TSTP Solution File: NUM926+6 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM926+6 : 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 : n022.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 49.98s 32.10s
% Output : CNFRefutation 49.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 87
% Syntax : Number of formulae : 115 ( 28 unt; 76 typ; 0 def)
% Number of atoms : 53 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 15 ~; 10 |; 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 : 86 ( 58 >; 28 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 1 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 18 con; 0-4 aty)
% Number of variables : 32 (; 26 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ zcong > ord_less_eq > ord_less > dvd_dvd > quadRes > zprime > zero_neq_one > twoSqu420862341sum2sq > semiring_1 > semiring_0 > semiring > semiri456707255roduct > ring_n68954251visors > ring_char_0 > ring_11004092258visors > ring_1 > ring > power > ordere453448008miring > order > number_semiring > number_ring > number > no_zero_divisors > mult_zero > monoid_mult > linordered_semidom > linordered_ring > linordered_idom > linorder > linord626643107strict > linord581940658strict > linord219039673up_add > dvd > comm_semiring_1 > comm_semiring > comm_ring_1 > comm_monoid_mult > ab_group_add > product_Pair > times_times > power_power > plus_plus > minus_minus > ti > product_prod > number_number_of > legendre > #nlpp > zero_zero > undefined > twoSqu579703163sum2sq > one_one > bit1 > bit0 > t > s1 > s > real > pls > nat > min > m > int > bool > #skF_11 > #skF_8 > #skF_7 > #skF_12 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_4 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(semiring_1,type,
semiring_1: $i > $o ).
tff(power,type,
power: $i > $o ).
tff(semiri456707255roduct,type,
semiri456707255roduct: $i > $o ).
tff(comm_semiring,type,
comm_semiring: $i > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(m,type,
m: $i ).
tff(ord_less_eq,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
tff(s1,type,
s1: $i ).
tff(ord_less,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(ring_n68954251visors,type,
ring_n68954251visors: $i > $o ).
tff(linord581940658strict,type,
linord581940658strict: $i > $o ).
tff(min,type,
min: $i ).
tff(one_one,type,
one_one: $i > $i ).
tff(ring_1,type,
ring_1: $i > $o ).
tff(number,type,
number: $i > $o ).
tff(t,type,
t: $i ).
tff(pls,type,
pls: $i ).
tff(twoSqu579703163sum2sq,type,
twoSqu579703163sum2sq: $i > $i ).
tff(linordered_ring,type,
linordered_ring: $i > $o ).
tff(ring_11004092258visors,type,
ring_11004092258visors: $i > $o ).
tff(linordered_semidom,type,
linordered_semidom: $i > $o ).
tff(zcong,type,
zcong: ( $i * $i * $i ) > $o ).
tff(zprime,type,
zprime: $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(s,type,
s: $i ).
tff(linord626643107strict,type,
linord626643107strict: $i > $o ).
tff(zero_neq_one,type,
zero_neq_one: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(bool,type,
bool: $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(minus_minus,type,
minus_minus: ( $i * $i * $i ) > $i ).
tff(number_ring,type,
number_ring: $i > $o ).
tff(power_power,type,
power_power: ( $i * $i * $i ) > $i ).
tff(comm_monoid_mult,type,
comm_monoid_mult: $i > $o ).
tff(comm_ring_1,type,
comm_ring_1: $i > $o ).
tff(quadRes,type,
quadRes: ( $i * $i ) > $o ).
tff(linord219039673up_add,type,
linord219039673up_add: $i > $o ).
tff(nat,type,
nat: $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(product_Pair,type,
product_Pair: ( $i * $i * $i * $i ) > $i ).
tff(product_prod,type,
product_prod: ( $i * $i ) > $i ).
