TSTP Solution File: NUM925+5 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM925+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/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 : n028.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 10:53:10 EDT 2023

% Result   : Theorem 19.85s 7.30s
% Output   : CNFRefutation 19.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   49
% Syntax   : Number of formulae    :   93 (  43 unt;  29 typ;   0 def)
%            Number of atoms       :   92 (  63 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   55 (  27   ~;  21   |;   0   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  24   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-3 aty)
%            Number of variables   :   52 (;  52   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ord_less > zero_neq_one > semiring_1 > semiring_0 > ring_char_0 > ring_11004092258visors > power > number_semiring > number_ring > number > no_zero_divisors > mult_zero > linordered_idom > linord219039673up_add > power_power > plus_plus > ti > semiring_1_of_nat > number_number_of > #nlpp > zero_zero > undefined > one_one > bit1 > bit0 > t > pls > nat > n > int

%Foreground sorts:

%Background operators:

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

tff(power,type,
    power: $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(ring_11004092258visors,type,
    ring_11004092258visors: $i > $o ).

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

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

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

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

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

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

tff(linord219039673up_add,type,
    linord219039673up_add: $i > $o ).

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

tff(semiring_1_of_nat,type,
    semiring_1_of_nat: ( $i * $i ) > $i ).

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

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

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

tff(semiring_0,type,
    semiring_0: $i > $o ).

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

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

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

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

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

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

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

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

tff(f_548,axiom,
    ! [K] : ( bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Bit1__def) ).

tff(f_479,axiom,
    ! [K] : ( plus_plus(int,K,pls) = K ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).

tff(f_475,axiom,
    pls = zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).

tff(f_177,axiom,
    ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).

tff(f_410,axiom,
    ~ ord_less(int,pls,zero_zero(int)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bin__less__0__simps_I1_J) ).

tff(f_82,hypothesis,
    ! [B_1] : ( bit0(ti(int,B_1)) = bit0(B_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).

tff(f_349,axiom,
    ! [K_1,L_1] :
      ( ( bit0(K_1) = bit0(L_1) )
    <=> ( K_1 = L_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).

tff(f_485,axiom,
    ! [K] : ( bit0(K) = plus_plus(int,K,K) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Bit0__def) ).

tff(f_583,axiom,
    linord219039673up_add(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).

tff(f_453,axiom,
    ! [X_a] :
      ( linord219039673up_add(X_a)
     => ! [A_2] :
          ( ( plus_plus(X_a,A_2,A_2) = zero_zero(X_a) )
        <=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_double__eq__0__iff) ).

tff(f_404,axiom,
    ! [K_1] :
      ( ord_less(int,pls,bit0(K_1))
    <=> ord_less(int,pls,K_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I4_J) ).

tff(f_584,axiom,
    ring_11004092258visors(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).

tff(f_593,axiom,
    number_ring(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).

tff(f_267,axiom,
    zero_zero(int) = number_number_of(int,pls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).

tff(f_506,axiom,
    ! [X_a] :
      ( number_ring(X_a)
     => ! [A_1] : ( plus_plus(X_a,number_number_of(X_a,pls),A_1) = ti(X_a,A_1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).

tff(f_481,axiom,
    ! [K] : ( plus_plus(int,pls,K) = K ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__Pls) ).

tff(f_544,axiom,
    ! [K,L] : ( plus_plus(int,bit1(K),bit0(L)) = bit1(plus_plus(int,K,L)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__Bit1__Bit0) ).

tff(f_362,axiom,
    ! [Z,W] : ( plus_plus(int,Z,W) = plus_plus(int,W,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zadd__commute) ).

tff(f_610,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f_202,axiom,
    ! [X_a] :
      ( ring_11004092258visors(X_a)
     => ! [A_2] :
          ( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
        <=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).

tff(c_2171,plain,
    ! [K_333] : ( plus_plus(int,plus_plus(int,one_one(int),K_333),K_333) = bit1(K_333) ),
    inference(cnfTransformation,[status(thm)],[f_548]) ).

tff(c_300,plain,
    ! [K_185] : ( plus_plus(int,K_185,pls) = K_185 ),
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_2188,plain,
    plus_plus(int,one_one(int),pls) = bit1(pls),
    inference(superposition,[status(thm),theory(equality)],[c_2171,c_300]) ).

tff(c_2290,plain,
    one_one(int) = bit1(pls),
    inference(superposition,[status(thm),theory(equality)],[c_2188,c_300]) ).

tff(c_296,plain,
    zero_zero(int) = pls,
    inference(cnfTransformation,[status(thm)],[f_475]) ).

tff(c_74,plain,
    ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_427,plain,
    ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    inference(demodulation,[status(thm),theory(equality)],[c_296,c_74]) ).

