TSTP Solution File: NUM924+7 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM924+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 : Thu Aug 31 10:41:26 EDT 2023
% Result : Theorem 0.67s 1.06s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 165
% Syntax : Number of formulae : 209 ( 61 unt; 148 typ; 0 def)
% Number of atoms : 61 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 218 ( 131 >; 87 *; 0 +; 0 <<)
% Number of predicates : 63 ( 61 usr; 1 prp; 0-3 aty)
% Number of functors : 87 ( 87 usr; 17 con; 0-5 aty)
% Number of variables : 46 ( 1 sgn; 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
fun: ( $i * $i ) > $i ).
tff(decl_23,type,
ti: ( $i * $i ) > $i ).
tff(decl_24,type,
combb: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_25,type,
combc: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_26,type,
combs: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_27,type,
semiring_div: $i > $o ).
tff(decl_28,type,
div_mod: ( $i * $i ) > $i ).
tff(decl_29,type,
group_add: $i > $o ).
tff(decl_30,type,
minus_minus: ( $i * $i ) > $i ).
tff(decl_31,type,
nat: $i ).
tff(decl_32,type,
one: $i > $o ).
tff(decl_33,type,
one_one: $i > $i ).
tff(decl_34,type,
plus: $i > $o ).
tff(decl_35,type,
linorder: $i > $o ).
tff(decl_36,type,
dvd: $i > $o ).
tff(decl_37,type,
plus_plus: ( $i * $i ) > $i ).
tff(decl_38,type,
monoid_add: $i > $o ).
tff(decl_39,type,
cancel_semigroup_add: $i > $o ).
tff(decl_40,type,
ab_semigroup_add: $i > $o ).
tff(decl_41,type,
ab_semigroup_mult: $i > $o ).
tff(decl_42,type,
times_times: ( $i * $i ) > $i ).
tff(decl_43,type,
power: $i > $o ).
tff(decl_44,type,
semiring: $i > $o ).
tff(decl_45,type,
mult_zero: $i > $o ).
tff(decl_46,type,
no_zero_divisors: $i > $o ).
tff(decl_47,type,
zero: $i > $o ).
tff(decl_48,type,
zero_zero: $i > $i ).
tff(decl_49,type,
undefined: $i > $i ).
tff(decl_50,type,
int: $i ).
tff(decl_51,type,
multInv: ( $i * $i ) > $i ).
tff(decl_52,type,
d22set: $i > $i ).
tff(decl_53,type,
bool: $i ).
tff(decl_54,type,
zfact: $i > $i ).
tff(decl_55,type,
zcong: ( $i * $i ) > $i ).
tff(decl_56,type,
zprime: $i ).
tff(decl_57,type,
bit0: $i > $i ).
tff(decl_58,type,
bit1: $i > $i ).
tff(decl_59,type,
min: $i ).
tff(decl_60,type,
pls: $i ).
tff(decl_61,type,
number: $i > $o ).
tff(decl_62,type,
number_number_of: ( $i * $i ) > $i ).
tff(decl_63,type,
order: $i > $o ).
tff(decl_64,type,
ord_less: $i > $i ).
tff(decl_65,type,
ord_less_eq: $i > $i ).
tff(decl_66,type,
power_power: ( $i * $i ) > $i ).
tff(decl_67,type,
product_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
product_prod: ( $i * $i ) > $i ).
tff(decl_69,type,
legendre: ( $i * $i ) > $i ).
tff(decl_70,type,
quadRes: $i > $i ).
tff(decl_71,type,
sr: $i > $i ).
tff(decl_72,type,
standardRes: ( $i * $i ) > $i ).
tff(decl_73,type,
dvd_dvd: $i > $i ).
tff(decl_74,type,
collect: ( $i * $i ) > $i ).
tff(decl_75,type,
twoSqu658283162sum2sq: $i ).
tff(decl_76,type,
twoSqu1929807760sum2sq: $i > $i ).
tff(decl_77,type,
inv: ( $i * $i ) > $i ).
