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/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 : n003.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 24.17s 8.22s
% Output : CNFRefutation 24.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 140
% Syntax : Number of formulae : 192 ( 57 unt; 122 typ; 0 def)
% Number of atoms : 85 ( 83 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 9 |; 1 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 118 ( 65 >; 53 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 108 ( 108 usr; 44 con; 0-3 aty)
% Number of variables : 46 (; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
%$ 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 > succ > quadRes > power_power_real > power_power_nat > power_power_int > number_number_of_nat > number_number_of_int > number267125858f_real > nat_1 > bit1 > bit0 > abs_abs_real > abs_abs_int > zprime > zero_zero_real > zero_zero_nat > zero_zero_int > y > x > twoSqu820444569sum2sq > 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 > fTrue > fFalse > dvd_dvd_nat > dvd_dvd_int > #skF_17 > #skF_15 > #skF_14 > #skF_30 > #skF_6 > #skF_38 > #skF_21 > #skF_36 > #skF_29 > #skF_8 > #skF_19 > #skF_5 > #skF_20 > #skF_25 > #skF_11 > #skF_12 > #skF_9 > #skF_39 > #skF_1 > #skF_28 > #skF_4 > #skF_32 > #skF_26 > #skF_10 > #skF_18 > #skF_13 > #skF_7 > #skF_23 > #skF_37 > #skF_27 > #skF_24 > #skF_41 > #skF_16 > #skF_2 > #skF_35 > #skF_33 > #skF_31 > #skF_34 > #skF_22 > #skF_3 > #skF_40
%Foreground sorts:
tff(fun_int_bool,type,
fun_int_bool: $tType ).
tff(fun_int_fun_int_bool,type,
fun_int_fun_int_bool: $tType ).
tff(real,type,
real: $tType ).
tff(fun_re413263731l_bool,type,
fun_re413263731l_bool: $tType ).
tff(fun_nat_bool,type,
fun_nat_bool: $tType ).
tff(nat,type,
nat: $tType ).
tff(fun_nat_fun_nat_bool,type,
fun_nat_fun_nat_bool: $tType ).
tff(bool,type,
bool: $tType ).
tff(fun_real_bool,type,
fun_real_bool: $tType ).
tff(int,type,
int: $tType ).
tff(fun_nat_nat,type,
fun_nat_nat: $tType ).
tff(fun_nat_int,type,
fun_nat_int: $tType ).
tff(fun_nat_real,type,
fun_nat_real: $tType ).
%Background operators:
%Foreground operators:
tff(abs_abs_int,type,
abs_abs_int: int > int ).
tff(ord_less_eq_real,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(bit1,type,
bit1: int > int ).
tff(hAPP_nat_real,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff('#skF_17',type,
'#skF_17': ( fun_nat_bool * int ) > nat ).
tff(times_times_nat,type,
times_times_nat: ( nat * nat ) > nat ).
tff('#skF_15',type,
'#skF_15': ( fun_nat_bool * nat * nat ) > nat ).
tff(s1,type,
s1: int ).
tff(n,type,
n: nat ).
tff(one_one_int,type,
one_one_int: int ).
tff(semiri132038758t_real,type,
semiri132038758t_real: fun_nat_real ).
tff(fTrue,type,
fTrue: bool ).
tff('#skF_14',type,
'#skF_14': ( int * int ) > nat ).
tff('#skF_30',type,
'#skF_30': int ).
tff(hAPP_int_bool,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff('#skF_6',type,
'#skF_6': fun_nat_bool > int ).
tff('#skF_38',type,
'#skF_38': ( int * fun_nat_int * nat ) > nat ).
tff(semiri1621563631at_int,type,
semiri1621563631at_int: fun_nat_int ).
tff('#skF_21',type,
'#skF_21': int ).
tff(number267125858f_real,type,
number267125858f_real: int > real ).
tff('#skF_36',type,
'#skF_36': ( nat * fun_nat_bool ) > nat ).
tff(one_one_real,type,
one_one_real: real ).