tff(c_2307,plain,
    ord_less(int,pls,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n))),
    inference(demodulation,[status(thm),theory(equality)],[c_2290,c_427]) ).

tff(c_246,plain,
    ~ ord_less(int,pls,zero_zero(int)),
    inference(cnfTransformation,[status(thm)],[f_410]) ).

tff(c_417,plain,
    ~ ord_less(int,pls,pls),
    inference(demodulation,[status(thm),theory(equality)],[c_296,c_246]) ).

tff(c_24,plain,
    ! [B_1_24] : ( bit0(ti(int,B_1_24)) = bit0(B_1_24) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_654,plain,
    ! [L_1_258,K_1_259] :
      ( ( L_1_258 = K_1_259 )
      | ( bit0(L_1_258) != bit0(K_1_259) ) ),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_660,plain,
    ! [B_1_24,L_1_258] :
      ( ( ti(int,B_1_24) = L_1_258 )
      | ( bit0(L_1_258) != bit0(B_1_24) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_654]) ).

tff(c_1129,plain,
    ! [B_1_24] : ( ti(int,B_1_24) = B_1_24 ),
    inference(reflexivity,[status(thm),theory(equality)],[c_660]) ).

tff(c_306,plain,
    ! [K_189] : ( plus_plus(int,K_189,K_189) = bit0(K_189) ),
    inference(cnfTransformation,[status(thm)],[f_485]) ).

tff(c_356,plain,
    linord219039673up_add(int),
    inference(cnfTransformation,[status(thm)],[f_583]) ).

tff(c_11711,plain,
    ! [X_a_518,A_2_519] :
      ( ( plus_plus(X_a_518,A_2_519,A_2_519) = zero_zero(X_a_518) )
      | ( ti(X_a_518,A_2_519) != zero_zero(X_a_518) )
      | ~ linord219039673up_add(X_a_518) ),
    inference(cnfTransformation,[status(thm)],[f_453]) ).

tff(c_11713,plain,
    ! [A_2_519] :
      ( ( plus_plus(int,A_2_519,A_2_519) = zero_zero(int) )
      | ( ti(int,A_2_519) != zero_zero(int) ) ),
    inference(resolution,[status(thm)],[c_356,c_11711]) ).

tff(c_11718,plain,
    ! [A_2_520] :
      ( ( bit0(A_2_520) = pls )
      | ( pls != A_2_520 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_296,c_1129,c_296,c_306,c_11713]) ).

tff(c_240,plain,
    ! [K_1_161] :
      ( ord_less(int,pls,bit0(K_1_161))
      | ~ ord_less(int,pls,K_1_161) ),
    inference(cnfTransformation,[status(thm)],[f_404]) ).

tff(c_11945,plain,
    ! [A_2_520] :
      ( ord_less(int,pls,pls)
      | ~ ord_less(int,pls,A_2_520)
      | ( pls != A_2_520 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_11718,c_240]) ).

tff(c_12445,plain,
    ! [A_2_527] :
      ( ~ ord_less(int,pls,A_2_527)
      | ( pls != A_2_527 ) ),
    inference(negUnitSimplification,[status(thm)],[c_417,c_11945]) ).

tff(c_12608,plain,
    plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)) != pls,
    inference(resolution,[status(thm)],[c_2307,c_12445]) ).

tff(c_358,plain,
    ring_11004092258visors(int),
    inference(cnfTransformation,[status(thm)],[f_584]) ).

tff(c_376,plain,
    number_ring(int),
    inference(cnfTransformation,[status(thm)],[f_593]) ).

tff(c_124,plain,
    number_number_of(int,pls) = zero_zero(int),
    inference(cnfTransformation,[status(thm)],[f_267]) ).

tff(c_426,plain,
    number_number_of(int,pls) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_296,c_124]) ).

tff(c_318,plain,
    ! [X_a_195,A_1_197] :
      ( ( plus_plus(X_a_195,number_number_of(X_a_195,pls),A_1_197) = ti(X_a_195,A_1_197) )
      | ~ number_ring(X_a_195) ),
    inference(cnfTransformation,[status(thm)],[f_506]) ).

tff(c_302,plain,
    ! [K_186] : ( plus_plus(int,pls,K_186) = K_186 ),
    inference(cnfTransformation,[status(thm)],[f_481]) ).

tff(c_3669,plain,
    ! [K_366,L_367] : ( plus_plus(int,bit1(K_366),bit0(L_367)) = bit1(plus_plus(int,K_366,L_367)) ),
    inference(cnfTransformation,[status(thm)],[f_544]) ).

tff(c_207,plain,
    ! [Z_145,W_146] : ( plus_plus(int,Z_145,W_146) = plus_plus(int,W_146,Z_145) ),
    inference(cnfTransformation,[status(thm)],[f_362]) ).