tff(decl_78,type,
wset: ( $i * $i ) > $i ).
tff(decl_79,type,
fconj: $i ).
tff(decl_80,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(decl_81,type,
hBOOL: $i > $o ).
tff(decl_82,type,
member: ( $i * $i ) > $i ).
tff(decl_83,type,
m: $i ).
tff(decl_84,type,
s1: $i ).
tff(decl_85,type,
s: $i ).
tff(decl_86,type,
t: $i ).
tff(decl_87,type,
linordered_idom: $i > $o ).
tff(decl_88,type,
semiring_1: $i > $o ).
tff(decl_89,type,
ring_11004092258visors: $i > $o ).
tff(decl_90,type,
number_ring: $i > $o ).
tff(decl_91,type,
number_semiring: $i > $o ).
tff(decl_92,type,
linord581940658strict: $i > $o ).
tff(decl_93,type,
linordered_ring: $i > $o ).
tff(decl_94,type,
ring_char_0: $i > $o ).
tff(decl_95,type,
linordered_semidom: $i > $o ).
tff(decl_96,type,
linord219039673up_add: $i > $o ).
tff(decl_97,type,
monoid_mult: $i > $o ).
tff(decl_98,type,
comm_semiring_1: $i > $o ).
tff(decl_99,type,
semiri456707255roduct: $i > $o ).
tff(decl_100,type,
zero_neq_one: $i > $o ).
tff(decl_101,type,
semiring_0: $i > $o ).
tff(decl_102,type,
linord626643107strict: $i > $o ).
tff(decl_103,type,
ring_n68954251visors: $i > $o ).
tff(decl_104,type,
comm_semiring: $i > $o ).
tff(decl_105,type,
comm_monoid_mult: $i > $o ).
tff(decl_106,type,
ordere453448008miring: $i > $o ).
tff(decl_107,type,
ordered_ring: $i > $o ).
tff(decl_108,type,
ordered_semiring: $i > $o ).
tff(decl_109,type,
ordere1490568538miring: $i > $o ).
tff(decl_110,type,
linord893533164strict: $i > $o ).
tff(decl_111,type,
linord20386208strict: $i > $o ).
tff(decl_112,type,
idom: $i > $o ).
tff(decl_113,type,
linordered_semiring: $i > $o ).
tff(decl_114,type,
real: $i ).
tff(decl_115,type,
linord1278240602ring_1: $i > $o ).
tff(decl_116,type,
comm_ring_1: $i > $o ).
tff(decl_117,type,
ring: $i > $o ).
tff(decl_118,type,
ab_group_add: $i > $o ).
tff(decl_119,type,
ring_1: $i > $o ).
tff(decl_120,type,
comm_ring: $i > $o ).
tff(decl_121,type,
ordere216010020id_add: $i > $o ).
tff(decl_122,type,
cancel146912293up_add: $i > $o ).
tff(decl_123,type,
comm_monoid_add: $i > $o ).
tff(decl_124,type,
ordere236663937imp_le: $i > $o ).
tff(decl_125,type,
ordere779506340up_add: $i > $o ).
tff(decl_126,type,
ordere223160158up_add: $i > $o ).
tff(decl_127,type,
ordered_ab_group_add: $i > $o ).
tff(decl_128,type,
real_normed_algebra: $i > $o ).
tff(decl_129,type,
ring_div: $i > $o ).
tff(decl_130,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_131,type,
esk1_0: $i ).
tff(decl_132,type,
esk2_0: $i ).
tff(decl_133,type,
esk3_0: $i ).
tff(decl_134,type,
esk4_1: $i > $i ).
tff(decl_135,type,
esk5_0: $i ).
tff(decl_136,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_137,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_140,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_142,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_143,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk14_1: $i > $i ).
tff(decl_145,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_146,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_147,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_148,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_149,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk20_1: $i > $i ).
tff(decl_151,type,
esk21_1: $i > $i ).
