TSTP Solution File: NUM926+5 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 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 : n020.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 10:53:11 EDT 2023

% Result   : Theorem 7.21s 2.59s
% Output   : CNFRefutation 7.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   58 (  16 unt;  33 typ;   0 def)
%            Number of atoms       :   36 (  24 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  13   ~;   7   |;   1   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  22   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-3 aty)
%            Number of variables   :   28 (;  22   !;   6   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ord_less_eq > ord_less > zprime > twoSqu33214720sum2sq > semiring_1 > ring_char_0 > number_semiring > number_ring > number > monoid_mult > linordered_idom > linorder > comm_semiring_1 > times_times > power_power > plus_plus > ti > number_number_of > #nlpp > undefined > one_one > bit1 > bit0 > t > s > pls > nat > m > int > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(semiring_1,type,
    semiring_1: $i > $o ).

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

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

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

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

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

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

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

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

tff(bit0,type,
    bit0: $i > $i ).

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

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

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

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

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

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

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

tff(twoSqu33214720sum2sq,type,
    twoSqu33214720sum2sq: $i > $o ).

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

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

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

tff(comm_semiring_1,type,
    comm_semiring_1: $i > $o ).

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

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

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

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

tff(bit1,type,
    bit1: $i > $i ).

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

tff(ring_char_0,type,
    ring_char_0: $i > $o ).

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

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

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

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

tff(f_498,axiom,
    ! [Z,W] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).

tff(f_500,axiom,
    ! [K_1] : ( number_number_of(int,K_1) = K_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).

tff(f_506,axiom,
    ! [Z,W] : ( plus_plus(int,Z,W) = plus_plus(int,W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).

tff(f_561,negated_conjecture,
    ~ ? [X,Y] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f_136,axiom,
    ( ( t = one_one(int) )
   => ? [X,Y] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

tff(f_140,axiom,
    ( ord_less(int,one_one(int),t)
   => ? [X,Y] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

tff(f_132,axiom,
    ord_less_eq(int,one_one(int),t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).

tff(f_212,axiom,
    ! [Z_1,W_1] :
      ( ord_less(int,Z_1,W_1)
    <=> ( ord_less_eq(int,Z_1,W_1)
        & ( Z_1 != W_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).

tff(c_299,plain,
    ! [Z_305,W_306] : ( times_times(int,Z_305,W_306) = times_times(int,W_306,Z_305) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_301,plain,
    ! [K_1_307] : ( number_number_of(int,K_1_307) = K_1_307 ),
    inference(cnfTransformation,[status(thm)],[f_500]) ).

tff(c_307,plain,
    ! [Z_314,W_315] : ( plus_plus(int,Z_314,W_315) = plus_plus(int,W_315,Z_314) ),
    inference(cnfTransformation,[status(thm)],[f_506]) ).

tff(c_373,plain,
    ! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(cnfTransformation,[status(thm)],[f_561]) ).

tff(c_374,plain,
    ! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_307,c_373]) ).

tff(c_375,plain,
    ! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,bit0(bit0(bit1(pls))),m)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_301,c_374]) ).

tff(c_376,plain,
    ! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_299,c_375]) ).

tff(c_70,plain,
    ( ( plus_plus(int,power_power(int,'#skF_1',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_2',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) )
    | ( one_one(int) != t ) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_394,plain,
    ( ( plus_plus(int,power_power(int,'#skF_1',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_2',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) )
    | ( one_one(int) != t ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_299,c_301,c_307,c_70]) ).

tff(c_395,plain,
    one_one(int) != t,
    inference(negUnitSimplification,[status(thm)],[c_376,c_394]) ).

tff(c_72,plain,
    ( ( plus_plus(int,power_power(int,'#skF_3',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_4',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) )
    | ~ ord_less(int,one_one(int),t) ),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_392,plain,
    ( ( plus_plus(int,power_power(int,'#skF_4',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_3',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) )
    | ~ ord_less(int,one_one(int),t) ),
    inference(demodulation,[status(thm),theory(equality)],[c_299,c_301,c_307,c_307,c_72]) ).

tff(c_393,plain,
    ~ ord_less(int,one_one(int),t),
    inference(negUnitSimplification,[status(thm)],[c_376,c_392]) ).

tff(c_68,plain,
    ord_less_eq(int,one_one(int),t),
    inference(cnfTransformation,[status(thm)],[f_132]) ).

tff(c_1182,plain,
    ! [Z_1_409,W_1_410] :
      ( ord_less(int,Z_1_409,W_1_410)
      | ( Z_1_409 = W_1_410 )
      | ~ ord_less_eq(int,Z_1_409,W_1_410) ),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_1218,plain,
    ( ord_less(int,one_one(int),t)
    | ( one_one(int) = t ) ),
    inference(resolution,[status(thm)],[c_68,c_1182]) ).

tff(c_1236,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_395,c_393,c_1218]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13  % 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
% 0.13/0.35  % Computer : n020.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 15:14:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 7.21/2.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.21/2.60  
% 7.21/2.60  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.21/2.63  
% 7.21/2.63  Inference rules
% 7.21/2.63  ----------------------
% 7.21/2.63  #Ref     : 3
% 7.21/2.63  #Sup     : 189
% 7.21/2.63  #Fact    : 2
% 7.21/2.63  #Define  : 0
% 7.21/2.63  #Split   : 0
% 7.21/2.63  #Chain   : 0
% 7.21/2.63  #Close   : 0
% 7.21/2.63  
% 7.21/2.63  Ordering : KBO
% 7.21/2.63  
% 7.21/2.63  Simplification rules
% 7.21/2.63  ----------------------
% 7.21/2.63  #Subsume      : 41
% 7.21/2.63  #Demod        : 128
% 7.21/2.63  #Tautology    : 171
% 7.21/2.63  #SimpNegUnit  : 3
% 7.21/2.63  #BackRed      : 1
% 7.21/2.63  
% 7.21/2.63  #Partial instantiations: 0
% 7.21/2.63  #Strategies tried      : 1
% 7.21/2.63  
% 7.21/2.63  Timing (in seconds)
% 7.21/2.63  ----------------------
% 7.21/2.63  Preprocessing        : 0.92
% 7.21/2.63  Parsing              : 0.46
% 7.21/2.63  CNF conversion       : 0.08
% 7.21/2.63  Main loop            : 0.64
% 7.21/2.63  Inferencing          : 0.17
% 7.21/2.63  Reduction            : 0.24
% 7.21/2.63  Demodulation         : 0.17
% 7.21/2.63  BG Simplification    : 0.07
% 7.21/2.63  Subsumption          : 0.14
% 7.21/2.63  Abstraction          : 0.03
% 7.21/2.63  MUC search           : 0.00
% 7.21/2.63  Cooper               : 0.00
% 7.21/2.63  Total                : 1.61
% 7.21/2.63  Index Insertion      : 0.00
% 7.21/2.63  Index Deletion       : 0.00
% 7.21/2.63  Index Matching       : 0.00
% 7.21/2.63  BG Taut test         : 0.00
%------------------------------------------------------------------------------