TSTP Solution File: NUM925+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM925+3 : 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 : 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 10:53:09 EDT 2023
% Result : Theorem 30.32s 11.16s
% Output : CNFRefutation 30.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 123
% Syntax : Number of formulae : 147 ( 28 unt; 113 typ; 0 def)
% Number of atoms : 44 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 6 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 121 ( 68 >; 53 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 110 ( 110 usr; 45 con; 0-3 aty)
% Number of variables : 25 (; 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_int > is_bool > hBOOL > if_nat > if_int > zcong > times_times_real > times_times_nat > times_times_int > plus_plus_real > plus_plus_nat > plus_plus_int > minus_minus_real > minus_minus_nat > minus_minus_int > legendre > hAPP_real_bool > hAPP_r1134773055l_bool > hAPP_nat_real > hAPP_nat_nat > hAPP_nat_int > hAPP_nat_bool > hAPP_n1699378549t_bool > hAPP_int_bool > hAPP_i1948725293t_bool > #nlpp > undefined_int > succ > quadRes > power_power_real > power_power_nat > power_power_int > number_number_of_nat > number_number_of_int > number267125858f_real > nat > bit1 > bit0 > abs_abs_real > abs_abs_int > zprime > zero_zero_real > zero_zero_nat > zero_zero_int > y > x > twoSqu1154269391sum2sq > tn > t > semiri984289939at_nat > semiri1621563631at_int > semiri132038758t_real > s1 > s > 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 > min > m1 > m > int > fTrue > fFalse > dvd_dvd_nat > dvd_dvd_int > #skF_9 > #skF_33 > #skF_7 > #skF_38 > #skF_22 > #skF_1 > #skF_20 > #skF_2 > #skF_18 > #skF_31 > #skF_17 > #skF_25 > #skF_8 > #skF_19 > #skF_3 > #skF_39 > #skF_34 > #skF_14 > #skF_29 > #skF_26 > #skF_10 > #skF_35 > #skF_37 > #skF_21 > #skF_36 > #skF_32 > #skF_15 > #skF_40 > #skF_30 > #skF_13 > #skF_11 > #skF_24 > #skF_23 > #skF_12 > #skF_41 > #skF_27 > #skF_5 > #skF_28 > #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(zcong,type,
zcong: ( $i * $i ) > $i ).
tff(hAPP_real_bool,type,
hAPP_real_bool: ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(ord_less_nat,type,
ord_less_nat: $i ).
tff(m,type,
m: $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i * $i ) > $i ).
tff(times_times_real,type,
times_times_real: ( $i * $i ) > $i ).
tff(one_one_int,type,
one_one_int: $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(minus_minus_real,type,
minus_minus_real: ( $i * $i ) > $i ).
tff(s1,type,
s1: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $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('#skF_18',type,
'#skF_18': $i ).
tff(min,type,
min: $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(pls,type,
pls: $i ).
tff(x,type,
x: $i ).
tff(number_number_of_nat,type,
number_number_of_nat: $i > $i ).
tff(undefined_int,type,
undefined_int: $i > $i ).
tff(is_bool,type,
is_bool: $i > $o ).
tff('#skF_31',type,
'#skF_31': $i ).
tff(power_power_nat,type,
power_power_nat: $i > $i ).
tff(hAPP_i1948725293t_bool,type,
hAPP_i1948725293t_bool: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff(if_nat,type,
if_nat: ( $i * $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(semiri984289939at_nat,type,
semiri984289939at_nat: $i ).
tff(is_int,type,
is_int: $i > $o ).
tff(abs_abs_int,type,
abs_abs_int: $i > $i ).
tff(bit0,type,
bit0: $i > $i ).
tff(ord_less_eq_int,type,
ord_less_eq_int: $i ).
tff(s,type,
s: $i ).
tff(semiri132038758t_real,type,
semiri132038758t_real: $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_19',type,
'#skF_19': $i ).
tff(hAPP_nat_int,type,
hAPP_nat_int: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff(one_one_real,type,
one_one_real: $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff(times_times_nat,type,
times_times_nat: ( $i * $i ) > $i ).
tff(hAPP_nat_nat,type,
hAPP_nat_nat: ( $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': $i > $i ).