tff(succ,type,
succ: int > int ).
tff(minus_minus_real,type,
minus_minus_real: ( real * real ) > real ).
tff(ord_less_int,type,
ord_less_int: fun_int_fun_int_bool ).
tff(min,type,
min: int ).
tff(power_power_real,type,
power_power_real: real > fun_nat_real ).
tff(zero_zero_real,type,
zero_zero_real: real ).
tff('#skF_29',type,
'#skF_29': int > int ).
tff('#skF_8',type,
'#skF_8': fun_nat_bool > nat ).
tff(dvd_dvd_int,type,
dvd_dvd_int: fun_int_fun_int_bool ).
tff(semiri984289939at_nat,type,
semiri984289939at_nat: fun_nat_nat ).
tff('#skF_19',type,
'#skF_19': int ).
tff('#skF_5',type,
'#skF_5': ( real * nat ) > real ).
tff(number_number_of_int,type,
number_number_of_int: int > int ).
tff(hAPP_n1699378549t_bool,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff('#skF_20',type,
'#skF_20': int ).
tff(ord_less_real,type,
ord_less_real: fun_re413263731l_bool ).
tff(s,type,
s: int ).
tff(zcong,type,
zcong: ( int * int ) > fun_int_bool ).
tff(power_power_nat,type,
power_power_nat: nat > fun_nat_nat ).
tff('#skF_25',type,
'#skF_25': int ).
tff(abs_abs_real,type,
abs_abs_real: real > real ).
tff('#skF_11',type,
'#skF_11': fun_int_bool > nat ).
tff('#skF_12',type,
'#skF_12': fun_int_bool > nat ).
tff(m1,type,
m1: int ).
tff('#skF_9',type,
'#skF_9': fun_nat_bool > int ).
tff('#skF_39',type,
'#skF_39': ( int * fun_nat_int * nat ) > nat ).
tff(m,type,
m: int ).
tff('#skF_1',type,
'#skF_1': ( fun_int_bool * int * int ) > int ).
tff('#skF_28',type,
'#skF_28': ( int * int * int ) > int ).
tff('#skF_4',type,
'#skF_4': ( real * nat ) > real ).
tff(nat_1,type,
nat_1: int > nat ).
tff(number_number_of_nat,type,
number_number_of_nat: int > nat ).
tff(dvd_dvd_nat,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(tn,type,
tn: nat ).
tff(legendre,type,
legendre: ( int * int ) > int ).
tff('#skF_32',type,
'#skF_32': int ).
tff(times_times_real,type,
times_times_real: ( real * real ) > real ).
tff('#skF_26',type,
'#skF_26': int ).
tff(twoSqu820444569sum2sq,type,
twoSqu820444569sum2sq: fun_int_bool ).
tff(x,type,
x: int ).
tff('#skF_10',type,
'#skF_10': fun_int_bool > int ).
tff('#skF_18',type,
'#skF_18': int ).
tff(plus_plus_real,type,
plus_plus_real: ( real * real ) > real ).
tff('#skF_13',type,
'#skF_13': fun_int_bool > int ).
tff(hAPP_i1948725293t_bool,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(hAPP_nat_bool,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff('#skF_7',type,
'#skF_7': fun_nat_bool > nat ).
tff('#skF_23',type,
'#skF_23': int ).
tff('#skF_37',type,
'#skF_37': ( int * fun_int_bool * int ) > int ).
tff(plus_plus_nat,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff('#skF_27',type,
'#skF_27': ( int * int ) > int ).
tff(one_one_nat,type,
one_one_nat: nat ).
tff(ord_less_eq_int,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(times_times_int,type,
times_times_int: ( int * int ) > int ).
tff(hAPP_nat_int,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff('#skF_24',type,
'#skF_24': int ).
tff(pls,type,
pls: int ).
tff(hAPP_nat_nat,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff('#skF_41',type,
'#skF_41': ( int * fun_nat_int * nat ) > nat ).
