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 : n013.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 13.08s 4.49s
% Output : CNFRefutation 13.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 65
% Syntax : Number of formulae : 88 ( 34 unt; 54 typ; 0 def)
% Number of atoms : 34 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 64 ( 35 >; 29 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 38 ( 38 usr; 16 con; 0-3 aty)
% Number of variables : 16 (; 16 !; 0 ?; 16 :)
% 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 > twoSqu512355103sum2sq > 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 > 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 > #skF_6 > #skF_7 > #skF_3 > #skF_1 > #skF_5 > #skF_2 > #skF_4 > #skF_8
%Foreground sorts:
tff(real,type,
real: $tType ).
tff(nat,type,
nat: $tType ).
tff(int,type,
int: $tType ).
%Background operators:
%Foreground operators:
tff(zprime,type,
zprime: int > $o ).
tff('#skF_6',type,
'#skF_6': ( int * int * int ) > int ).
tff(bit1,type,
bit1: int > int ).
tff(times_times_nat,type,
times_times_nat: ( nat * nat ) > nat ).
tff(dvd_dvd_int,type,
dvd_dvd_int: ( int * int ) > $o ).
tff(s1,type,
s1: int ).
tff(one_one_int,type,
one_one_int: int ).
tff('#skF_7',type,
'#skF_7': ( int * int ) > int ).
tff(power_power_nat,type,
power_power_nat: ( nat * nat ) > nat ).
tff(dvd_dvd_real,type,
dvd_dvd_real: ( real * real ) > $o ).
tff(number267125858f_real,type,
number267125858f_real: int > real ).
tff(one_one_real,type,
one_one_real: real ).
tff(minus_minus_real,type,
minus_minus_real: ( real * real ) > real ).
tff('#skF_3',type,
'#skF_3': int ).
tff(zcong,type,
zcong: ( int * int * int ) > $o ).
tff(min,type,
min: int ).
tff(ord_less_eq_nat,type,
ord_less_eq_nat: ( nat * nat ) > $o ).
tff(zero_zero_real,type,
zero_zero_real: real ).
tff('#skF_1',type,
'#skF_1': int ).
tff('#skF_5',type,
'#skF_5': int ).
tff(number_number_of_int,type,
number_number_of_int: int > int ).
tff(s,type,
s: int ).
tff(m,type,
m: int ).
tff(number_number_of_nat,type,
number_number_of_nat: int > nat ).
tff(legendre,type,
legendre: ( int * int ) > int ).
tff(power_power_real,type,
power_power_real: ( real * nat ) > real ).
tff(twoSqu512355103sum2sq,type,
twoSqu512355103sum2sq: int > $o ).
tff(times_times_real,type,
times_times_real: ( real * real ) > real ).
tff('#skF_2',type,
'#skF_2': int ).
tff(ord_less_real,type,
ord_less_real: ( real * real ) > $o ).
tff(plus_plus_real,type,
plus_plus_real: ( real * real ) > real ).
tff(plus_plus_nat,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(one_one_nat,type,
one_one_nat: nat ).
tff(power_power_int,type,
power_power_int: ( int * nat ) > int ).
tff(ord_less_eq_int,type,
ord_less_eq_int: ( int * int ) > $o ).
tff(quadRes,type,
quadRes: ( int * int ) > $o ).
tff('#skF_4',type,
'#skF_4': int > int ).
tff(ord_less_eq_real,type,
ord_less_eq_real: ( real * real ) > $o ).
tff(ord_less_nat,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(times_times_int,type,
times_times_int: ( int * int ) > int ).
tff(pls,type,
pls: int ).
tff(zero_zero_nat,type,
zero_zero_nat: nat ).
tff('#skF_8',type,
'#skF_8': ( real * nat ) > real ).
tff(dvd_dvd_nat,type,
dvd_dvd_nat: ( nat * nat ) > $o ).
tff(bit0,type,
bit0: int > int ).
tff(minus_minus_int,type,
minus_minus_int: ( int * int ) > int ).
tff(ord_less_int,type,
ord_less_int: ( int * int ) > $o ).
tff(plus_plus_int,type,
plus_plus_int: ( int * int ) > int ).
tff(t,type,
t: int ).
tff(zero_zero_int,type,
zero_zero_int: int ).
tff(minus_minus_nat,type,
minus_minus_nat: ( nat * nat ) > nat ).
tff(f_124,axiom,
! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
tff(f_1095,axiom,
! [A_46: int,C_12: int] : ( 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_1502,axiom,
! [X_10: int] : ( 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_1760,axiom,
minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
tff(f_650,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Pls__def) ).
tff(f_2739,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_860,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_1089,axiom,
! [A_47: int,B_18: int] : ( 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_35,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_1185,axiom,
! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(f_34,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_94,plain,
! [K_1_24: int] : ( number_number_of_int(K_1_24) = K_1_24 ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_914,plain,
! [C_12_512: int,A_46_511: int] : ( plus_plus_int(C_12_512,A_46_511) = plus_plus_int(A_46_511,C_12_512) ),
inference(cnfTransformation,[status(thm)],[f_1095]) ).
tff(c_1196,plain,
! [X_10_761: int] : ( times_times_int(X_10_761,X_10_761) = power_power_int(X_10_761,number_number_of_nat(bit0(bit1(pls)))) ),
inference(cnfTransformation,[status(thm)],[f_1502]) ).