tff('#skF_26',type,
'#skF_26': $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(ord_less_real,type,
ord_less_real: $i ).
tff(quadRes,type,
quadRes: $i > $i ).
tff(y,type,
y: $i ).
tff(abs_abs_real,type,
abs_abs_real: $i > $i ).
tff(one_one_nat,type,
one_one_nat: $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(nat,type,
nat: $i > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i ) > $i ).
tff(zero_zero_int,type,
zero_zero_int: $i ).
tff(ord_less_eq_nat,type,
ord_less_eq_nat: $i ).
tff(dvd_dvd_int,type,
dvd_dvd_int: $i ).
tff(plus_plus_real,type,
plus_plus_real: ( $i * $i ) > $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i ) > $i ).
tff(dvd_dvd_nat,type,
dvd_dvd_nat: $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff(plus_plus_int,type,
plus_plus_int: ( $i * $i ) > $i ).
tff(zprime,type,
zprime: $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(int,type,
int: $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff('#skF_13',type,
'#skF_13': $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(legendre,type,
legendre: ( $i * $i ) > $i ).
tff(power_power_real,type,
power_power_real: $i > $i ).
tff(if_int,type,
if_int: ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(hAPP_int_bool,type,
hAPP_int_bool: ( $i * $i ) > $i ).
tff(hAPP_nat_real,type,
hAPP_nat_real: ( $i * $i ) > $i ).
tff(twoSqu1154269391sum2sq,type,
twoSqu1154269391sum2sq: $i ).
tff(plus_plus_nat,type,
plus_plus_nat: ( $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_41',type,
'#skF_41': ( $i * $i * $i ) > $i ).
tff(minus_minus_int,type,
minus_minus_int: ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $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_28',type,
'#skF_28': ( $i * $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_449,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
tff(f_1188,axiom,
! [M_5] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_5)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_of__nat__less__0__iff) ).
tff(f_95,hypothesis,
! [B_1_1,B_2_1] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
tff(f_79,axiom,
! [B_1_1] :
( is_int(B_1_1)
=> is_int(succ(B_1_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_Osucc) ).
tff(f_3616,axiom,
! [K_1] : ( succ(K_1) = plus_plus_int(K_1,one_one_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_succ__def) ).
tff(f_1416,axiom,
! [A_76,C_35] : ( plus_plus_int(A_76,C_35) = plus_plus_int(C_35,A_76) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f_228,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_nat__1__add__1) ).
tff(f_5795,negated_conjecture,
hAPP_nat_int(power_power_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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f_1171,axiom,
! [A_1,Na] :
( is_int(A_1)
=> ( ( hAPP_nat_int(power_power_int(A_1),Na) = zero_zero_int )
<=> ( ( A_1 = zero_zero_int )
& ( Na != zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_power__eq__0__iff) ).
tff(f_1086,axiom,
! [A_91] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_91),plus_plus_int(A_91,one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__add__one) ).
tff(c_367,plain,
zero_zero_int = pls,
inference(cnfTransformation,[status(thm)],[f_449]) ).
tff(c_900,plain,
! [M_5_420] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_5_420)),zero_zero_int)),
inference(cnfTransformation,[status(thm)],[f_1188]) ).
tff(c_4151,plain,
! [M_5_420] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_5_420)),pls)),
inference(demodulation,[status(thm),theory(equality)],[c_367,c_900]) ).
tff(c_40,plain,
! [B_1_1_21,B_2_1_22] : is_int(hAPP_nat_int(B_1_1_21,B_2_1_22)),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_28,plain,
! [B_1_1_14] :
( is_int(succ(B_1_1_14))
| ~ is_int(B_1_1_14) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_2424,plain,
! [K_1_1694] : ( plus_plus_int(K_1_1694,one_one_int) = succ(K_1_1694) ),
inference(cnfTransformation,[status(thm)],[f_3616]) ).
tff(c_7121,plain,
! [C_35_2648,A_76_2649] : ( plus_plus_int(C_35_2648,A_76_2649) = plus_plus_int(A_76_2649,C_35_2648) ),
inference(cnfTransformation,[status(thm)],[f_1416]) ).
tff(c_7371,plain,
! [K_1_1694] : ( plus_plus_int(one_one_int,K_1_1694) = succ(K_1_1694) ),
inference(superposition,[status(thm),theory(equality)],[c_2424,c_7121]) ).