tff(zero_zero_nat,type,
zero_zero_nat: nat ).
tff('#skF_16',type,
'#skF_16': ( fun_nat_bool * nat * nat ) > nat ).
tff(fFalse,type,
fFalse: bool ).
tff('#skF_2',type,
'#skF_2': int > nat ).
tff(hAPP_real_bool,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(ord_less_nat,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(y,type,
y: int ).
tff('#skF_35',type,
'#skF_35': ( int * fun_int_bool * int ) > int ).
tff('#skF_33',type,
'#skF_33': int ).
tff(bit0,type,
bit0: int > int ).
tff(hBOOL,type,
hBOOL: bool > $o ).
tff('#skF_31',type,
'#skF_31': int ).
tff('#skF_34',type,
'#skF_34': ( int * int ) > int ).
tff(if_nat,type,
if_nat: ( bool * nat * nat ) > nat ).
tff(power_power_int,type,
power_power_int: int > fun_nat_int ).
tff('#skF_22',type,
'#skF_22': ( nat * nat ) > nat ).
tff(minus_minus_int,type,
minus_minus_int: ( int * int ) > int ).
tff(plus_plus_int,type,
plus_plus_int: ( int * int ) > int ).
tff(quadRes,type,
quadRes: int > fun_int_bool ).
tff(if_int,type,
if_int: ( bool * int * int ) > int ).
tff(hAPP_r1134773055l_bool,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(ord_less_eq_nat,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(zprime,type,
zprime: fun_int_bool ).
tff(t,type,
t: int ).
tff('#skF_3',type,
'#skF_3': ( nat * nat ) > nat ).
tff(zero_zero_int,type,
zero_zero_int: int ).
tff(minus_minus_nat,type,
minus_minus_nat: ( nat * nat ) > nat ).
tff('#skF_40',type,
'#skF_40': ( int * fun_nat_int * nat ) > nat ).
tff(f_4183,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_rel__simps_I37_J) ).
tff(f_461,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_semiring__numeral__1__eq__1) ).
tff(f_591,axiom,
! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_number__of__is__id) ).
tff(f_4192,axiom,
! [K: int] :
( ( bit1(K) = min )
<=> ( K = min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_rel__simps_I47_J) ).
tff(f_1246,axiom,
! [A_76: int,C_35: int] : ( plus_plus_int(A_76,C_35) = plus_plus_int(C_35,A_76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f_4195,axiom,
! [K_1: int] : ( minus_minus_int(K_1,min) = succ(K_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_diff__bin__simps_I2_J) ).
tff(f_4071,axiom,
! [A: int,B_1: int,C: int] :
( ( minus_minus_int(A,B_1) = C )
=> ( A = plus_plus_int(C,B_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_Int2_Oaux1) ).
tff(f_357,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).
tff(f_1266,axiom,
! [B: int,A_1: int] :
( ( B = plus_plus_int(B,A_1) )
<=> ( A_1 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_add__0__iff) ).
tff(f_3310,axiom,
! [K_1: int] : ( succ(K_1) = plus_plus_int(K_1,one_one_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_succ__def) ).
tff(f_3102,axiom,
! [V_1: int] : ( number_number_of_nat(V_1) = nat_1(number_number_of_int(V_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_nat__number__of__def) ).
tff(f_5377,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_3292,axiom,
succ(pls) = bit1(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_succ__Pls) ).
tff(f_2457,axiom,
! [A_31: int,B_16: int] : ( minus_minus_int(plus_plus_int(A_31,B_16),B_16) = A_31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_add__diff__cancel) ).
tff(f_144,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_45_nat__1__add__1) ).
tff(f_1025,axiom,
! [A_1: int,Na: nat] :
( ( hAPP_nat_int(power_power_int(A_1),Na) = zero_zero_int )
<=> ( ( A_1 = zero_zero_int )
& ( Na != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_power__eq__0__iff) ).
