( V != create_slb )
          & contains_slb(V,findmin_pqp_res(U))
          & less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_co) ).

tff(f_251,axiom,
    ! [U,V,W,X] :
      ( ( ( V != create_slb )
        & ~ contains_slb(V,findmin_pqp_res(U)) )
     => ( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax47) ).

tff(f_243,axiom,
    ! [U,V] : ( findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax46) ).

tff(f_69,axiom,
    ! [U,V] :
      ( strictly_less_than(U,V)
    <=> ( less_than(U,V)
        & ~ less_than(V,U) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).

tff(f_260,axiom,
    ! [U,V,W,X] :
      ( ( ( V != create_slb )
        & contains_slb(V,findmin_pqp_res(U))
        & strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) )
     => ( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax48) ).

tff(f_104,axiom,
    ! [U] : ~ contains_slb(create_slb,U),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax20) ).

tff(c_4,plain,
    ! [V_5,U_4] :
      ( less_than(V_5,U_4)
      | less_than(U_4,V_5) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_74,plain,
    ! [U_75,V_76] : ~ ok(triple(U_75,V_76,bad)),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_102,plain,
    ( ~ less_than(lookup_slb('#skF_2',findmin_pqp_res('#skF_1')),findmin_pqp_res('#skF_1'))
    | ~ contains_slb('#skF_2',findmin_pqp_res('#skF_1'))
    | ( create_slb = '#skF_2' ) ),
    inference(cnfTransformation,[status(thm)],[f_293]) ).

tff(c_164,plain,
    ~ contains_slb('#skF_2',findmin_pqp_res('#skF_1')),
    inference(splitLeft,[status(thm)],[c_102]) ).

tff(c_104,plain,
    ok(findmin_cpq_eff(triple('#skF_1','#skF_2','#skF_3'))),
    inference(cnfTransformation,[status(thm)],[f_293]) ).

tff(c_1072,plain,
    ! [U_350,V_351,W_352] :
      ( ( triple(U_350,update_slb(V_351,findmin_pqp_res(U_350)),bad) = findmin_cpq_eff(triple(U_350,V_351,W_352)) )
      | contains_slb(V_351,findmin_pqp_res(U_350))
      | ( create_slb = V_351 ) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_1170,plain,
    ! [U_353,V_354,W_355] :
      ( ~ ok(findmin_cpq_eff(triple(U_353,V_354,W_355)))
      | contains_slb(V_354,findmin_pqp_res(U_353))
      | ( create_slb = V_354 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1072,c_74]) ).

tff(c_1185,plain,
    ( contains_slb('#skF_2',findmin_pqp_res('#skF_1'))
    | ( create_slb = '#skF_2' ) ),
    inference(resolution,[status(thm)],[c_104,c_1170]) ).

tff(c_1189,plain,
    create_slb = '#skF_2',
    inference(negUnitSimplification,[status(thm)],[c_164,c_1185]) ).

tff(c_86,plain,
    ! [U_96,V_97] : ( findmin_cpq_eff(triple(U_96,create_slb,V_97)) = triple(U_96,create_slb,bad) ),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_1198,plain,
    ! [U_96,V_97] : ( findmin_cpq_eff(triple(U_96,'#skF_2',V_97)) = triple(U_96,'#skF_2',bad) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1189,c_1189,c_86]) ).

tff(c_1330,plain,
    ok(triple('#skF_1','#skF_2',bad)),
    inference(demodulation,[status(thm),theory(equality)],[c_1198,c_104]) ).

tff(c_1332,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_74,c_1330]) ).

tff(c_1333,plain,
    ( ~ less_than(lookup_slb('#skF_2',findmin_pqp_res('#skF_1')),findmin_pqp_res('#skF_1'))
    | ( create_slb = '#skF_2' ) ),
    inference(splitRight,[status(thm)],[c_102]) ).

tff(c_1373,plain,
    ~ less_than(lookup_slb('#skF_2',findmin_pqp_res('#skF_1')),findmin_pqp_res('#skF_1')),
    inference(splitLeft,[status(thm)],[c_1333]) ).

tff(c_1380,plain,
    less_than(findmin_pqp_res('#skF_1'),lookup_slb('#skF_2',findmin_pqp_res('#skF_1'))),
    inference(resolution,[status(thm)],[c_4,c_1373]) ).

tff(c_1334,plain,
    contains_slb('#skF_2',findmin_pqp_res('#skF_1')),
    inference(splitRight,[status(thm)],[c_102]) ).

tff(c_8,plain,
    ! [U_7,V_8] :
      ( strictly_less_than(U_7,V_8)
      | less_than(V_8,U_7)
      | ~ less_than(U_7,V_8) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_5261,plain,
    ! [U_800,V_801,W_802] :
      ( ( triple(U_800,update_slb(V_801,findmin_pqp_res(U_800)),bad) = findmin_cpq_eff(triple(U_800,V_801,W_802)) )
      | ~ strictly_less_than(findmin_pqp_res(U_800),lookup_slb(V_801,findmin_pqp_res(U_800)))
      | ~ contains_slb(V_801,findmin_pqp_res(U_800))
      | ( create_slb = V_801 ) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_398864,plain,
    ! [U_43906,V_43907,W_43908] :
      ( ( triple(U_43906,update_slb(V_43907,findmin_pqp_res(U_43906)),bad) = findmin_cpq_eff(triple(U_43906,V_43907,W_43908)) )
      | ~ contains_slb(V_43907,findmin_pqp_res(U_43906))
      | ( create_slb = V_43907 )
      | less_than(lookup_slb(V_43907,findmin_pqp_res(U_43906)),findmin_pqp_res(U_43906))
      | ~ less_than(findmin_pqp_res(U_43906),lookup_slb(V_43907,findmin_pqp_res(U_43906))) ),
    inference(resolution,[status(thm)],[c_8,c_5261]) ).

