TSTP Solution File: NUM924+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM924+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 : n027.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 20.08s 7.98s
% Output : CNFRefutation 20.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 132
% Syntax : Number of formulae : 166 ( 50 unt; 116 typ; 0 def)
% Number of atoms : 50 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 158 ( 87 >; 71 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 113 ( 113 usr; 29 con; 0-3 aty)
% Number of variables : 29 (; 29 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_int > is_bool > hBOOL > zcong > wset > standardRes > product_Pair_int_int > multInv > member_int > legendre > inv > 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_i68813070l_bool > hAPP_i1948725293t_bool > hAPP_bool_bool > hAPP_b589554111l_bool > cOMBS_int_bool_bool > cOMBC_int_int_bool > cOMBB_1652995168ol_int > #nlpp > zfact > undefined_int > twoSqu1241645765sum2sq > times_times_real > times_times_nat > times_times_int > sr > quadRes > 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 > minus_minus_real > minus_minus_nat > minus_minus_int > div_mod_nat > div_mod_int > d22set > collect_int > bit1 > bit0 > zprime > zero_zero_real > zero_zero_nat > zero_zero_int > twoSqu1154269391sum2sq > t > 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 > min > m > int > fconj > dvd_dvd_real > dvd_dvd_nat > dvd_dvd_int > #skF_32 > #skF_26 > #skF_24 > #skF_35 > #skF_31 > #skF_33 > #skF_4 > #skF_18 > #skF_6 > #skF_19 > #skF_17 > #skF_22 > #skF_12 > #skF_36 > #skF_13 > #skF_34 > #skF_30 > #skF_5 > #skF_23 > #skF_2 > #skF_10 > #skF_3 > #skF_1 > #skF_37 > #skF_8 > #skF_11 > #skF_20 > #skF_28 > #skF_15 > #skF_14 > #skF_25 > #skF_7 > #skF_29 > #skF_27 > #skF_21 > #skF_9 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(fconj,type,
fconj: $i ).
tff(hAPP_i68813070l_bool,type,
hAPP_i68813070l_bool: ( $i * $i ) > $i ).
tff(power_power_int,type,
power_power_int: $i > $i ).
tff(zcong,type,
zcong: ( $i * $i ) > $i ).
tff(hAPP_real_bool,type,
hAPP_real_bool: ( $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff(ord_less_nat,type,
ord_less_nat: $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff(m,type,
m: $i ).
tff(hAPP_bool_bool,type,
hAPP_bool_bool: ( $i * $i ) > $i ).
tff(one_one_int,type,
one_one_int: $i ).
tff(s1,type,
s1: $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff(hAPP_nat_bool,type,
hAPP_nat_bool: ( $i * $i ) > $i ).
tff(times_times_int,type,
times_times_int: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff(min,type,
min: $i ).
tff(dvd_dvd_real,type,
dvd_dvd_real: $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(minus_minus_real,type,
minus_minus_real: $i > $i ).
tff(t,type,
t: $i ).
tff(pls,type,
pls: $i ).
tff(number_number_of_nat,type,
number_number_of_nat: $i > $i ).
tff(sr,type,
sr: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(undefined_int,type,
undefined_int: $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('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff(d22set,type,
d22set: $i > $i ).
tff(is_int,type,
is_int: $i > $o ).
tff(bit0,type,
bit0: $i > $i ).
tff(standardRes,type,
standardRes: ( $i * $i ) > $i ).
tff(ord_less_eq_int,type,
ord_less_eq_int: $i ).
tff(s,type,
s: $i ).
tff(member_int,type,
member_int: ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i ) > $i ).
tff(cOMBS_int_bool_bool,type,
cOMBS_int_bool_bool: ( $i * $i ) > $i ).
tff(hAPP_int_int,type,
hAPP_int_int: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(minus_minus_nat,type,
minus_minus_nat: $i > $i ).
tff(cOMBB_1652995168ol_int,type,
cOMBB_1652995168ol_int: ( $i * $i ) > $i ).