tff(f_5146,axiom,
! [Z_1: int] :
( ( abs_abs_int(Z_1) = one_one_int )
<=> ( ( Z_1 = one_one_int )
| ( Z_1 = number_number_of_int(min) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_abs__eq__1__iff) ).
tff(f_5130,axiom,
! [M: nat] : ( abs_abs_int(hAPP_nat_int(semiri1621563631at_int,M)) = hAPP_nat_int(semiri1621563631at_int,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_abs__int__eq) ).
tff(c_2929,plain,
pls != min,
inference(cnfTransformation,[status(thm)],[f_4183]) ).
tff(c_429,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(cnfTransformation,[status(thm)],[f_461]) ).
tff(c_513,plain,
! [K_1_196: int] : ( number_number_of_int(K_1_196) = K_1_196 ),
inference(cnfTransformation,[status(thm)],[f_591]) ).
tff(c_4852,plain,
bit1(pls) = one_one_int,
inference(superposition,[status(thm),theory(equality)],[c_429,c_513]) ).
tff(c_5286,plain,
! [K_3194: int] :
( ( min = K_3194 )
| ( bit1(K_3194) != min ) ),
inference(cnfTransformation,[status(thm)],[f_4192]) ).
tff(c_5289,plain,
( ( pls = min )
| ( one_one_int != min ) ),
inference(superposition,[status(thm),theory(equality)],[c_4852,c_5286]) ).
tff(c_5293,plain,
one_one_int != min,
inference(negUnitSimplification,[status(thm)],[c_2929,c_5289]) ).
tff(c_1012,plain,
! [C_35_534: int,A_76_533: int] : ( plus_plus_int(C_35_534,A_76_533) = plus_plus_int(A_76_533,C_35_534) ),
inference(cnfTransformation,[status(thm)],[f_1246]) ).
tff(c_2943,plain,
! [K_1_2073: int] : ( minus_minus_int(K_1_2073,min) = succ(K_1_2073) ),
inference(cnfTransformation,[status(thm)],[f_4195]) ).
tff(c_6319,plain,
! [A_3550: int,B_1_3551: int] : ( plus_plus_int(minus_minus_int(A_3550,B_1_3551),B_1_3551) = A_3550 ),
inference(cnfTransformation,[status(thm)],[f_4071]) ).
tff(c_6412,plain,
! [K_1_3579: int] : ( plus_plus_int(succ(K_1_3579),min) = K_1_3579 ),
inference(superposition,[status(thm),theory(equality)],[c_2943,c_6319]) ).
tff(c_6521,plain,
! [K_1_3612: int] : ( plus_plus_int(min,succ(K_1_3612)) = K_1_3612 ),
inference(superposition,[status(thm),theory(equality)],[c_1012,c_6412]) ).
tff(c_337,plain,
number_number_of_int(pls) = zero_zero_int,
inference(cnfTransformation,[status(thm)],[f_357]) ).
tff(c_4158,plain,
zero_zero_int = pls,
inference(demodulation,[status(thm),theory(equality)],[c_513,c_337]) ).
tff(c_1036,plain,
! [A_1_543: int,B_542: int] :
( ( zero_zero_int = A_1_543 )
| ( plus_plus_int(B_542,A_1_543) != B_542 ) ),
inference(cnfTransformation,[status(thm)],[f_1266]) ).
tff(c_4185,plain,
! [A_1_543: int,B_542: int] :
( ( pls = A_1_543 )
| ( plus_plus_int(B_542,A_1_543) != B_542 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4158,c_1036]) ).
tff(c_6657,plain,
! [K_1_3660: int] :
( ( succ(K_1_3660) = pls )
| ( min != K_1_3660 ) ),
inference(superposition,[status(thm),theory(equality)],[c_6521,c_4185]) ).
tff(c_5694,plain,
! [C_35_3320: int,A_76_3321: int] : ( plus_plus_int(C_35_3320,A_76_3321) = plus_plus_int(A_76_3321,C_35_3320) ),
inference(cnfTransformation,[status(thm)],[f_1246]) ).