tff(decl_152,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_156,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_157,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_158,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_159,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_165,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_166,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_167,type,
esk37_3: ( $i * $i * $i ) > $i ).
tff(decl_168,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_169,type,
esk39_3: ( $i * $i * $i ) > $i ).
fof(fact_132_Bit0__def,axiom,
! [X15] : bit0(X15) = hAPP(int,int,plus_plus(int,X15),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Bit0__def) ).
fof(fact_130_add__Pls,axiom,
! [X15] : hAPP(int,int,plus_plus(int,pls),X15) = ti(int,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_add__Pls) ).
fof(fact_22_number__of__is__id,axiom,
! [X15] : number_number_of(int,X15) = ti(int,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(tsy_c_Int_OBit1_res,hypothesis,
! [X4] : ti(int,bit1(X4)) = bit1(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
fof(fact_161_add__Bit1__Bit0,axiom,
! [X15,X32] : hAPP(int,int,plus_plus(int,bit1(X15)),bit0(X32)) = bit1(hAPP(int,int,plus_plus(int,X15),X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_add__Bit1__Bit0) ).
fof(conj_0,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) ).
fof(fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,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) ).
fof(fact_61_nat__1__add__1,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_61_nat__1__add__1) ).
fof(fact_98_zadd__commute,axiom,
! [X16,X12] : hAPP(int,int,plus_plus(int,X16),X12) = hAPP(int,int,plus_plus(int,X12),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zadd__commute) ).
fof(fact_3_t,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) ).
fof(fact_96_zadd__assoc,axiom,
! [X19,X20,X21] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X19),X20)),X21) = hAPP(int,int,plus_plus(int,X19),hAPP(int,int,plus_plus(int,X20),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_zadd__assoc) ).
fof(fact_23_zmult__commute,axiom,
! [X16,X12] : hAPP(int,int,times_times(int,X16),X12) = hAPP(int,int,times_times(int,X12),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(tsy_c_Int_OMin_res,axiom,
ti(int,min) = min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OMin_res) ).
fof(fact_111_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_one__is__num__one) ).
fof(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,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) ).
fof(fact_62_mult__Pls,axiom,
! [X12] : hAPP(int,int,times_times(int,pls),X12) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(fact_122_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Pls__def) ).
fof(c_0_17,plain,
! [X524] : bit0(X524) = hAPP(int,int,plus_plus(int,X524),X524),
inference(variable_rename,[status(thm)],[fact_132_Bit0__def]) ).
fof(c_0_18,plain,
! [X521] : hAPP(int,int,plus_plus(int,pls),X521) = ti(int,X521),
inference(variable_rename,[status(thm)],[fact_130_add__Pls]) ).
fof(c_0_19,plain,
! [X312] : number_number_of(int,X312) = ti(int,X312),
inference(variable_rename,[status(thm)],[fact_22_number__of__is__id]) ).
fof(c_0_20,hypothesis,
! [X220] : ti(int,bit1(X220)) = bit1(X220),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit1_res]) ).
fof(c_0_21,plain,
! [X575,X576] : hAPP(int,int,plus_plus(int,bit1(X575)),bit0(X576)) = bit1(hAPP(int,int,plus_plus(int,X575),X576)),
inference(variable_rename,[status(thm)],[fact_161_add__Bit1__Bit0]) ).
fof(c_0_22,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))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_23,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,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
inference(split_conjunct,[status(thm)],[fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
cnf(c_0_24,plain,
bit0(X1) = hAPP(int,int,plus_plus(int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_61_nat__1__add__1]) ).
cnf(c_0_26,plain,
hAPP(int,int,plus_plus(int,pls),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
number_number_of(int,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_28,plain,
! [X466,X467] : hAPP(int,int,plus_plus(int,X466),X467) = hAPP(int,int,plus_plus(int,X467),X466),
inference(variable_rename,[status(thm)],[fact_98_zadd__commute]) ).