tff(hAPP_nat_int,type,
hAPP_nat_int: ( $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff(times_times_nat,type,
times_times_nat: $i > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff(one_one_real,type,
one_one_real: $i ).
tff(wset,type,
wset: ( $i * $i ) > $i ).
tff(times_times_real,type,
times_times_real: $i > $i ).
tff(hAPP_nat_nat,type,
hAPP_nat_nat: ( $i * $i ) > $i ).
tff(number_number_of_int,type,
number_number_of_int: $i > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i * $i ) > $i ).
tff(ord_less_real,type,
ord_less_real: $i ).
tff(div_mod_nat,type,
div_mod_nat: $i > $i ).
tff(quadRes,type,
quadRes: $i > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $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(collect_int,type,
collect_int: $i > $i ).
tff(cOMBC_int_int_bool,type,
cOMBC_int_int_bool: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(twoSqu1241645765sum2sq,type,
twoSqu1241645765sum2sq: $i > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff(dvd_dvd_int,type,
dvd_dvd_int: $i ).
tff(plus_plus_nat,type,
plus_plus_nat: $i > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(hAPP_real_real,type,
hAPP_real_real: ( $i * $i ) > $i ).
tff(dvd_dvd_nat,type,
dvd_dvd_nat: $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff(zprime,type,
zprime: $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff(plus_plus_int,type,
plus_plus_int: $i > $i ).
tff(int,type,
int: $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i ) > $i ).
tff(multInv,type,
multInv: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff(zfact,type,
zfact: $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('#skF_14',type,
'#skF_14': $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(hAPP_int_bool,type,
hAPP_int_bool: ( $i * $i ) > $i ).
tff(minus_minus_int,type,
minus_minus_int: $i > $i ).
tff(hAPP_nat_real,type,
hAPP_nat_real: ( $i * $i ) > $i ).
tff(hAPP_b589554111l_bool,type,
hAPP_b589554111l_bool: ( $i * $i ) > $i ).
tff(twoSqu1154269391sum2sq,type,
twoSqu1154269391sum2sq: $i ).
tff(product_Pair_int_int,type,
product_Pair_int_int: ( $i * $i ) > $i ).
tff(zero_zero_nat,type,
zero_zero_nat: $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(inv,type,
inv: ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(div_mod_int,type,
div_mod_int: $i > $i ).
tff(f_1015,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_semiring__norm_I110_J) ).
tff(f_843,axiom,
! [K_1] : ( bit0(K_1) = hAPP_int_int(plus_plus_int(K_1),K_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Bit0__def) ).
tff(f_1581,axiom,
! [M_11] : ( hAPP_int_int(plus_plus_int(M_11),M_11) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),M_11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
tff(f_859,axiom,
! [W_9] : ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(W_9)) = number_number_of_int(bit0(W_9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_double__number__of__Bit0) ).
tff(f_1286,axiom,
! [A_100,B_66] : ( hAPP_int_int(times_times_int(A_100),B_66) = hAPP_int_int(times_times_int(B_66),A_100) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f_1292,axiom,
! [A_99,C_41] : ( hAPP_int_int(plus_plus_int(A_99),C_41) = hAPP_int_int(plus_plus_int(C_41),A_99) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f_5157,axiom,
twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
tff(f_1037,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_semiring__one__add__one__is__two) ).
tff(f_1109,axiom,
! [X_16] : ( hAPP_int_int(times_times_int(X_16),X_16) = hAPP_nat_int(power_power_int(X_16),number_number_of_nat(bit0(bit1(pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(f_1040,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_one__add__one__is__two) ).
tff(f_106,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(f_811,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Pls__def) ).
tff(f_6079,axiom,
! [P,Q,R] : ( hAPP_int_bool(cOMBC_int_int_bool(P,Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).
tff(f_6086,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f_2099,axiom,
! [A_71] : ( hAPP_int_int(times_times_int(zero_zero_int),A_71) = zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_mult__zero__left) ).
