TSTP Solution File: SWV157+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n018.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 11:03:02 EDT 2023

% Result   : Theorem 10.80s 3.51s
% Output   : CNFRefutation 11.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   80
% Syntax   : Number of formulae    :   95 (   9 unt;  77 typ;   0 def)
%            Number of atoms       :   44 (  14 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :   42 (  16   ~;   9   |;  10   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  166 (  53   >; 113   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   2 prp; 0-2 aty)
%            Number of functors    :   72 (  72 usr;  23 con; 0-8 aty)
%            Number of variables   :   13 (;  13   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ lt > leq > gt > geq > tptp_update3 > tptp_update2 > tptp_const_array2 > sum > a_select3 > uniform_int_rnd > tptp_msub > tptp_mmul > tptp_madd > tptp_const_array1 > times > plus > minus > divide > dim > a_select2 > #nlpp > trans > succ > sqrt > pred > inv > exp > x > use > true > tptp_sum_index > tptp_pi > tptp_minus_2 > tptp_minus_1 > tptp_float_0_0 > sigma > rho > q > pv84 > pv47 > pv10 > n5 > n4 > n3 > n2 > n135299 > n1 > n0 > mu > def > #skF_13 > #skF_24 > #skF_17 > #skF_23 > #skF_6 > #skF_19 > #skF_27 > #skF_21 > #skF_25 > #skF_12 > #skF_18 > #skF_3 > #skF_26 > #skF_20 > #skF_11 > #skF_7 > #skF_9 > #skF_15 > #skF_22 > #skF_14 > #skF_28 > #skF_2 > #skF_8 > #skF_1 > #skF_5 > #skF_4 > #skF_16 > #skF_10

%Foreground sorts:

%Background operators:

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

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

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

tff(true,type,
    true: $o ).

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

tff(tptp_const_array2,type,
    tptp_const_array2: ( $i * $i * $i ) > $i ).

tff(n135299,type,
    n135299: $i ).

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

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

tff(tptp_minus_1,type,
    tptp_minus_1: $i ).

tff(tptp_minus_2,type,
    tptp_minus_2: $i ).

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

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

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

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

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

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

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

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

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

tff(a_select3,type,
    a_select3: ( $i * $i * $i ) > $i ).

tff(tptp_float_0_0,type,
    tptp_float_0_0: $i ).

tff(a_select2,type,
    a_select2: ( $i * $i ) > $i ).

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

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

tff(tptp_update3,type,
    tptp_update3: ( $i * $i * $i * $i ) > $i ).

tff(n3,type,
    n3: $i ).

tff(pv10,type,
    pv10: $i ).

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

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

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

tff(n1,type,
    n1: $i ).

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

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

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

tff(n0,type,
    n0: $i ).

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

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

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

tff(pv47,type,
    pv47: $i ).

tff(tptp_update2,type,
    tptp_update2: ( $i * $i * $i ) > $i ).

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

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

tff(n4,type,
    n4: $i ).

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

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

tff(pv84,type,
    pv84: $i ).

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

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

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

tff(tptp_const_array1,type,
    tptp_const_array1: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(n2,type,
    n2: $i ).

tff(n5,type,
    n5: $i ).

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

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

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

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

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

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

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

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

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

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

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

tff(f_513,negated_conjecture,
    ~ ( ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) )
        & leq(n0,pv10)
        & leq(n0,pv47)
        & leq(pv10,n135299)
        & leq(pv47,n4)
        & ! [A] :
            ( ( leq(n0,A)
              & leq(A,pred(pv47)) )
           => ( a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) )
        & ! [B] :
            ( ( leq(n0,B)
              & leq(B,pred(pv10)) )
           => ( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ) )
     => ! [C] :
          ( ( leq(n0,C)
            & leq(C,pv47) )
         => ( ( pv47 != C )
           => ( a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0007) ).

tff(f_105,axiom,
    ! [X,Y] :
      ( leq(X,pred(Y))
    <=> gt(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).

tff(f_100,axiom,
    ! [X,Y] :
      ( ( leq(X,Y)
        & ( X != Y ) )
     => gt(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).

tff(c_514,plain,
    pv47 != '#skF_28',
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_2436,plain,
    ! [X_248,Y_249] :
      ( leq(X_248,pred(Y_249))
      | ~ gt(Y_249,X_248) ),
    inference(cnfTransformation,[status(thm)],[f_105]) ).

