TSTP Solution File: NUM925+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM925+2 : 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 : 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 10:53:08 EDT 2023

% Result   : Theorem 15.59s 4.80s
% Output   : CNFRefutation 16.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   85
% Syntax   : Number of formulae    :  115 (  40 unt;  72 typ;   0 def)
%            Number of atoms       :   47 (  39 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   11 (   7   ~;   2   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   83 (  50   >;  33   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   70 (  70 usr;  22 con; 0-3 aty)
%            Number of variables   :   24 (;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ is_bool > hBOOL > times_times_int > if_nat > hAPP_real_real > hAPP_real_bool > hAPP_r1134773055l_bool > hAPP_nat_real > hAPP_nat_nat > hAPP_nat_int > hAPP_nat_bool > hAPP_n1699378549t_bool > hAPP_int_int > hAPP_int_bool > hAPP_i1948725293t_bool > #nlpp > succ > sqrt > power_power_real > power_power_nat > power_power_int > plus_plus_real > plus_plus_nat > plus_plus_int > number_number_of_nat > number_number_of_int > number267125858f_real > bit1 > bit0 > zero_zero_real > zero_zero_nat > zero_zero_int > tn > t > semiri984289939at_nat > semiri1621563631at_int > semiri132038758t_real > pls > ord_less_real > ord_less_nat > ord_less_int > ord_less_eq_real > ord_less_eq_nat > ord_less_eq_int > one_one_real > one_one_nat > one_one_int > n > m1 > fTrue > fFalse > #skF_9 > #skF_7 > #skF_22 > #skF_17 > #skF_1 > #skF_2 > #skF_18 > #skF_8 > #skF_3 > #skF_13 > #skF_14 > #skF_15 > #skF_19 > #skF_10 > #skF_20 > #skF_11 > #skF_12 > #skF_21 > #skF_5 > #skF_6 > #skF_4 > #skF_16

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(number267125858f_real,type,
    number267125858f_real: $i > $i ).

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

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

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

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

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

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

tff(hAPP_i1948725293t_bool,type,
    hAPP_i1948725293t_bool: ( $i * $i ) > $i ).

tff(semiri984289939at_nat,type,
    semiri984289939at_nat: $i ).

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

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

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

tff(semiri132038758t_real,type,
    semiri132038758t_real: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(hAPP_r1134773055l_bool,type,
    hAPP_r1134773055l_bool: ( $i * $i ) > $i ).

tff(hAPP_n1699378549t_bool,type,
    hAPP_n1699378549t_bool: ( $i * $i ) > $i ).

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

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

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

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

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

tff(semiri1621563631at_int,type,
    semiri1621563631at_int: $i ).

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

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

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

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

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

tff(m1,type,
    m1: $i ).

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

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

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

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

tff(f_596,axiom,
    ! [K] : ( number_number_of_int(K) = K ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).

tff(f_363,axiom,
    zero_zero_int = number_number_of_int(pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).

tff(f_1053,axiom,
    ! [M_4] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_4)),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_of__nat__less__0__iff) ).

tff(f_1288,axiom,
    ! [A_40] : ( hAPP_int_int(plus_plus_int(zero_zero_int),A_40) = A_40 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__0__left) ).

tff(f_460,axiom,
    ! [W_3] : ( number_number_of_int(bit0(W_3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(W_3))),number_number_of_int(W_3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_number__of__Bit0) ).

tff(f_2245,axiom,
    ! [K] : ( succ(K) = hAPP_int_int(plus_plus_int(K),one_one_int) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_succ__def) ).

tff(f_76,axiom,
    hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_semiring__one__add__one__is__two) ).

tff(f_74,axiom,
    hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__add__one__is__two) ).

tff(f_150,axiom,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_nat__1__add__1) ).

tff(f_2302,axiom,
    ! [K_3] : ( number_number_of_int(succ(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_number__of__succ) ).

tff(f_2955,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f_1044,axiom,
    ! [A_24,Na] :
      ( ( hAPP_nat_int(power_power_int(A_24),Na) = zero_zero_int )
    <=> ( ( A_24 = zero_zero_int )
        & ( Na != zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_power__eq__0__iff) ).

tff(f_951,axiom,
    ! [A_59] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_59),hAPP_int_int(plus_plus_int(A_59),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_less__add__one) ).

tff(c_521,plain,
    ! [K_202] : ( number_number_of_int(K_202) = K_202 ),
    inference(cnfTransformation,[status(thm)],[f_596]) ).

tff(c_347,plain,
    number_number_of_int(pls) = zero_zero_int,
    inference(cnfTransformation,[status(thm)],[f_363]) ).

tff(c_2270,plain,
    zero_zero_int = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_521,c_347]) ).

tff(c_854,plain,
    ! [M_4_404] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_4_404)),zero_zero_int)),
    inference(cnfTransformation,[status(thm)],[f_1053]) ).

tff(c_2299,plain,
    ! [M_4_404] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_4_404)),pls)),
    inference(demodulation,[status(thm),theory(equality)],[c_2270,c_854]) ).

tff(c_1088,plain,
    ! [A_40_561] : ( hAPP_int_int(plus_plus_int(zero_zero_int),A_40_561) = A_40_561 ),
    inference(cnfTransformation,[status(thm)],[f_1288]) ).

tff(c_431,plain,
    ! [W_3_163] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(W_3_163))),number_number_of_int(W_3_163)) = number_number_of_int(bit0(W_3_163)) ),
    inference(cnfTransformation,[status(thm)],[f_460]) ).

