TSTP Solution File: NUM925+7 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM925+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 : n022.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 10:41:30 EDT 2023
% Result : Theorem 0.68s 1.49s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 162
% Syntax : Number of formulae : 210 ( 62 unt; 145 typ; 0 def)
% Number of atoms : 71 ( 52 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 166 ( 114 >; 52 *; 0 +; 0 <<)
% Number of predicates : 61 ( 59 usr; 1 prp; 0-2 aty)
% Number of functors : 86 ( 86 usr; 31 con; 0-4 aty)
% Number of variables : 41 ( 1 sgn; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ordere142940540dd_abs: $i > $o ).
tff(decl_23,type,
ti: ( $i * $i ) > $i ).
tff(decl_24,type,
abs_abs: ( $i * $i ) > $i ).
tff(decl_25,type,
group_add: $i > $o ).
tff(decl_26,type,
minus_minus: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
nat: $i ).
tff(decl_28,type,
one: $i > $o ).
tff(decl_29,type,
one_one: $i > $i ).
tff(decl_30,type,
monoid_add: $i > $o ).
tff(decl_31,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
ab_semigroup_add: $i > $o ).
tff(decl_33,type,
cancel_semigroup_add: $i > $o ).
tff(decl_34,type,
dvd: $i > $o ).
tff(decl_35,type,
times_times: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
power: $i > $o ).
tff(decl_37,type,
semiring: $i > $o ).
tff(decl_38,type,
no_zero_divisors: $i > $o ).
tff(decl_39,type,
mult_zero: $i > $o ).
tff(decl_40,type,
ab_semigroup_mult: $i > $o ).
tff(decl_41,type,
zero: $i > $o ).
tff(decl_42,type,
zero_zero: $i > $i ).
tff(decl_43,type,
undefined: $i > $i ).
tff(decl_44,type,
bool: $i ).
tff(decl_45,type,
if: ( $i * $i * $i * $i ) > $i ).
tff(decl_46,type,
int: $i ).
tff(decl_47,type,
zcong: ( $i * $i ) > $i ).
tff(decl_48,type,
fun: ( $i * $i ) > $i ).
tff(decl_49,type,
zprime: $i ).
tff(decl_50,type,
bit0: $i > $i ).
tff(decl_51,type,
bit1: $i > $i ).
tff(decl_52,type,
min: $i ).
tff(decl_53,type,
pls: $i ).
tff(decl_54,type,
nat_1: $i > $i ).
tff(decl_55,type,
number: $i > $o ).
tff(decl_56,type,
number_number_of: ( $i * $i ) > $i ).
tff(decl_57,type,
succ: $i > $i ).
tff(decl_58,type,
semiring_1: $i > $o ).
tff(decl_59,type,
semiring_1_of_nat: $i > $i ).
tff(decl_60,type,
order: $i > $o ).
tff(decl_61,type,
ord_less: $i > $i ).
tff(decl_62,type,
ord_less_eq: $i > $i ).
tff(decl_63,type,
power_power: ( $i * $i ) > $i ).
tff(decl_64,type,
legendre: ( $i * $i ) > $i ).
tff(decl_65,type,
quadRes: $i > $i ).
tff(decl_66,type,
dvd_dvd: $i > $i ).
tff(decl_67,type,
twoSqu658283162sum2sq: $i ).
tff(decl_68,type,
fFalse: $i ).
tff(decl_69,type,
fTrue: $i ).
tff(decl_70,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(decl_71,type,
hBOOL: $i > $o ).
tff(decl_72,type,
m: $i ).
tff(decl_73,type,
m1: $i ).
tff(decl_74,type,
n: $i ).
tff(decl_75,type,
s1: $i ).
tff(decl_76,type,
s: $i ).
tff(decl_77,type,
t: $i ).
tff(decl_78,type,
tn: $i ).
tff(decl_79,type,
x: $i ).
tff(decl_80,type,
y: $i ).
