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