cnf(c_0_29,hypothesis,
ti(int,bit1(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,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,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),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
fof(c_0_31,plain,
! [X460,X461,X462] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X460),X461)),X462) = hAPP(int,int,plus_plus(int,X460),hAPP(int,int,plus_plus(int,X461),X462)),
inference(variable_rename,[status(thm)],[fact_96_zadd__assoc]) ).
cnf(c_0_32,plain,
hAPP(int,int,plus_plus(int,bit1(X1)),bit0(X2)) = bit1(hAPP(int,int,plus_plus(int,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_33,plain,
! [X313,X314] : hAPP(int,int,times_times(int,X313),X314) = hAPP(int,int,times_times(int,X314),X313),
inference(variable_rename,[status(thm)],[fact_23_zmult__commute]) ).
cnf(c_0_34,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))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),one_one(int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_36,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),
inference(rw,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_37,plain,
number_number_of(int,X1) = hAPP(int,int,plus_plus(int,pls),X1),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_38,plain,
hAPP(int,int,plus_plus(int,X1),X2) = hAPP(int,int,plus_plus(int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
ti(int,min) = min,
inference(split_conjunct,[status(thm)],[tsy_c_Int_OMin_res]) ).
cnf(c_0_40,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_111_one__is__num__one]) ).
cnf(c_0_41,hypothesis,
number_number_of(int,bit1(X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_42,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(split_conjunct,[status(thm)],[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]) ).
cnf(c_0_43,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),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,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),m)),one_one(int))),t),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_44,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X1),X2)),X3) = hAPP(int,int,plus_plus(int,X1),hAPP(int,int,plus_plus(int,X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,plain,
hAPP(int,int,plus_plus(int,bit1(X1)),hAPP(int,int,plus_plus(int,X2),X2)) = bit1(hAPP(int,int,plus_plus(int,X1),X2)),
inference(rw,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_46,plain,
hAPP(int,int,times_times(int,X1),X2) = hAPP(int,int,times_times(int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_47,plain,
! [X392] : hAPP(int,int,times_times(int,pls),X392) = pls,
inference(variable_rename,[status(thm)],[fact_62_mult__Pls]) ).
cnf(c_0_48,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,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),one_one(int))),zero_zero(int))),
inference(rw,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_49,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_122_Pls__def]) ).
cnf(c_0_50,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),hAPP(int,int,plus_plus(int,pls),min)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_36]),c_0_38]) ).
cnf(c_0_51,plain,
hAPP(int,int,plus_plus(int,pls),min) = min,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_27]),c_0_37]) ).
cnf(c_0_52,plain,
one_one(int) = bit1(pls),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_53,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,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),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,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),m)),one_one(int))),zero_zero(int)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_24]),c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_54,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(hAPP(int,int,plus_plus(int,pls),bit1(pls)))))))) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_37]),c_0_46]),c_0_38]),c_0_46]),c_0_36]),c_0_38]) ).
cnf(c_0_55,plain,
hAPP(int,int,times_times(int,pls),X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,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),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),one_one(int))),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_36]),c_0_49]) ).
cnf(c_0_57,plain,
hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_58,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_44]),c_0_45]),c_0_37]),c_0_46]),c_0_38]),c_0_46]),c_0_54]),c_0_44]),c_0_45]),c_0_37]),c_0_46]),c_0_38]),c_0_49]),c_0_46]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min)),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_38]),c_0_52]),c_0_57]) ).
cnf(c_0_60,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_52]),c_0_57]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM924+7 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n020.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 09:30:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 start to proof: theBenchmark
% 0.67/1.06 % Version : CSE_E---1.5
% 0.67/1.06 % Problem : theBenchmark.p
% 0.67/1.06 % Proof found
% 0.67/1.06 % SZS status Theorem for theBenchmark.p
% 0.67/1.06 % SZS output start Proof
% See solution above
% 0.67/1.07 % Total time : 0.374000 s
% 0.67/1.07 % SZS output end Proof
% 0.67/1.07 % Total time : 0.463000 s
%------------------------------------------------------------------------------