tff(c_2358,plain,
! [K_1_1670: int] : ( plus_plus_int(K_1_1670,one_one_int) = succ(K_1_1670) ),
inference(cnfTransformation,[status(thm)],[f_3310]) ).
tff(c_5710,plain,
! [A_76_3321: int] : ( plus_plus_int(one_one_int,A_76_3321) = succ(A_76_3321) ),
inference(superposition,[status(thm),theory(equality)],[c_5694,c_2358]) ).
tff(c_2184,plain,
! [V_1_1570: int] : ( nat_1(number_number_of_int(V_1_1570)) = number_number_of_nat(V_1_1570) ),
inference(cnfTransformation,[status(thm)],[f_3102]) ).
tff(c_3964,plain,
! [V_1_1570: int] : ( number_number_of_nat(V_1_1570) = nat_1(V_1_1570) ),
inference(demodulation,[status(thm),theory(equality)],[c_513,c_2184]) ).
tff(c_3603,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_5377]) ).
tff(c_4051,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(bit0(bit1(pls)))) = zero_zero_int,
inference(demodulation,[status(thm),theory(equality)],[c_3964,c_3603]) ).
tff(c_4196,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(bit0(bit1(pls)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_4158,c_4051]) ).
tff(c_4885,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(bit0(one_one_int))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_4852,c_4196]) ).
tff(c_5777,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),nat_1(bit0(one_one_int))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_5710,c_4885]) ).
tff(c_6681,plain,
( ( hAPP_nat_int(power_power_int(pls),nat_1(bit0(one_one_int))) = pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != min ) ),
inference(superposition,[status(thm),theory(equality)],[c_6657,c_5777]) ).
tff(c_6723,plain,
hAPP_nat_int(semiri1621563631at_int,n) != min,
inference(splitLeft,[status(thm)],[c_6681]) ).
tff(c_2342,plain,
succ(pls) = bit1(pls),
inference(cnfTransformation,[status(thm)],[f_3292]) ).
tff(c_4903,plain,
succ(pls) = one_one_int,
inference(demodulation,[status(thm),theory(equality)],[c_4852,c_2342]) ).
tff(c_6448,plain,
plus_plus_int(one_one_int,min) = pls,
inference(superposition,[status(thm),theory(equality)],[c_4903,c_6412]) ).
tff(c_6468,plain,
plus_plus_int(min,one_one_int) = pls,
inference(superposition,[status(thm),theory(equality)],[c_6448,c_1012]) ).
tff(c_6853,plain,
! [A_31_3742: int,B_16_3743: int] : ( minus_minus_int(plus_plus_int(A_31_3742,B_16_3743),B_16_3743) = A_31_3742 ),
inference(cnfTransformation,[status(thm)],[f_2457]) ).
tff(c_6893,plain,
minus_minus_int(pls,one_one_int) = min,
inference(superposition,[status(thm),theory(equality)],[c_6468,c_6853]) ).
tff(c_118,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_7696,plain,
nat_1(bit0(one_one_int)) = plus_plus_nat(one_one_nat,one_one_nat),
inference(demodulation,[status(thm),theory(equality)],[c_3964,c_4852,c_118]) ).
tff(c_7697,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_7696,c_5777]) ).
tff(c_828,plain,
! [A_1_390: int,Na_391: nat] :
( ( zero_zero_int = A_1_390 )
| ( hAPP_nat_int(power_power_int(A_1_390),Na_391) != zero_zero_int ) ),
inference(cnfTransformation,[status(thm)],[f_1025]) ).
tff(c_9560,plain,
! [A_1_4202: int,Na_4203: nat] :
( ( pls = A_1_4202 )
| ( hAPP_nat_int(power_power_int(A_1_4202),Na_4203) != pls ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4158,c_4158,c_828]) ).
tff(c_9573,plain,
succ(hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(superposition,[status(thm),theory(equality)],[c_7697,c_9560]) ).
tff(c_6918,plain,
! [K_1_1670: int] : ( minus_minus_int(succ(K_1_1670),one_one_int) = K_1_1670 ),
inference(superposition,[status(thm),theory(equality)],[c_2358,c_6853]) ).