tff(c_2243,plain,
    ! [W_3_163] : ( hAPP_int_int(plus_plus_int(W_3_163),W_3_163) = bit0(W_3_163) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_521,c_521,c_521,c_431]) ).

tff(c_1646,plain,
    ! [K_1012] : ( hAPP_int_int(plus_plus_int(K_1012),one_one_int) = succ(K_1012) ),
    inference(cnfTransformation,[status(thm)],[f_2245]) ).

tff(c_60,plain,
    number_number_of_int(bit0(bit1(pls))) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_2468,plain,
    bit0(bit1(pls)) = succ(one_one_int),
    inference(demodulation,[status(thm),theory(equality)],[c_1646,c_521,c_60]) ).

tff(c_56,plain,
    number_number_of_int(bit0(bit1(pls))) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_2519,plain,
    succ(one_one_int) = bit0(one_one_int),
    inference(demodulation,[status(thm),theory(equality)],[c_2243,c_2468,c_521,c_56]) ).

tff(c_128,plain,
    number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_2471,plain,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(succ(one_one_int)),
    inference(demodulation,[status(thm),theory(equality)],[c_2468,c_128]) ).

tff(c_1666,plain,
    ! [K_3_1030] : ( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3_1030)) = number_number_of_int(succ(K_3_1030)) ),
    inference(cnfTransformation,[status(thm)],[f_2302]) ).

tff(c_2200,plain,
    ! [K_3_1030] : ( hAPP_int_int(plus_plus_int(one_one_int),K_3_1030) = succ(K_3_1030) ),
    inference(demodulation,[status(thm),theory(equality)],[c_521,c_521,c_1666]) ).

tff(c_2062,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(cnfTransformation,[status(thm)],[f_2955]) ).

tff(c_2225,plain,
    hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(demodulation,[status(thm),theory(equality)],[c_2200,c_2062]) ).

tff(c_2293,plain,
    hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_2270,c_2225]) ).

tff(c_2405,plain,
    hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_2293]) ).

tff(c_2479,plain,
    hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(succ(one_one_int))) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_2471,c_2405]) ).

tff(c_2528,plain,
    hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_2519,c_2479]) ).

tff(c_848,plain,
    ! [A_24_400,Na_401] :
      ( ( zero_zero_int = A_24_400 )
      | ( hAPP_nat_int(power_power_int(A_24_400),Na_401) != zero_zero_int ) ),
    inference(cnfTransformation,[status(thm)],[f_1044]) ).

tff(c_3984,plain,
    ! [A_24_1398,Na_1399] :
      ( ( pls = A_24_1398 )
      | ( hAPP_nat_int(power_power_int(A_24_1398),Na_1399) != pls ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2270,c_2270,c_848]) ).

tff(c_4008,plain,
    succ(hAPP_nat_int(semiri1621563631at_int,n)) = pls,
    inference(superposition,[status(thm),theory(equality)],[c_2528,c_3984]) ).

tff(c_791,plain,
    ! [A_59_359] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_59_359),hAPP_int_int(plus_plus_int(A_59_359),one_one_int))),
    inference(cnfTransformation,[status(thm)],[f_951]) ).

tff(c_2182,plain,
    ! [A_59_359] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_59_359),succ(A_59_359))),
    inference(demodulation,[status(thm),theory(equality)],[c_1646,c_791]) ).

tff(c_4026,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,n)),pls)),
    inference(superposition,[status(thm),theory(equality)],[c_4008,c_2182]) ).

tff(c_4435,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2299,c_4026]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM925+2 : 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
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 15:15:22 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 15.59/4.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.59/4.80  
% 15.59/4.80  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.01/4.84  
% 16.01/4.84  Inference rules
% 16.01/4.84  ----------------------
% 16.01/4.84  #Ref     : 6
% 16.01/4.84  #Sup     : 452
% 16.01/4.84  #Fact    : 0
% 16.01/4.84  #Define  : 0
% 16.01/4.84  #Split   : 1
% 16.01/4.84  #Chain   : 0
% 16.01/4.84  #Close   : 0
% 16.01/4.84  
% 16.01/4.84  Ordering : KBO
% 16.01/4.84  
% 16.01/4.84  Simplification rules
% 16.01/4.84  ----------------------
% 16.01/4.84  #Subsume      : 307
% 16.01/4.84  #Demod        : 860
% 16.01/4.84  #Tautology    : 584
% 16.01/4.84  #SimpNegUnit  : 72
% 16.01/4.84  #BackRed      : 7
% 16.01/4.84  
% 16.01/4.84  #Partial instantiations: 0
% 16.01/4.84  #Strategies tried      : 1
% 16.01/4.84  
% 16.01/4.84  Timing (in seconds)
% 16.01/4.84  ----------------------
% 16.01/4.84  Preprocessing        : 1.61
% 16.01/4.84  Parsing              : 0.85
% 16.01/4.84  CNF conversion       : 0.15
% 16.01/4.84  Main loop            : 2.17
% 16.01/4.84  Inferencing          : 0.20
% 16.01/4.84  Reduction            : 1.23
% 16.01/4.84  Demodulation         : 0.93
% 16.01/4.84  BG Simplification    : 0.15
% 16.01/4.84  Subsumption          : 0.47
% 16.01/4.84  Abstraction          : 0.05
% 16.01/4.84  MUC search           : 0.00
% 16.01/4.84  Cooper               : 0.00
% 16.01/4.84  Total                : 3.83
% 16.01/4.84  Index Insertion      : 0.00
% 16.01/4.84  Index Deletion       : 0.00
% 16.01/4.84  Index Matching       : 0.00
% 16.01/4.84  BG Taut test         : 0.00
%------------------------------------------------------------------------------