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('#skF_9',type,
'#skF_9': $i ).
tff(twoSqu420862341sum2sq,type,
twoSqu420862341sum2sq: $i > $o ).
tff(ring,type,
ring: $i > $o ).
tff(int,type,
int: $i ).
tff(ti,type,
ti: ( $i * $i ) > $i ).
tff(semiring_0,type,
semiring_0: $i > $o ).
tff(linordered_idom,type,
linordered_idom: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(bit1,type,
bit1: $i > $i ).
tff(ab_group_add,type,
ab_group_add: $i > $o ).
tff(ordere453448008miring,type,
ordere453448008miring: $i > $o ).
tff(mult_zero,type,
mult_zero: $i > $o ).
tff(legendre,type,
legendre: ( $i * $i ) > $i ).
tff(number_number_of,type,
number_number_of: ( $i * $i ) > $i ).
tff(ring_char_0,type,
ring_char_0: $i > $o ).
tff(dvd_dvd,type,
dvd_dvd: ( $i * $i * $i ) > $o ).
tff(times_times,type,
times_times: ( $i * $i * $i ) > $i ).
tff(zero_zero,type,
zero_zero: $i > $i ).
tff(number_semiring,type,
number_semiring: $i > $o ).
tff(monoid_mult,type,
monoid_mult: $i > $o ).
tff(real,type,
real: $i ).
tff(semiring,type,
semiring: $i > $o ).
tff(order,type,
order: $i > $o ).
tff(dvd,type,
dvd: $i > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(linorder,type,
linorder: $i > $o ).
tff(f_640,axiom,
! [K] : ( number_number_of(int,K) = ti(int,K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
tff(f_180,hypothesis,
! [B_1_1] : ( ti(int,bit1(B_1_1)) = bit1(B_1_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
tff(f_952,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_one__is__num__one) ).
tff(f_638,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_646,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_3064,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_276,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_280,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_270,axiom,
ti(int,t) = t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
tff(f_272,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(f_352,axiom,
! [Z_1,W_1] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).
tff(c_398,plain,
! [K_405] : ( ti(int,K_405) = number_number_of(int,K_405) ),
inference(cnfTransformation,[status(thm)],[f_640]) ).
tff(c_2256,plain,
! [B_1_1_1707] : ( ti(int,bit1(B_1_1_1707)) = bit1(B_1_1_1707) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_2271,plain,
! [B_1_1_1707] : ( number_number_of(int,bit1(B_1_1_1707)) = bit1(B_1_1_1707) ),
inference(superposition,[status(thm),theory(equality)],[c_398,c_2256]) ).
tff(c_586,plain,
number_number_of(int,bit1(pls)) = one_one(int),
inference(cnfTransformation,[status(thm)],[f_952]) ).
tff(c_2419,plain,
one_one(int) = bit1(pls),
inference(demodulation,[status(thm),theory(equality)],[c_2271,c_586]) ).
tff(c_396,plain,
! [Z_403,W_404] : ( times_times(int,Z_403,W_404) = times_times(int,W_404,Z_403) ),
inference(cnfTransformation,[status(thm)],[f_638]) ).
tff(c_404,plain,
! [Z_412,W_413] : ( plus_plus(int,Z_412,W_413) = plus_plus(int,W_413,Z_412) ),
inference(cnfTransformation,[status(thm)],[f_646]) ).
tff(c_1711,plain,
! [X_1676,Y_1677] : ( plus_plus(int,power_power(int,X_1676,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_1677,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_3064]) ).
tff(c_1807,plain,
! [X_1676,Y_1677] : ( plus_plus(int,power_power(int,X_1676,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_1677,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_404,c_1711]) ).
tff(c_1866,plain,
! [X_1676,Y_1677] : ( plus_plus(int,power_power(int,X_1676,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_1677,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls)))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_1807]) ).
tff(c_170,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_276]) ).
tff(c_1903,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,number_number_of(int,bit0(bit0(bit1(pls)))))) )
| ( one_one(int) != t ) ),
inference(demodulation,[status(thm),theory(equality)],[c_404,c_396,c_170]) ).
tff(c_1904,plain,
one_one(int) != t,
inference(negUnitSimplification,[status(thm)],[c_1866,c_1903]) ).
tff(c_2464,plain,
bit1(pls) != t,
inference(demodulation,[status(thm),theory(equality)],[c_2419,c_1904]) ).
tff(c_172,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_280]) ).
tff(c_1901,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,number_number_of(int,bit0(bit0(bit1(pls)))))) )
| ~ ord_less(int,one_one(int),t) ),
inference(demodulation,[status(thm),theory(equality)],[c_404,c_404,c_396,c_172]) ).