tff(c_1362,plain,
minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnfTransformation,[status(thm)],[f_1760]) ).
tff(c_1913,plain,
minus_minus_int(times_times_int(s,s),number_number_of_int(min)) = plus_plus_int(times_times_int(s,s),one_one_int),
inference(demodulation,[status(thm),theory(equality)],[c_1196,c_1196,c_1362]) ).
tff(c_1961,plain,
minus_minus_int(times_times_int(s,s),number_number_of_int(min)) = plus_plus_int(one_one_int,times_times_int(s,s)),
inference(demodulation,[status(thm),theory(equality)],[c_914,c_1913]) ).
tff(c_2394,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = minus_minus_int(times_times_int(s,s),min),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_1961]) ).
tff(c_520,plain,
zero_zero_int = pls,
inference(cnfTransformation,[status(thm)],[f_650]) ).
tff(c_1883,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_2739]) ).
tff(c_1912,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_1196,c_1883]) ).
tff(c_1958,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_914,c_1912]) ).
tff(c_2195,plain,
~ ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(demodulation,[status(thm),theory(equality)],[c_520,c_1958]) ).
tff(c_2405,plain,
~ ord_less_int(minus_minus_int(times_times_int(s,s),min),pls),
inference(demodulation,[status(thm),theory(equality)],[c_2394,c_2195]) ).
tff(c_744,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnfTransformation,[status(thm)],[f_860]) ).
tff(c_2038,plain,
! [X_10_761: int] : ( times_times_int(X_10_761,X_10_761) = power_power_int(X_10_761,plus_plus_nat(one_one_nat,one_one_nat)) ),
inference(demodulation,[status(thm),theory(equality)],[c_744,c_1196]) ).
tff(c_908,plain,
! [B_18_506: int,A_47_505: int] : ( times_times_int(B_18_506,A_47_505) = times_times_int(A_47_505,B_18_506) ),
inference(cnfTransformation,[status(thm)],[f_1089]) ).
tff(c_8,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_35]) ).
tff(c_2452,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) = minus_minus_int(times_times_int(s,s),min),
inference(demodulation,[status(thm),theory(equality)],[c_2394,c_2038,c_908,c_908,c_744,c_914,c_914,c_94,c_8]) ).
tff(c_990,plain,
! [A_37_588: int] : ( times_times_int(A_37_588,zero_zero_int) = zero_zero_int ),
inference(cnfTransformation,[status(thm)],[f_1185]) ).
tff(c_2192,plain,
! [A_37_588: int] : ( times_times_int(A_37_588,pls) = pls ),
inference(demodulation,[status(thm),theory(equality)],[c_520,c_520,c_990]) ).
tff(c_6,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_34]) ).
tff(c_2454,plain,
ord_less_int(minus_minus_int(times_times_int(s,s),min),pls),
inference(demodulation,[status(thm),theory(equality)],[c_2452,c_908,c_908,c_2192,c_914,c_914,c_520,c_94,c_94,c_6]) ).
tff(c_2455,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2405,c_2454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM924_2 : TPTP v8.1.2. Released v5.3.0.
% 0.14/0.15 % 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
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 3 14:47:32 EDT 2023
% 0.14/0.37 % CPUTime :
% 13.08/4.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.08/4.50
% 13.08/4.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.08/4.53
% 13.08/4.53 Inference rules
% 13.08/4.53 ----------------------
% 13.08/4.53 #Ref : 0
% 13.08/4.53 #Sup : 0
% 13.08/4.53 #Fact : 0
% 13.08/4.53 #Define : 0
% 13.08/4.53 #Split : 0
% 13.08/4.53 #Chain : 0
% 13.08/4.53 #Close : 0
% 13.08/4.53
% 13.08/4.53 Ordering : KBO
% 13.08/4.53
% 13.08/4.53 Simplification rules
% 13.08/4.53 ----------------------
% 13.08/4.53 #Subsume : 745
% 13.08/4.53 #Demod : 977
% 13.08/4.53 #Tautology : 185
% 13.08/4.53 #SimpNegUnit : 1
% 13.08/4.53 #BackRed : 0
% 13.08/4.53
% 13.08/4.53 #Partial instantiations: 0
% 13.08/4.53 #Strategies tried : 1
% 13.08/4.53
% 13.08/4.53 Timing (in seconds)
% 13.08/4.53 ----------------------
% 13.08/4.53 Preprocessing : 1.60
% 13.08/4.53 Parsing : 0.85
% 13.08/4.53 CNF conversion : 0.15
% 13.08/4.53 Main loop : 1.83
% 13.08/4.53 Inferencing : 0.00
% 13.08/4.53 Reduction : 1.20
% 13.08/4.53 Demodulation : 0.88
% 13.08/4.53 BG Simplification : 0.16
% 13.08/4.53 Subsumption : 0.44
% 13.08/4.53 Abstraction : 0.05
% 13.08/4.53 MUC search : 0.00
% 13.08/4.53 Cooper : 0.00
% 13.08/4.53 Total : 3.49
% 13.08/4.53 Index Insertion : 0.00
% 13.08/4.53 Index Deletion : 0.00
% 13.08/4.53 Index Matching : 0.00
% 13.08/4.53 BG Taut test : 0.00
%------------------------------------------------------------------------------