tff(c_3693,plain,
    ! [L_367,K_366] : ( plus_plus(int,bit0(L_367),bit1(K_366)) = bit1(plus_plus(int,K_366,L_367)) ),
    inference(superposition,[status(thm),theory(equality)],[c_3669,c_207]) ).

tff(c_11838,plain,
    ! [K_366,A_2_520] :
      ( ( plus_plus(int,pls,bit1(K_366)) = bit1(plus_plus(int,K_366,A_2_520)) )
      | ( pls != A_2_520 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_11718,c_3693]) ).

tff(c_14765,plain,
    ! [K_560,A_2_561] :
      ( ( bit1(plus_plus(int,K_560,A_2_561)) = bit1(K_560) )
      | ( pls != A_2_561 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_302,c_11838]) ).

tff(c_15113,plain,
    ! [A_1_197] :
      ( ( bit1(ti(int,A_1_197)) = bit1(number_number_of(int,pls)) )
      | ( pls != A_1_197 )
      | ~ number_ring(int) ),
    inference(superposition,[status(thm),theory(equality)],[c_318,c_14765]) ).

tff(c_15260,plain,
    ! [A_1_564] :
      ( ( bit1(pls) = bit1(A_1_564) )
      | ( pls != A_1_564 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_376,c_426,c_1129,c_15113]) ).

tff(c_400,plain,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
    inference(cnfTransformation,[status(thm)],[f_610]) ).

tff(c_404,plain,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_296,c_400]) ).

tff(c_2319,plain,
    power_power(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_2290,c_404]) ).

tff(c_15738,plain,
    ! [A_1_564] :
      ( ( power_power(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(A_1_564)))) = pls )
      | ( pls != A_1_564 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15260,c_2319]) ).

tff(c_38926,plain,
    ! [X_a_749,A_2_750] :
      ( ( ti(X_a_749,A_2_750) = zero_zero(X_a_749) )
      | ( power_power(X_a_749,A_2_750,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(X_a_749) )
      | ~ ring_11004092258visors(X_a_749) ),
    inference(cnfTransformation,[status(thm)],[f_202]) ).

tff(c_38973,plain,
    ( ( ti(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n))) = zero_zero(int) )
    | ( zero_zero(int) != pls )
    | ~ ring_11004092258visors(int) ),
    inference(superposition,[status(thm),theory(equality)],[c_15738,c_38926]) ).

tff(c_39045,plain,
    plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)) = pls,
    inference(demodulation,[status(thm),theory(equality)],[c_358,c_296,c_296,c_1129,c_38973]) ).

tff(c_39047,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_12608,c_39045]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : NUM925+5 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.15  % 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
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 15:11:24 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 19.85/7.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.85/7.30  
% 19.85/7.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.93/7.33  
% 19.93/7.33  Inference rules
% 19.93/7.33  ----------------------
% 19.93/7.33  #Ref     : 27
% 19.93/7.33  #Sup     : 10264
% 19.93/7.33  #Fact    : 4
% 19.93/7.33  #Define  : 0
% 19.93/7.33  #Split   : 5
% 19.93/7.33  #Chain   : 0
% 19.93/7.33  #Close   : 0
% 19.93/7.33  
% 19.93/7.33  Ordering : KBO
% 19.93/7.33  
% 19.93/7.33  Simplification rules
% 19.93/7.33  ----------------------
% 19.93/7.33  #Subsume      : 5161
% 19.93/7.33  #Demod        : 5724
% 19.93/7.33  #Tautology    : 1724
% 19.93/7.33  #SimpNegUnit  : 428
% 19.93/7.33  #BackRed      : 43
% 19.93/7.33  
% 19.93/7.33  #Partial instantiations: 0
% 19.93/7.33  #Strategies tried      : 1
% 19.93/7.33  
% 19.93/7.33  Timing (in seconds)
% 19.93/7.34  ----------------------
% 19.93/7.34  Preprocessing        : 0.83
% 19.93/7.34  Parsing              : 0.43
% 19.93/7.34  CNF conversion       : 0.07
% 19.93/7.34  Main loop            : 5.38
% 19.93/7.34  Inferencing          : 0.94
% 19.93/7.34  Reduction            : 2.53
% 19.93/7.34  Demodulation         : 2.04
% 19.93/7.34  BG Simplification    : 0.12
% 19.93/7.34  Subsumption          : 1.54
% 19.93/7.34  Abstraction          : 0.11
% 19.93/7.34  MUC search           : 0.00
% 19.93/7.34  Cooper               : 0.00
% 19.93/7.34  Total                : 6.26
% 19.93/7.34  Index Insertion      : 0.00
% 19.93/7.34  Index Deletion       : 0.00
% 19.93/7.34  Index Matching       : 0.00
% 19.93/7.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------