tff(c_9607,plain,
minus_minus_int(pls,one_one_int) = hAPP_nat_int(semiri1621563631at_int,n),
inference(superposition,[status(thm),theory(equality)],[c_9573,c_6918]) ).
tff(c_9645,plain,
hAPP_nat_int(semiri1621563631at_int,n) = min,
inference(demodulation,[status(thm),theory(equality)],[c_6893,c_9607]) ).
tff(c_9647,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6723,c_9645]) ).
tff(c_9649,plain,
hAPP_nat_int(semiri1621563631at_int,n) = min,
inference(splitRight,[status(thm)],[c_6681]) ).
tff(c_3457,plain,
abs_abs_int(number_number_of_int(min)) = one_one_int,
inference(cnfTransformation,[status(thm)],[f_5146]) ).
tff(c_3962,plain,
abs_abs_int(min) = one_one_int,
inference(demodulation,[status(thm),theory(equality)],[c_513,c_3457]) ).
tff(c_11921,plain,
! [M_4739: nat] : ( abs_abs_int(hAPP_nat_int(semiri1621563631at_int,M_4739)) = hAPP_nat_int(semiri1621563631at_int,M_4739) ),
inference(cnfTransformation,[status(thm)],[f_5130]) ).
tff(c_11930,plain,
hAPP_nat_int(semiri1621563631at_int,n) = abs_abs_int(min),
inference(superposition,[status(thm),theory(equality)],[c_9649,c_11921]) ).
tff(c_11939,plain,
one_one_int = min,
inference(demodulation,[status(thm),theory(equality)],[c_9649,c_3962,c_11930]) ).
tff(c_11941,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5293,c_11939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM925_3 : TPTP v8.1.2. Released v5.3.0.
% 0.08/0.15 % 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 : n003.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 15:23:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 24.17/8.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.17/8.23
% 24.17/8.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.17/8.27
% 24.17/8.27 Inference rules
% 24.17/8.27 ----------------------
% 24.17/8.27 #Ref : 12
% 24.17/8.27 #Sup : 1922
% 24.17/8.27 #Fact : 1
% 24.17/8.27 #Define : 0
% 24.17/8.27 #Split : 6
% 24.17/8.27 #Chain : 0
% 24.17/8.27 #Close : 0
% 24.17/8.27
% 24.17/8.27 Ordering : KBO
% 24.17/8.27
% 24.17/8.27 Simplification rules
% 24.17/8.27 ----------------------
% 24.17/8.27 #Subsume : 846
% 24.17/8.27 #Demod : 1824
% 24.17/8.27 #Tautology : 1478
% 24.17/8.27 #SimpNegUnit : 228
% 24.17/8.27 #BackRed : 7
% 24.17/8.27
% 24.17/8.27 #Partial instantiations: 303
% 24.17/8.27 #Strategies tried : 1
% 24.17/8.27
% 24.17/8.27 Timing (in seconds)
% 24.17/8.27 ----------------------
% 24.17/8.27 Preprocessing : 2.25
% 24.17/8.27 Parsing : 1.24
% 24.17/8.27 CNF conversion : 0.18
% 24.17/8.27 Main loop : 4.93
% 24.17/8.27 Inferencing : 0.45
% 24.17/8.27 Reduction : 2.74
% 24.17/8.27 Demodulation : 2.05
% 24.17/8.27 BG Simplification : 0.22
% 24.17/8.27 Subsumption : 1.17
% 24.17/8.27 Abstraction : 0.09
% 24.17/8.27 MUC search : 0.00
% 24.17/8.27 Cooper : 0.00
% 24.17/8.27 Total : 7.24
% 24.17/8.27 Index Insertion : 0.00
% 24.17/8.27 Index Deletion : 0.00
% 24.17/8.28 Index Matching : 0.00
% 24.17/8.28 BG Taut test : 0.00
%------------------------------------------------------------------------------