tff(decl_81,type,
linordered_idom: $i > $o ).
tff(decl_82,type,
ring_11004092258visors: $i > $o ).
tff(decl_83,type,
number_ring: $i > $o ).
tff(decl_84,type,
number_semiring: $i > $o ).
tff(decl_85,type,
semiring_0: $i > $o ).
tff(decl_86,type,
ring_char_0: $i > $o ).
tff(decl_87,type,
linord219039673up_add: $i > $o ).
tff(decl_88,type,
zero_neq_one: $i > $o ).
tff(decl_89,type,
real: $i ).
tff(decl_90,type,
linordered_semidom: $i > $o ).
tff(decl_91,type,
monoid_mult: $i > $o ).
tff(decl_92,type,
semiring_char_0: $i > $o ).
tff(decl_93,type,
comm_semiring_1: $i > $o ).
tff(decl_94,type,
ordere216010020id_add: $i > $o ).
tff(decl_95,type,
cancel146912293up_add: $i > $o ).
tff(decl_96,type,
semiri456707255roduct: $i > $o ).
tff(decl_97,type,
comm_monoid_add: $i > $o ).
tff(decl_98,type,
ordere236663937imp_le: $i > $o ).
tff(decl_99,type,
ordere223160158up_add: $i > $o ).
tff(decl_100,type,
ordered_ab_group_add: $i > $o ).
tff(decl_101,type,
ab_group_add: $i > $o ).
tff(decl_102,type,
ring: $i > $o ).
tff(decl_103,type,
ordere453448008miring: $i > $o ).
tff(decl_104,type,
ordered_ring: $i > $o ).
tff(decl_105,type,
ordered_semiring: $i > $o ).
tff(decl_106,type,
ordere1490568538miring: $i > $o ).
tff(decl_107,type,
linord581940658strict: $i > $o ).
tff(decl_108,type,
linordered_ring: $i > $o ).
tff(decl_109,type,
ring_1: $i > $o ).
tff(decl_110,type,
linord20386208strict: $i > $o ).
tff(decl_111,type,
linordered_semiring: $i > $o ).
tff(decl_112,type,
ring_n68954251visors: $i > $o ).
tff(decl_113,type,
comm_semiring: $i > $o ).
tff(decl_114,type,
comm_monoid_mult: $i > $o ).
tff(decl_115,type,
ordere779506340up_add: $i > $o ).
tff(decl_116,type,
linord1278240602ring_1: $i > $o ).
tff(decl_117,type,
linord626643107strict: $i > $o ).
tff(decl_118,type,
linord893533164strict: $i > $o ).
tff(decl_119,type,
linorder: $i > $o ).
tff(decl_120,type,
comm_ring_1: $i > $o ).
tff(decl_121,type,
idom: $i > $o ).
tff(decl_122,type,
comm_ring: $i > $o ).
tff(decl_123,type,
ordered_ring_abs: $i > $o ).
tff(decl_124,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_125,type,
esk2_1: $i > $i ).
tff(decl_126,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_127,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_129,type,
esk6_1: $i > $i ).
tff(decl_130,type,
esk7_1: $i > $i ).
tff(decl_131,type,
esk8_1: $i > $i ).
tff(decl_132,type,
esk9_1: $i > $i ).
tff(decl_133,type,
esk10_1: $i > $i ).
tff(decl_134,type,
esk11_1: $i > $i ).
tff(decl_135,type,
esk12_1: $i > $i ).
tff(decl_136,type,
esk13_1: $i > $i ).
tff(decl_137,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_139,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk18_0: $i ).
tff(decl_142,type,
esk19_0: $i ).
tff(decl_143,type,
esk20_0: $i ).
tff(decl_144,type,
esk21_0: $i ).
tff(decl_145,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_146,type,
esk23_0: $i ).
tff(decl_147,type,
esk24_0: $i ).
tff(decl_148,type,
esk25_0: $i ).