tff(f_105,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox2/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_778,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(cnfTransformation,[status(thm)],[f_1015]) ).
tff(c_606,plain,
! [K_1_305] : ( hAPP_int_int(plus_plus_int(K_1_305),K_1_305) = bit0(K_1_305) ),
inference(cnfTransformation,[status(thm)],[f_843]) ).
tff(c_1190,plain,
! [M_11_733] : ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),M_11_733) = hAPP_int_int(plus_plus_int(M_11_733),M_11_733) ),
inference(cnfTransformation,[status(thm)],[f_1581]) ).
tff(c_4388,plain,
! [M_11_733] : ( hAPP_int_int(times_times_int(bit0(one_one_int)),M_11_733) = bit0(M_11_733) ),
inference(demodulation,[status(thm),theory(equality)],[c_606,c_606,c_1190]) ).
tff(c_616,plain,
! [W_9_312] : ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(W_9_312)) = number_number_of_int(bit0(W_9_312)) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_4387,plain,
! [W_9_312] : ( hAPP_int_int(times_times_int(bit0(one_one_int)),number_number_of_int(W_9_312)) = number_number_of_int(bit0(W_9_312)) ),
inference(demodulation,[status(thm),theory(equality)],[c_606,c_616]) ).
tff(c_4426,plain,
! [W_9_312] : ( number_number_of_int(bit0(W_9_312)) = bit0(number_number_of_int(W_9_312)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4388,c_4387]) ).
tff(c_976,plain,
! [B_66_539,A_100_538] : ( hAPP_int_int(times_times_int(B_66_539),A_100_538) = hAPP_int_int(times_times_int(A_100_538),B_66_539) ),
inference(cnfTransformation,[status(thm)],[f_1286]) ).
tff(c_982,plain,
! [C_41_545,A_99_544] : ( hAPP_int_int(plus_plus_int(C_41_545),A_99_544) = hAPP_int_int(plus_plus_int(A_99_544),C_41_545) ),
inference(cnfTransformation,[status(thm)],[f_1292]) ).
tff(c_3120,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
inference(cnfTransformation,[status(thm)],[f_5157]) ).
tff(c_4129,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m))),t) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
inference(demodulation,[status(thm),theory(equality)],[c_982,c_3120]) ).
tff(c_4174,plain,
hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),number_number_of_int(bit0(bit0(bit1(pls))))))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_976,c_4129]) ).
tff(c_4445,plain,
hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),bit0(bit0(number_number_of_int(bit1(pls))))))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
inference(demodulation,[status(thm),theory(equality)],[c_4426,c_4426,c_4174]) ).
tff(c_4464,plain,
hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),bit0(bit0(one_one_int))))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
inference(demodulation,[status(thm),theory(equality)],[c_778,c_4445]) ).
tff(c_802,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_1037]) ).
tff(c_860,plain,
! [X_16_413] : ( hAPP_nat_int(power_power_int(X_16_413),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(X_16_413),X_16_413) ),
inference(cnfTransformation,[status(thm)],[f_1109]) ).
tff(c_4280,plain,
! [X_16_413] : ( hAPP_nat_int(power_power_int(X_16_413),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = hAPP_int_int(times_times_int(X_16_413),X_16_413) ),
inference(demodulation,[status(thm),theory(equality)],[c_802,c_860]) ).
tff(c_808,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_1040]) ).
tff(c_4389,plain,
number_number_of_int(bit0(bit1(pls))) = bit0(one_one_int),
inference(demodulation,[status(thm),theory(equality)],[c_606,c_808]) ).
tff(c_58,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_4905,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
inference(demodulation,[status(thm),theory(equality)],[c_4464,c_4280,c_4389,c_4426,c_802,c_976,c_976,c_982,c_982,c_58]) ).
tff(c_578,plain,
zero_zero_int = pls,
inference(cnfTransformation,[status(thm)],[f_811]) ).
