TSTP Solution File: NUM924+7 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM924+7 : 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 : n013.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 10:53:07 EDT 2023
% Result : Theorem 24.09s 9.52s
% Output : CNFRefutation 24.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 161
% Syntax : Number of formulae : 182 ( 31 unt; 151 typ; 0 def)
% Number of atoms : 31 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 227 ( 134 >; 93 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 1 prp; 0-2 aty)
% Number of functors : 91 ( 91 usr; 17 con; 0-5 aty)
% Number of variables : 22 (; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ zero_neq_one > zero > semiring_div > semiring_1 > semiring_0 > semiring > semiri456707255roduct > ring_n68954251visors > ring_div > ring_char_0 > ring_11004092258visors > ring_1 > ring > real_normed_algebra > power > plus > ordered_semiring > ordered_ring > ordered_ab_group_add > ordere779506340up_add > ordere453448008miring > ordere236663937imp_le > ordere223160158up_add > ordere216010020id_add > ordere1490568538miring > order > one > number_semiring > number_ring > number > no_zero_divisors > mult_zero > monoid_mult > monoid_add > linordered_semiring > linordered_semidom > linordered_ring > linordered_idom > linorder > linord893533164strict > linord626643107strict > linord581940658strict > linord219039673up_add > linord20386208strict > linord1278240602ring_1 > idom > hBOOL > group_add > dvd > comm_semiring_1 > comm_semiring > comm_ring_1 > comm_ring > comm_monoid_mult > comm_monoid_add > cancel_semigroup_add > cancel146912293up_add > ab_semigroup_mult > ab_semigroup_add > ab_group_add > combs > combc > combb > product_Pair > hAPP > zcong > wset > times_times > ti > standardRes > product_prod > power_power > plus_plus > number_number_of > multInv > minus_minus > member > legendre > inv > fun > div_mod > collect > #nlpp > zfact > zero_zero > undefined > twoSqu1929807760sum2sq > sr > quadRes > ord_less_eq > ord_less > one_one > dvd_dvd > d22set > bit1 > bit0 > zprime > twoSqu658283162sum2sq > t > s1 > s > real > pls > nat > min > m > int > fconj > bool > #skF_32 > #skF_26 > #skF_24 > #skF_35 > #skF_38 > #skF_21 > #skF_41 > #skF_17 > #skF_31 > #skF_33 > #skF_4 > #skF_6 > #skF_30 > #skF_27 > #skF_18 > #skF_22 > #skF_12 > #skF_36 > #skF_13 > #skF_39 > #skF_5 > #skF_19 > #skF_2 > #skF_10 > #skF_3 > #skF_1 > #skF_37 > #skF_8 > #skF_11 > #skF_43 > #skF_34 > #skF_15 > #skF_23 > #skF_14 > #skF_40 > #skF_25 > #skF_7 > #skF_29 > #skF_9 > #skF_28 > #skF_42 > #skF_20 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(fconj,type,
fconj: $i ).
tff(minus_minus,type,
minus_minus: ( $i * $i ) > $i ).
tff(linord1278240602ring_1,type,
linord1278240602ring_1: $i > $o ).
tff(hAPP,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(ordered_semiring,type,
ordered_semiring: $i > $o ).
tff(zcong,type,
zcong: ( $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i * $i ) > $i ).
tff(semiring_1,type,
semiring_1: $i > $o ).
tff(ab_semigroup_mult,type,
ab_semigroup_mult: $i > $o ).
tff(power,type,
power: $i > $o ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff(semiri456707255roduct,type,
semiri456707255roduct: $i > $o ).
tff(comm_semiring,type,
comm_semiring: $i > $o ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff(m,type,
m: $i ).
tff(ord_less_eq,type,
ord_less_eq: $i > $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff('#skF_41',type,
'#skF_41': ( $i * $i ) > $i ).
tff(s1,type,
s1: $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i ) > $i ).
tff(group_add,type,
group_add: $i > $o ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff(idom,type,
idom: $i > $o ).
