TSTP Solution File: NUM924+2 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM924+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 : n011.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 10:53:06 EDT 2023

% Result   : Theorem 13.34s 4.48s
% Output   : CNFRefutation 13.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   67
% Syntax   : Number of formulae    :   91 (  37 unt;  54 typ;   0 def)
%            Number of atoms       :   37 (  28 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   66 (  37   >;  29   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;  17 con; 0-3 aty)
%            Number of variables   :   23 (;  23   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ zcong > quadRes > ord_less_real > ord_less_nat > ord_less_int > ord_less_eq_real > ord_less_eq_nat > ord_less_eq_int > dvd_dvd_real > dvd_dvd_nat > dvd_dvd_int > zprime > twoSqu142715416sum2sq > is_int > times_times_real > times_times_nat > times_times_int > power_power_real > power_power_nat > power_power_int > plus_plus_real > plus_plus_nat > plus_plus_int > minus_minus_real > minus_minus_nat > minus_minus_int > legendre > #nlpp > undefined_int > number_number_of_nat > number_number_of_int > number267125858f_real > bit1 > bit0 > zero_zero_real > zero_zero_nat > zero_zero_int > t > s1 > s > pls > one_one_real > one_one_nat > one_one_int > min > m > int > #skF_4 > #skF_6 > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_7

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(power_power_int,type,
    power_power_int: ( $i * $i ) > $i ).

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

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

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

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

tff(s1,type,
    s1: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(twoSqu142715416sum2sq,type,
    twoSqu142715416sum2sq: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_781,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Pls__def) ).

tff(f_1256,axiom,
    ! [A_46,C_12] : ( plus_plus_int(A_46,C_12) = plus_plus_int(C_12,A_46) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

tff(f_1703,axiom,
    ! [X_10] : ( times_times_int(X_10,X_10) = power_power_int(X_10,number_number_of_nat(bit0(bit1(pls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

tff(f_2998,negated_conjecture,
    ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f_1007,axiom,
    plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_semiring__one__add__one__is__two) ).

tff(f_985,axiom,
    one_one_int = number_number_of_int(bit1(pls)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_semiring__norm_I110_J) ).

tff(f_813,axiom,
    ! [K_1] : ( bit0(K_1) = plus_plus_int(K_1,K_1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Bit0__def) ).

tff(f_1545,axiom,
    ! [M_11] : ( plus_plus_int(M_11,M_11) = times_times_int(plus_plus_int(one_one_int,one_one_int),M_11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

tff(f_829,axiom,
    ! [W_11] : ( times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(W_11)) = number_number_of_int(bit0(W_11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_double__number__of__Bit0) ).

tff(f_1250,axiom,
    ! [A_47,B_18] : ( times_times_int(A_47,B_18) = times_times_int(B_18,A_47) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

tff(f_82,axiom,
    plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).

tff(f_1344,axiom,
    ! [A_38] : ( times_times_int(zero_zero_int,A_38) = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

tff(f_81,axiom,
    ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).

tff(c_556,plain,
    zero_zero_int = pls,
    inference(cnfTransformation,[status(thm)],[f_781]) ).

tff(c_954,plain,
    ! [C_12_525,A_46_524] : ( plus_plus_int(C_12_525,A_46_524) = plus_plus_int(A_46_524,C_12_525) ),
    inference(cnfTransformation,[status(thm)],[f_1256]) ).

tff(c_1236,plain,
    ! [X_10_774] : ( times_times_int(X_10_774,X_10_774) = power_power_int(X_10_774,number_number_of_nat(bit0(bit1(pls)))) ),
    inference(cnfTransformation,[status(thm)],[f_1703]) ).

tff(c_1931,plain,
    ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
    inference(cnfTransformation,[status(thm)],[f_2998]) ).

tff(c_1959,plain,
    ~ ord_less_int(plus_plus_int(times_times_int(s,s),one_one_int),zero_zero_int),
    inference(demodulation,[status(thm),theory(equality)],[c_1236,c_1931]) ).

tff(c_2002,plain,
    ~ ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),zero_zero_int),
    inference(demodulation,[status(thm),theory(equality)],[c_954,c_1959]) ).

tff(c_2223,plain,
    ~ ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
    inference(demodulation,[status(thm),theory(equality)],[c_556,c_2002]) ).

tff(c_780,plain,
    number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
    inference(cnfTransformation,[status(thm)],[f_1007]) ).

tff(c_2074,plain,
    ! [X_10_774] : ( times_times_int(X_10_774,X_10_774) = power_power_int(X_10_774,plus_plus_nat(one_one_nat,one_one_nat)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_780,c_1236]) ).

tff(c_756,plain,
    number_number_of_int(bit1(pls)) = one_one_int,
    inference(cnfTransformation,[status(thm)],[f_985]) ).