tff(c_518,plain,
    leq(n0,'#skF_28'),
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_532,plain,
    sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) = pv84,
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_522,plain,
    ! [A_181] :
      ( ( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A_181)),minus(a_select2(x,pv10),a_select2(mu,A_181))),tptp_minus_2),times(a_select2(sigma,A_181),a_select2(sigma,A_181)))),a_select2(rho,A_181)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A_181))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) = a_select3(q,pv10,A_181) )
      | ~ leq(A_181,pred(pv47))
      | ~ leq(n0,A_181) ),
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_1464,plain,
    ! [A_224] :
      ( ( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A_224)),minus(a_select2(x,pv10),a_select2(mu,A_224))),tptp_minus_2),times(a_select2(sigma,A_224),a_select2(sigma,A_224)))),a_select2(rho,A_224)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A_224))),pv84) = a_select3(q,pv10,A_224) )
      | ~ leq(A_224,pred(pv47))
      | ~ leq(n0,A_224) ),
    inference(demodulation,[status(thm),theory(equality)],[c_532,c_522]) ).

tff(c_512,plain,
    divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,'#skF_28')),minus(a_select2(x,pv10),a_select2(mu,'#skF_28'))),tptp_minus_2),times(a_select2(sigma,'#skF_28'),a_select2(sigma,'#skF_28')))),a_select2(rho,'#skF_28')),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,'#skF_28'))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) != a_select3(q,pv10,'#skF_28'),
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_633,plain,
    divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,'#skF_28')),minus(a_select2(x,pv10),a_select2(mu,'#skF_28'))),tptp_minus_2),times(a_select2(sigma,'#skF_28'),a_select2(sigma,'#skF_28')))),a_select2(rho,'#skF_28')),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,'#skF_28'))),pv84) != a_select3(q,pv10,'#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_532,c_512]) ).

tff(c_1470,plain,
    ( ~ leq('#skF_28',pred(pv47))
    | ~ leq(n0,'#skF_28') ),
    inference(superposition,[status(thm),theory(equality)],[c_1464,c_633]) ).

tff(c_1477,plain,
    ~ leq('#skF_28',pred(pv47)),
    inference(demodulation,[status(thm),theory(equality)],[c_518,c_1470]) ).

tff(c_2489,plain,
    ~ gt(pv47,'#skF_28'),
    inference(resolution,[status(thm)],[c_2436,c_1477]) ).

tff(c_516,plain,
    leq('#skF_28',pv47),
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_3846,plain,
    ! [Y_278,X_279] :
      ( gt(Y_278,X_279)
      | ( Y_278 = X_279 )
      | ~ leq(X_279,Y_278) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_3906,plain,
    ( gt(pv47,'#skF_28')
    | ( pv47 = '#skF_28' ) ),
    inference(resolution,[status(thm)],[c_516,c_3846]) ).

tff(c_3934,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_514,c_2489,c_3906]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.15  % 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
% 0.15/0.37  % Computer : n018.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 23:05:36 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 10.80/3.51  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.80/3.52  
% 10.80/3.52  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.07/3.54  
% 11.07/3.54  Inference rules
% 11.07/3.54  ----------------------
% 11.07/3.54  #Ref     : 0
% 11.07/3.54  #Sup     : 868
% 11.07/3.54  #Fact    : 2
% 11.07/3.54  #Define  : 0
% 11.07/3.54  #Split   : 3
% 11.07/3.54  #Chain   : 0
% 11.07/3.54  #Close   : 0
% 11.07/3.54  
% 11.07/3.54  Ordering : KBO
% 11.07/3.54  
% 11.07/3.54  Simplification rules
% 11.07/3.54  ----------------------
% 11.07/3.54  #Subsume      : 112
% 11.07/3.54  #Demod        : 315
% 11.07/3.54  #Tautology    : 273
% 11.07/3.54  #SimpNegUnit  : 7
% 11.07/3.54  #BackRed      : 0
% 11.07/3.54  
% 11.07/3.54  #Partial instantiations: 0
% 11.07/3.54  #Strategies tried      : 1
% 11.07/3.54  
% 11.07/3.54  Timing (in seconds)
% 11.07/3.54  ----------------------
% 11.07/3.55  Preprocessing        : 0.95
% 11.07/3.55  Parsing              : 0.37
% 11.07/3.55  CNF conversion       : 0.07
% 11.07/3.55  Main loop            : 1.40
% 11.07/3.55  Inferencing          : 0.36
% 11.07/3.55  Reduction            : 0.56
% 11.07/3.55  Demodulation         : 0.41
% 11.07/3.55  BG Simplification    : 0.11
% 11.07/3.55  Subsumption          : 0.31
% 11.07/3.55  Abstraction          : 0.07
% 11.07/3.55  MUC search           : 0.00
% 11.07/3.55  Cooper               : 0.00
% 11.07/3.55  Total                : 2.40
% 11.07/3.55  Index Insertion      : 0.00
% 11.07/3.55  Index Deletion       : 0.00
% 11.07/3.55  Index Matching       : 0.00
% 11.07/3.55  BG Taut test         : 0.00
%------------------------------------------------------------------------------