tff(c_1902,plain,
~ ord_less(int,one_one(int),t),
inference(negUnitSimplification,[status(thm)],[c_1866,c_1901]) ).
tff(c_2463,plain,
~ ord_less(int,bit1(pls),t),
inference(demodulation,[status(thm),theory(equality)],[c_2419,c_1902]) ).
tff(c_2036,plain,
! [K_1699] : ( ti(int,K_1699) = number_number_of(int,K_1699) ),
inference(cnfTransformation,[status(thm)],[f_640]) ).
tff(c_166,plain,
ti(int,t) = t,
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_2058,plain,
number_number_of(int,t) = t,
inference(superposition,[status(thm),theory(equality)],[c_2036,c_166]) ).
tff(c_168,plain,
ord_less_eq(int,one_one(int),t),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_2461,plain,
ord_less_eq(int,bit1(pls),t),
inference(demodulation,[status(thm),theory(equality)],[c_2419,c_168]) ).
tff(c_212,plain,
! [Z_1_185,W_1_186] :
( ord_less(int,Z_1_185,W_1_186)
| ( ti(int,Z_1_185) = ti(int,W_1_186) )
| ~ ord_less_eq(int,Z_1_185,W_1_186) ),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_118129,plain,
! [Z_1_3311,W_1_3312] :
( ord_less(int,Z_1_3311,W_1_3312)
| ( number_number_of(int,Z_1_3311) = number_number_of(int,W_1_3312) )
| ~ ord_less_eq(int,Z_1_3311,W_1_3312) ),
inference(demodulation,[status(thm),theory(equality)],[c_398,c_398,c_212]) ).
tff(c_118531,plain,
( ord_less(int,bit1(pls),t)
| ( number_number_of(int,bit1(pls)) = number_number_of(int,t) ) ),
inference(resolution,[status(thm)],[c_2461,c_118129]) ).
tff(c_118803,plain,
( ord_less(int,bit1(pls),t)
| ( bit1(pls) = t ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2271,c_2058,c_118531]) ).
tff(c_118805,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2464,c_2463,c_118803]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM926+6 : 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 : n022.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 15:15:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 49.98/32.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.98/32.10
% 49.98/32.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 49.98/32.13
% 49.98/32.13 Inference rules
% 49.98/32.13 ----------------------
% 49.98/32.13 #Ref : 68
% 49.98/32.13 #Sup : 29476
% 49.98/32.13 #Fact : 6
% 49.98/32.13 #Define : 0
% 49.98/32.13 #Split : 100
% 49.98/32.13 #Chain : 0
% 49.98/32.13 #Close : 0
% 49.98/32.13
% 49.98/32.13 Ordering : KBO
% 49.98/32.13
% 49.98/32.13 Simplification rules
% 49.98/32.13 ----------------------
% 49.98/32.13 #Subsume : 12132
% 49.98/32.13 #Demod : 18291
% 49.98/32.13 #Tautology : 6808
% 49.98/32.13 #SimpNegUnit : 1110
% 49.98/32.13 #BackRed : 20
% 49.98/32.13
% 49.98/32.13 #Partial instantiations: 0
% 49.98/32.13 #Strategies tried : 1
% 49.98/32.13
% 49.98/32.13 Timing (in seconds)
% 49.98/32.13 ----------------------
% 49.98/32.14 Preprocessing : 1.57
% 49.98/32.14 Parsing : 0.84
% 49.98/32.14 CNF conversion : 0.14
% 49.98/32.14 Main loop : 29.50
% 49.98/32.14 Inferencing : 3.96
% 49.98/32.14 Reduction : 14.30
% 49.98/32.14 Demodulation : 10.98
% 49.98/32.14 BG Simplification : 0.25
% 49.98/32.14 Subsumption : 9.41
% 49.98/32.14 Abstraction : 0.28
% 49.98/32.14 MUC search : 0.00
% 49.98/32.14 Cooper : 0.00
% 49.98/32.14 Total : 31.12
% 49.98/32.14 Index Insertion : 0.00
% 49.98/32.14 Index Deletion : 0.00
% 49.98/32.14 Index Matching : 0.00
% 49.98/32.14 BG Taut test : 0.00
%------------------------------------------------------------------------------