tff(c_399496,plain,
    ! [W_43908] :
      ( ( triple('#skF_1',update_slb('#skF_2',findmin_pqp_res('#skF_1')),bad) = findmin_cpq_eff(triple('#skF_1','#skF_2',W_43908)) )
      | ~ contains_slb('#skF_2',findmin_pqp_res('#skF_1'))
      | ( create_slb = '#skF_2' )
      | ~ less_than(findmin_pqp_res('#skF_1'),lookup_slb('#skF_2',findmin_pqp_res('#skF_1'))) ),
    inference(resolution,[status(thm)],[c_398864,c_1373]) ).

tff(c_402622,plain,
    ! [W_43908] :
      ( ( triple('#skF_1',update_slb('#skF_2',findmin_pqp_res('#skF_1')),bad) = findmin_cpq_eff(triple('#skF_1','#skF_2',W_43908)) )
      | ( create_slb = '#skF_2' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1380,c_1334,c_399496]) ).

tff(c_402680,plain,
    create_slb = '#skF_2',
    inference(splitLeft,[status(thm)],[c_402622]) ).

tff(c_20,plain,
    ! [U_13] : ~ contains_slb(create_slb,U_13),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_402770,plain,
    ! [U_13] : ~ contains_slb('#skF_2',U_13),
    inference(demodulation,[status(thm),theory(equality)],[c_402680,c_20]) ).

tff(c_402871,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_402770,c_1334]) ).

tff(c_402882,plain,
    ! [W_44169] : ( triple('#skF_1',update_slb('#skF_2',findmin_pqp_res('#skF_1')),bad) = findmin_cpq_eff(triple('#skF_1','#skF_2',W_44169)) ),
    inference(splitRight,[status(thm)],[c_402622]) ).

tff(c_403417,plain,
    ! [W_44169] : ~ ok(findmin_cpq_eff(triple('#skF_1','#skF_2',W_44169))),
    inference(superposition,[status(thm),theory(equality)],[c_402882,c_74]) ).

tff(c_405396,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_403417,c_104]) ).

tff(c_405397,plain,
    create_slb = '#skF_2',
    inference(splitRight,[status(thm)],[c_1333]) ).

tff(c_405403,plain,
    ! [U_13] : ~ contains_slb('#skF_2',U_13),
    inference(demodulation,[status(thm),theory(equality)],[c_405397,c_20]) ).

tff(c_405410,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_405403,c_1334]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWV374+1 : 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
% 0.13/0.35  % Computer : n029.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 23:19:52 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 71.86/33.81  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.86/33.82  
% 71.86/33.82  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 71.86/33.85  
% 71.86/33.85  Inference rules
% 71.86/33.85  ----------------------
% 71.86/33.85  #Ref     : 0
% 71.86/33.85  #Sup     : 68718
% 71.86/33.85  #Fact    : 286
% 71.86/33.85  #Define  : 0
% 71.86/33.85  #Split   : 19
% 71.86/33.85  #Chain   : 0
% 71.86/33.85  #Close   : 0
% 71.86/33.85  
% 71.86/33.85  Ordering : KBO
% 71.86/33.85  
% 71.86/33.85  Simplification rules
% 71.86/33.85  ----------------------
% 71.86/33.85  #Subsume      : 4309
% 71.86/33.85  #Demod        : 11291
% 71.86/33.85  #Tautology    : 1555
% 71.86/33.85  #SimpNegUnit  : 246
% 71.86/33.85  #BackRed      : 209
% 71.86/33.85  
% 71.86/33.85  #Partial instantiations: 33894
% 71.86/33.85  #Strategies tried      : 1
% 71.86/33.85  
% 71.86/33.85  Timing (in seconds)
% 71.86/33.85  ----------------------
% 71.86/33.85  Preprocessing        : 0.64
% 71.86/33.85  Parsing              : 0.33
% 71.86/33.85  CNF conversion       : 0.04
% 71.86/33.85  Main loop            : 32.15
% 71.86/33.85  Inferencing          : 6.30
% 71.86/33.85  Reduction            : 12.61
% 71.86/33.85  Demodulation         : 8.45
% 71.86/33.85  BG Simplification    : 0.75
% 71.86/33.85  Subsumption          : 10.94
% 71.86/33.85  Abstraction          : 0.57
% 71.86/33.85  MUC search           : 0.00
% 71.86/33.85  Cooper               : 0.00
% 71.86/33.85  Total                : 32.84
% 71.86/33.85  Index Insertion      : 0.00
% 71.86/33.85  Index Deletion       : 0.00
% 71.86/33.85  Index Matching       : 0.00
% 71.86/33.85  BG Taut test         : 0.00
%------------------------------------------------------------------------------