tff(c_174,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_3705,plain,
hAPP_nat_int(power_power_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_5795]) ).
tff(c_4159,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_367,c_3705]) ).
tff(c_4383,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(one_one_nat,one_one_nat)) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_174,c_4159]) ).
tff(c_7841,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(one_one_nat,one_one_nat)) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_7371,c_4383]) ).
tff(c_886,plain,
! [A_1_414,Na_415] :
( ( zero_zero_int = A_1_414 )
| ( hAPP_nat_int(power_power_int(A_1_414),Na_415) != zero_zero_int )
| ~ is_int(A_1_414) ),
inference(cnfTransformation,[status(thm)],[f_1171]) ).
tff(c_19758,plain,
! [A_1_2919,Na_2920] :
( ( pls = A_1_2919 )
| ( hAPP_nat_int(power_power_int(A_1_2919),Na_2920) != pls )
| ~ is_int(A_1_2919) ),
inference(demodulation,[status(thm),theory(equality)],[c_367,c_367,c_886]) ).
tff(c_19790,plain,
( ( succ(hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ is_int(succ(hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(superposition,[status(thm),theory(equality)],[c_7841,c_19758]) ).
tff(c_19797,plain,
~ is_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),
inference(splitLeft,[status(thm)],[c_19790]) ).
tff(c_19800,plain,
~ is_int(hAPP_nat_int(semiri1621563631at_int,n)),
inference(resolution,[status(thm)],[c_28,c_19797]) ).
tff(c_19804,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_19800]) ).
tff(c_19805,plain,
succ(hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(splitRight,[status(thm)],[c_19790]) ).
tff(c_837,plain,
! [A_91_375] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_91_375),plus_plus_int(A_91_375,one_one_int))),
inference(cnfTransformation,[status(thm)],[f_1086]) ).
tff(c_4033,plain,
! [A_91_375] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_91_375),succ(A_91_375))),
inference(demodulation,[status(thm),theory(equality)],[c_2424,c_837]) ).
tff(c_19821,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_19805,c_4033]) ).
tff(c_19834,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4151,c_19821]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % 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
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 14:48:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 30.32/11.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.32/11.17
% 30.32/11.17 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.32/11.20
% 30.32/11.20 Inference rules
% 30.32/11.20 ----------------------
% 30.32/11.20 #Ref : 7
% 30.32/11.20 #Sup : 4110
% 30.32/11.20 #Fact : 0
% 30.32/11.20 #Define : 0
% 30.32/11.20 #Split : 74
% 30.32/11.20 #Chain : 0
% 30.32/11.20 #Close : 0
% 30.32/11.20
% 30.32/11.20 Ordering : KBO
% 30.32/11.20
% 30.32/11.20 Simplification rules
% 30.32/11.20 ----------------------
% 30.32/11.20 #Subsume : 794
% 30.32/11.20 #Demod : 3226
% 30.32/11.20 #Tautology : 2415
% 30.32/11.20 #SimpNegUnit : 105
% 30.32/11.20 #BackRed : 12
% 30.32/11.20
% 30.32/11.20 #Partial instantiations: 0
% 30.32/11.20 #Strategies tried : 1
% 30.32/11.20
% 30.32/11.20 Timing (in seconds)
% 30.32/11.20 ----------------------
% 30.32/11.20 Preprocessing : 2.12
% 30.32/11.20 Parsing : 1.16
% 30.32/11.20 CNF conversion : 0.18
% 30.32/11.20 Main loop : 8.03
% 30.32/11.20 Inferencing : 1.03
% 30.32/11.20 Reduction : 4.48
% 30.32/11.20 Demodulation : 3.47
% 30.32/11.20 BG Simplification : 0.22
% 30.32/11.20 Subsumption : 1.76
% 30.32/11.20 Abstraction : 0.11
% 30.32/11.20 MUC search : 0.00
% 30.32/11.20 Cooper : 0.00
% 30.32/11.20 Total : 10.20
% 30.32/11.20 Index Insertion : 0.00
% 30.32/11.20 Index Deletion : 0.00
% 30.32/11.20 Index Matching : 0.00
% 30.32/11.20 BG Taut test : 0.00
%------------------------------------------------------------------------------