tff(decl_149,type,
esk26_0: $i ).
tff(decl_150,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_151,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_152,type,
esk29_1: $i > $i ).
tff(decl_153,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk32_0: $i ).
tff(decl_156,type,
esk33_0: $i ).
tff(decl_157,type,
esk34_0: $i ).
tff(decl_158,type,
esk35_0: $i ).
tff(decl_159,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk37_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_163,type,
esk40_3: ( $i * $i * $i ) > $i ).
tff(decl_164,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_165,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_166,type,
esk43_3: ( $i * $i * $i ) > $i ).
fof(fact_514_succ__Bit0,axiom,
! [X20] : succ(bit0(X20)) = bit1(X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_succ__Bit0) ).
fof(fact_78_Bit0__def,axiom,
! [X20] : bit0(X20) = plus_plus(int,X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
fof(fact_777_diff__bin__simps_I2_J,axiom,
! [X20] : minus_minus(int,X20,min) = succ(X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_diff__bin__simps_I2_J) ).
fof(fact_79_zadd__0__right,axiom,
! [X16] : plus_plus(int,X16,zero_zero(int)) = ti(int,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zadd__0__right) ).
fof(fact_120_number__of__is__id,axiom,
! [X20] : number_number_of(int,X20) = ti(int,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_number__of__is__id) ).
fof(conj_0,conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_29_nat__1__add__1,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_29_nat__1__add__1) ).
fof(fact_72_Bit0__Pls,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
fof(fact_645_diff__bin__simps_I3_J,axiom,
! [X30] : minus_minus(int,pls,bit0(X30)) = bit0(minus_minus(int,pls,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_diff__bin__simps_I3_J) ).
fof(fact_37_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(tsy_c_Int_Osucc_res,axiom,
! [X1] : ti(int,succ(X1)) = succ(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Osucc_res) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(fact_47_zadd__commute,axiom,
! [X16,X8] : plus_plus(int,X16,X8) = plus_plus(int,X8,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(fact_179_zero__less__power,axiom,
! [X2] :
( linordered_semidom(X2)
=> ! [X15,X31] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),X31))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),hAPP(nat,X2,power_power(X2,X31),X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_zero__less__power) ).
fof(fact_32_rel__simps_I2_J,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
fof(arity_Int_Oint___Rings_Olinordered__semidom,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
fof(c_0_17,plain,
! [X1582] : succ(bit0(X1582)) = bit1(X1582),
inference(variable_rename,[status(thm)],[fact_514_succ__Bit0]) ).
fof(c_0_18,plain,
! [X392] : bit0(X392) = plus_plus(int,X392,X392),
inference(variable_rename,[status(thm)],[fact_78_Bit0__def]) ).
fof(c_0_19,plain,
! [X2159] : minus_minus(int,X2159,min) = succ(X2159),
inference(variable_rename,[status(thm)],[fact_777_diff__bin__simps_I2_J]) ).
fof(c_0_20,plain,
! [X393] : plus_plus(int,X393,zero_zero(int)) = ti(int,X393),
inference(variable_rename,[status(thm)],[fact_79_zadd__0__right]) ).
fof(c_0_21,plain,
! [X464] : number_number_of(int,X464) = ti(int,X464),
inference(variable_rename,[status(thm)],[fact_120_number__of__is__id]) ).
fof(c_0_22,negated_conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_23,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_29_nat__1__add__1]) ).
cnf(c_0_24,plain,
succ(bit0(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
bit0(X1) = plus_plus(int,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
minus_minus(int,X1,min) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
bit0(pls) = pls,
inference(split_conjunct,[status(thm)],[fact_72_Bit0__Pls]) ).
fof(c_0_28,plain,
! [X1868] : minus_minus(int,pls,bit0(X1868)) = bit0(minus_minus(int,pls,X1868)),
inference(variable_rename,[status(thm)],[fact_645_diff__bin__simps_I3_J]) ).