tff(ring_n68954251visors,type,
ring_n68954251visors: $i > $o ).
tff(linord581940658strict,type,
linord581940658strict: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(min,type,
min: $i ).
tff(one_one,type,
one_one: $i > $i ).
tff(ring_1,type,
ring_1: $i > $o ).
tff(combs,type,
combs: ( $i * $i * $i * $i * $i ) > $i ).
tff(number,type,
number: $i > $o ).
tff(member,type,
member: ( $i * $i ) > $i ).
tff(t,type,
t: $i ).
tff(pls,type,
pls: $i ).
tff(collect,type,
collect: ( $i * $i ) > $i ).
tff(monoid_add,type,
monoid_add: $i > $o ).
tff(linordered_ring,type,
linordered_ring: $i > $o ).
tff(ring_11004092258visors,type,
ring_11004092258visors: $i > $o ).
tff(sr,type,
sr: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i ) > $i ).
tff(linordered_semidom,type,
linordered_semidom: $i > $o ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i ) > $i ).
tff(ab_semigroup_add,type,
ab_semigroup_add: $i > $o ).
tff(d22set,type,
d22set: $i > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(twoSqu658283162sum2sq,type,
twoSqu658283162sum2sq: $i ).
tff(bit0,type,
bit0: $i > $i ).
tff(standardRes,type,
standardRes: ( $i * $i ) > $i ).
tff(no_zero_divisors,type,
no_zero_divisors: $i > $o ).
tff(s,type,
s: $i ).
tff(linord626643107strict,type,
linord626643107strict: $i > $o ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(zero_neq_one,type,
zero_neq_one: $i > $o ).
tff(bool,type,
bool: $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i ) > $i ).
tff(number_ring,type,
number_ring: $i > $o ).
tff(comm_monoid_mult,type,
comm_monoid_mult: $i > $o ).
tff(comm_ring_1,type,
comm_ring_1: $i > $o ).
tff(linord219039673up_add,type,
linord219039673up_add: $i > $o ).
tff(wset,type,
wset: ( $i * $i ) > $i ).
tff(nat,type,
nat: $i ).
tff(fun,type,
fun: ( $i * $i ) > $i ).
tff(ordere779506340up_add,type,
ordere779506340up_add: $i > $o ).
tff(twoSqu1929807760sum2sq,type,
twoSqu1929807760sum2sq: $i > $i ).
tff(quadRes,type,
quadRes: $i > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(linordered_semiring,type,
linordered_semiring: $i > $o ).
tff(dvd_dvd,type,
dvd_dvd: $i > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(ordered_ring,type,
ordered_ring: $i > $o ).
tff(ordere1490568538miring,type,
ordere1490568538miring: $i > $o ).
tff(ordere236663937imp_le,type,
ordere236663937imp_le: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(product_Pair,type,
product_Pair: ( $i * $i * $i * $i ) > $i ).
tff(cancel146912293up_add,type,
cancel146912293up_add: $i > $o ).
tff('#skF_10',type,
'#skF_10': ( $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(semiring_div,type,
semiring_div: $i > $o ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i ) > $i ).
tff(plus_plus,type,
plus_plus: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(comm_monoid_add,type,
comm_monoid_add: $i > $o ).
tff(combb,type,
combb: ( $i * $i * $i * $i * $i ) > $i ).
tff(ordere223160158up_add,type,
ordere223160158up_add: $i > $o ).
tff(comm_semiring_1,type,
comm_semiring_1: $i > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff(zprime,type,
zprime: $i ).
tff(comm_ring,type,
comm_ring: $i > $o ).
tff('#skF_43',type,
'#skF_43': ( $i * $i * $i ) > $i ).
tff(ordered_ab_group_add,type,
ordered_ab_group_add: $i > $o ).
tff(ring,type,
ring: $i > $o ).
tff(int,type,
int: $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i ) > $i ).
tff(multInv,type,
multInv: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff(zfact,type,
zfact: $i > $i ).