tff(c_3701,plain,
! [P_2638,R_2640,Q_2639] : ( hAPP_int_bool(hAPP_i1948725293t_bool(P_2638,R_2640),Q_2639) = hAPP_int_bool(cOMBC_int_int_bool(P_2638,Q_2639),R_2640) ),
inference(cnfTransformation,[status(thm)],[f_6079]) ).
tff(c_3707,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(cnfTransformation,[status(thm)],[f_6086]) ).
tff(c_3708,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int))),
inference(demodulation,[status(thm),theory(equality)],[c_3701,c_3707]) ).
tff(c_4126,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))))),
inference(demodulation,[status(thm),theory(equality)],[c_982,c_3708]) ).
tff(c_4219,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)))),
inference(demodulation,[status(thm),theory(equality)],[c_860,c_4126]) ).
tff(c_4508,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)))),
inference(demodulation,[status(thm),theory(equality)],[c_578,c_4219]) ).
tff(c_4908,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
inference(demodulation,[status(thm),theory(equality)],[c_4905,c_4508]) ).
tff(c_1450,plain,
! [A_71_896] : ( hAPP_int_int(times_times_int(zero_zero_int),A_71_896) = zero_zero_int ),
inference(cnfTransformation,[status(thm)],[f_2099]) ).
tff(c_4482,plain,
! [A_71_896] : ( hAPP_int_int(times_times_int(pls),A_71_896) = pls ),
inference(demodulation,[status(thm),theory(equality)],[c_578,c_578,c_1450]) ).
tff(c_56,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_4911,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
inference(demodulation,[status(thm),theory(equality)],[c_4464,c_4389,c_4426,c_4482,c_976,c_976,c_976,c_976,c_982,c_982,c_3701,c_578,c_56]) ).
tff(c_4912,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4908,c_4911]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM924+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
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 15:03:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 20.08/7.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.08/7.99
% 20.08/7.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.20/8.02
% 20.20/8.02 Inference rules
% 20.20/8.02 ----------------------
% 20.20/8.02 #Ref : 0
% 20.20/8.02 #Sup : 0
% 20.20/8.02 #Fact : 0
% 20.20/8.02 #Define : 0
% 20.20/8.02 #Split : 0
% 20.20/8.02 #Chain : 0
% 20.20/8.02 #Close : 0
% 20.20/8.02
% 20.20/8.02 Ordering : KBO
% 20.20/8.02
% 20.20/8.02 Simplification rules
% 20.20/8.02 ----------------------
% 20.20/8.02 #Subsume : 1539
% 20.20/8.02 #Demod : 1881
% 20.20/8.02 #Tautology : 299
% 20.20/8.02 #SimpNegUnit : 4
% 20.20/8.02 #BackRed : 0
% 20.20/8.02
% 20.20/8.02 #Partial instantiations: 0
% 20.20/8.02 #Strategies tried : 1
% 20.20/8.02
% 20.20/8.02 Timing (in seconds)
% 20.20/8.02 ----------------------
% 20.20/8.03 Preprocessing : 2.26
% 20.20/8.03 Parsing : 1.20
% 20.20/8.03 CNF conversion : 0.18
% 20.20/8.03 Main loop : 4.62
% 20.20/8.03 Inferencing : 0.00
% 20.20/8.03 Reduction : 3.12
% 20.20/8.03 Demodulation : 2.38
% 20.20/8.03 BG Simplification : 0.21
% 20.20/8.03 Subsumption : 0.99
% 20.20/8.03 Abstraction : 0.09
% 20.20/8.03 MUC search : 0.00
% 20.20/8.03 Cooper : 0.00
% 20.20/8.03 Total : 6.94
% 20.20/8.03 Index Insertion : 0.00
% 20.20/8.03 Index Deletion : 0.00
% 20.20/8.03 Index Matching : 0.00
% 20.20/8.03 BG Taut test : 0.00
%------------------------------------------------------------------------------