tff(c_584,plain,
    ! [K_1_288] : ( plus_plus_int(K_1_288,K_1_288) = bit0(K_1_288) ),
    inference(cnfTransformation,[status(thm)],[f_813]) ).

tff(c_1162,plain,
    ! [M_11_713] : ( times_times_int(plus_plus_int(one_one_int,one_one_int),M_11_713) = plus_plus_int(M_11_713,M_11_713) ),
    inference(cnfTransformation,[status(thm)],[f_1545]) ).

tff(c_2164,plain,
    ! [M_11_713] : ( times_times_int(bit0(one_one_int),M_11_713) = bit0(M_11_713) ),
    inference(demodulation,[status(thm),theory(equality)],[c_584,c_584,c_1162]) ).

tff(c_594,plain,
    ! [W_11_295] : ( times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(W_11_295)) = number_number_of_int(bit0(W_11_295)) ),
    inference(cnfTransformation,[status(thm)],[f_829]) ).

tff(c_2169,plain,
    ! [W_11_295] : ( times_times_int(bit0(one_one_int),number_number_of_int(W_11_295)) = number_number_of_int(bit0(W_11_295)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_584,c_594]) ).

tff(c_2179,plain,
    ! [W_11_295] : ( number_number_of_int(bit0(W_11_295)) = bit0(number_number_of_int(W_11_295)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2164,c_2169]) ).

tff(c_948,plain,
    ! [B_18_519,A_47_518] : ( times_times_int(B_18_519,A_47_518) = times_times_int(A_47_518,B_18_519) ),
    inference(cnfTransformation,[status(thm)],[f_1250]) ).

tff(c_42,plain,
    times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_2426,plain,
    times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(one_one_int))))) = plus_plus_int(one_one_int,times_times_int(s,s)),
    inference(demodulation,[status(thm),theory(equality)],[c_2074,c_780,c_756,c_2179,c_2179,c_948,c_948,c_954,c_954,c_42]) ).

tff(c_1024,plain,
    ! [A_38_598] : ( times_times_int(zero_zero_int,A_38_598) = zero_zero_int ),
    inference(cnfTransformation,[status(thm)],[f_1344]) ).

tff(c_2229,plain,
    ! [A_38_598] : ( times_times_int(pls,A_38_598) = pls ),
    inference(demodulation,[status(thm),theory(equality)],[c_556,c_556,c_1024]) ).

tff(c_40,plain,
    ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_2428,plain,
    ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
    inference(demodulation,[status(thm),theory(equality)],[c_2426,c_2229,c_756,c_2179,c_2179,c_756,c_2179,c_2179,c_948,c_948,c_948,c_948,c_954,c_954,c_556,c_40]) ).

tff(c_2429,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2223,c_2428]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM924+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.15  % 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
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 15:21:05 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 13.34/4.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.34/4.49  
% 13.34/4.49  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.34/4.52  
% 13.34/4.52  Inference rules
% 13.34/4.52  ----------------------
% 13.34/4.52  #Ref     : 0
% 13.34/4.52  #Sup     : 0
% 13.34/4.52  #Fact    : 0
% 13.34/4.52  #Define  : 0
% 13.34/4.52  #Split   : 0
% 13.34/4.52  #Chain   : 0
% 13.34/4.52  #Close   : 0
% 13.34/4.52  
% 13.34/4.52  Ordering : KBO
% 13.34/4.52  
% 13.34/4.52  Simplification rules
% 13.34/4.52  ----------------------
% 13.34/4.52  #Subsume      : 806
% 13.34/4.52  #Demod        : 888
% 13.34/4.52  #Tautology    : 148
% 13.34/4.52  #SimpNegUnit  : 1
% 13.34/4.52  #BackRed      : 0
% 13.34/4.52  
% 13.34/4.52  #Partial instantiations: 0
% 13.34/4.52  #Strategies tried      : 1
% 13.34/4.52  
% 13.34/4.52  Timing (in seconds)
% 13.34/4.52  ----------------------
% 13.34/4.52  Preprocessing        : 1.61
% 13.34/4.52  Parsing              : 0.87
% 13.34/4.52  CNF conversion       : 0.13
% 13.34/4.52  Main loop            : 1.76
% 13.34/4.52  Inferencing          : 0.00
% 13.34/4.52  Reduction            : 1.14
% 13.34/4.52  Demodulation         : 0.87
% 13.34/4.52  BG Simplification    : 0.14
% 13.34/4.52  Subsumption          : 0.41
% 13.34/4.52  Abstraction          : 0.05
% 13.34/4.52  MUC search           : 0.00
% 13.34/4.52  Cooper               : 0.00
% 13.34/4.52  Total                : 3.42
% 13.34/4.52  Index Insertion      : 0.00
% 13.34/4.52  Index Deletion       : 0.00
% 13.34/4.52  Index Matching       : 0.00
% 13.34/4.52  BG Taut test         : 0.00
%------------------------------------------------------------------------------