tff(ti,type,
ti: ( $i * $i ) > $i ).
tff(semiring_0,type,
semiring_0: $i > $o ).
tff(div_mod,type,
div_mod: ( $i * $i ) > $i ).
tff(times_times,type,
times_times: ( $i * $i ) > $i ).
tff(linord20386208strict,type,
linord20386208strict: $i > $o ).
tff(ring_div,type,
ring_div: $i > $o ).
tff(combc,type,
combc: ( $i * $i * $i * $i * $i ) > $i ).
tff(linordered_idom,type,
linordered_idom: $i > $o ).
tff(bit1,type,
bit1: $i > $i ).
tff(ab_group_add,type,
ab_group_add: $i > $o ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(ordere216010020id_add,type,
ordere216010020id_add: $i > $o ).
tff(ordere453448008miring,type,
ordere453448008miring: $i > $o ).
tff(hBOOL,type,
hBOOL: $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(cancel_semigroup_add,type,
cancel_semigroup_add: $i > $o ).
tff(ring_char_0,type,
ring_char_0: $i > $o ).
tff(power_power,type,
power_power: ( $i * $i ) > $i ).
tff(zero_zero,type,
zero_zero: $i > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i ) > $i ).
tff(plus,type,
plus: $i > $o ).
tff(number_semiring,type,
number_semiring: $i > $o ).
tff(monoid_mult,type,
monoid_mult: $i > $o ).
tff(ord_less,type,
ord_less: $i > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(real,type,
real: $i ).
tff(one,type,
one: $i > $o ).
tff('#skF_29',type,
'#skF_29': ( $i * $i ) > $i ).
tff(real_normed_algebra,type,
real_normed_algebra: $i > $o ).
tff(inv,type,
inv: ( $i * $i ) > $i ).
tff(semiring,type,
semiring: $i > $o ).
tff(order,type,
order: $i > $o ).
tff(dvd,type,
dvd: $i > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i ) > $i ).
tff(zero,type,
zero: $i > $o ).
tff(linord893533164strict,type,
linord893533164strict: $i > $o ).
tff('#skF_42',type,
'#skF_42': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(linorder,type,
linorder: $i > $o ).
tff(f_378,axiom,
! [Z_1,W] : ( hAPP(int,int,times_times(int,Z_1),W) = hAPP(int,int,times_times(int,W),Z_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
tff(f_728,axiom,
! [Z_1,W] : ( hAPP(int,int,plus_plus(int,Z_1),W) = hAPP(int,int,plus_plus(int,W),Z_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zadd__commute) ).
tff(f_4645,axiom,
twoSqu1929807760sum2sq(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/sandbox/benchmark/theBenchmark.p',fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
tff(f_294,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/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
tff(f_3049,axiom,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
tff(f_850,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Pls__def) ).
tff(f_6448,axiom,
! [X_a,X_c,X_b,P,Q,R] : ( hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f_6471,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_568,axiom,
! [W] : ( hAPP(int,int,times_times(int,pls),W) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
tff(f_293,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,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/sandbox/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_256,plain,
! [Z_1_221,W_222] : ( hAPP(int,int,times_times(int,Z_1_221),W_222) = hAPP(int,int,times_times(int,W_222),Z_1_221) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_496,plain,
! [Z_1_409,W_410] : ( hAPP(int,int,plus_plus(int,Z_1_409),W_410) = hAPP(int,int,plus_plus(int,W_410),Z_1_409) ),
inference(cnfTransformation,[status(thm)],[f_728]) ).
tff(c_2450,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) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(cnfTransformation,[status(thm)],[f_4645]) ).
tff(c_4571,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) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(demodulation,[status(thm),theory(equality)],[c_496,c_2450]) ).
tff(c_4705,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))))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_256,c_4571]) ).
tff(c_204,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_294]) ).
tff(c_4836,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(demodulation,[status(thm),theory(equality)],[c_4705,c_256,c_256,c_496,c_496,c_204]) ).
tff(c_1477,plain,
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,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),
inference(cnfTransformation,[status(thm)],[f_3049]) ).
tff(c_4566,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = 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_496,c_1477]) ).
tff(c_562,plain,
zero_zero(int) = pls,
inference(cnfTransformation,[status(thm)],[f_850]) ).
tff(c_3503,plain,
! [X_a_3716,X_c_3717,X_b_3718,P_3719,Q_3720,R_3721] : ( hAPP(X_b_3718,X_c_3717,hAPP(X_a_3716,fun(X_b_3718,X_c_3717),P_3719,R_3721),Q_3720) = hAPP(X_a_3716,X_c_3717,combc(X_a_3716,X_b_3718,X_c_3717,P_3719,Q_3720),R_3721) ),
inference(cnfTransformation,[status(thm)],[f_6448]) ).
tff(c_3513,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_6471]) ).
tff(c_3517,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_3503,c_3513]) ).
tff(c_4076,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)))),
inference(demodulation,[status(thm),theory(equality)],[c_1477,c_3517]) ).
tff(c_4392,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)))),
inference(demodulation,[status(thm),theory(equality)],[c_562,c_4076]) ).
tff(c_4600,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),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_4566,c_4392]) ).
tff(c_4838,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))),
inference(demodulation,[status(thm),theory(equality)],[c_4836,c_4600]) ).
tff(c_380,plain,
! [W_321] : ( hAPP(int,int,times_times(int,pls),W_321) = pls ),
inference(cnfTransformation,[status(thm)],[f_568]) ).
tff(c_202,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_293]) ).
tff(c_4842,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))),
inference(demodulation,[status(thm),theory(equality)],[c_4705,c_256,c_256,c_380,c_256,c_256,c_3503,c_496,c_496,c_562,c_202]) ).
tff(c_4843,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4838,c_4842]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM924+7 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % 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 : n013.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 14:29:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 24.09/9.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.09/9.53
% 24.09/9.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.09/9.56
% 24.09/9.56 Inference rules
% 24.09/9.56 ----------------------
% 24.09/9.56 #Ref : 0
% 24.09/9.56 #Sup : 0
% 24.09/9.56 #Fact : 0
% 24.09/9.56 #Define : 0
% 24.09/9.56 #Split : 0
% 24.09/9.56 #Chain : 0
% 24.09/9.56 #Close : 0
% 24.09/9.56
% 24.09/9.56 Ordering : KBO
% 24.09/9.56
% 24.09/9.56 Simplification rules
% 24.09/9.56 ----------------------
% 24.09/9.56 #Subsume : 1601
% 24.09/9.56 #Demod : 2577
% 24.09/9.56 #Tautology : 149
% 24.09/9.56 #SimpNegUnit : 1
% 24.09/9.56 #BackRed : 0
% 24.09/9.56
% 24.09/9.56 #Partial instantiations: 0
% 24.09/9.56 #Strategies tried : 1
% 24.09/9.56
% 24.09/9.56 Timing (in seconds)
% 24.09/9.56 ----------------------
% 24.09/9.57 Preprocessing : 2.94
% 24.09/9.57 Parsing : 1.64
% 24.09/9.57 CNF conversion : 0.23
% 24.09/9.57 Main loop : 5.48
% 24.09/9.57 Inferencing : 0.00
% 24.09/9.57 Reduction : 3.86
% 24.09/9.57 Demodulation : 3.05
% 24.09/9.57 BG Simplification : 0.26
% 24.09/9.57 Subsumption : 1.07
% 24.09/9.57 Abstraction : 0.12
% 24.09/9.57 MUC search : 0.00
% 24.09/9.57 Cooper : 0.00
% 24.09/9.57 Total : 8.47
% 24.09/9.57 Index Insertion : 0.00
% 24.09/9.57 Index Deletion : 0.00
% 24.09/9.57 Index Matching : 0.00
% 24.09/9.57 BG Taut test : 0.00
%------------------------------------------------------------------------------