cnf(c_0_29,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_37_one__is__num__one]) ).
fof(c_0_30,plain,
! [X222] : ti(int,succ(X222)) = succ(X222),
inference(variable_rename,[status(thm)],[tsy_c_Int_Osucc_res]) ).
cnf(c_0_31,plain,
plus_plus(int,X1,zero_zero(int)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_73_Pls__def]) ).
cnf(c_0_33,plain,
number_number_of(int,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,negated_conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_25]),c_0_26]),c_0_26]) ).
cnf(c_0_36,plain,
plus_plus(int,pls,pls) = pls,
inference(rw,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_37,plain,
minus_minus(int,pls,bit0(X1)) = bit0(minus_minus(int,pls,X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
one_one(int) = number_number_of(int,minus_minus(int,plus_plus(int,pls,pls),min)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_24]),c_0_25]),c_0_26]) ).
fof(c_0_39,plain,
! [X353,X354] : plus_plus(int,X353,X354) = plus_plus(int,X354,X353),
inference(variable_rename,[status(thm)],[fact_47_zadd__commute]) ).
cnf(c_0_40,plain,
ti(int,succ(X1)) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
number_number_of(int,X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min)))) = zero_zero(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_24]),c_0_25]),c_0_25]),c_0_26]),c_0_26]) ).
cnf(c_0_43,plain,
number_number_of(nat,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_44,plain,
minus_minus(int,pls,plus_plus(int,X1,X1)) = plus_plus(int,minus_minus(int,pls,X1),minus_minus(int,pls,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_25]),c_0_25]) ).
cnf(c_0_45,plain,
number_number_of(int,minus_minus(int,pls,min)) = one_one(int),
inference(rw,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_46,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
ti(int,minus_minus(int,X1,min)) = minus_minus(int,X1,min),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_26]),c_0_26]) ).
cnf(c_0_48,plain,
ti(int,X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),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)],[c_0_42,c_0_36]),c_0_36]),c_0_43]),c_0_32]) ).
cnf(c_0_50,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,minus_minus(int,pls,plus_plus(int,min,min))),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
plus_plus(int,pls,minus_minus(int,pls,min)) = one_one(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_41]),c_0_46]) ).
cnf(c_0_52,plain,
plus_plus(int,pls,minus_minus(int,X1,min)) = minus_minus(int,X1,min),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_46]) ).
cnf(c_0_53,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
fof(c_0_54,plain,
! [X591,X592,X593] :
( ~ linordered_semidom(X591)
| ~ hBOOL(hAPP(X591,bool,hAPP(X591,fun(X591,bool),ord_less(X591),zero_zero(X591)),X593))
| hBOOL(hAPP(X591,bool,hAPP(X591,fun(X591,bool),ord_less(X591),zero_zero(X591)),hAPP(nat,X591,power_power(X591,X593),X592))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_179_zero__less__power])])]) ).
cnf(c_0_55,negated_conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,minus_minus(int,pls,plus_plus(int,min,min)))) = pls,
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
one_one(int) = minus_minus(int,pls,min),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(rw,[status(thm)],[c_0_53,c_0_32]) ).
fof(c_0_58,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(fof_simplification,[status(thm)],[fact_32_rel__simps_I2_J]) ).
cnf(c_0_59,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,negated_conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,minus_minus(int,pls,min),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,minus_minus(int,pls,plus_plus(int,min,min)))) = pls,
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
linordered_semidom(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semidom]) ).
cnf(c_0_62,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),plus_plus(int,minus_minus(int,pls,min),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(rw,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_63,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_32]),c_0_61]),c_0_32]),c_0_62])]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n022.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 : Fri Aug 25 14:51:55 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.68/1.49 % Version : CSE_E---1.5
% 0.68/1.49 % Problem : theBenchmark.p
% 0.68/1.49 % Proof found
% 0.68/1.49 % SZS status Theorem for theBenchmark.p
% 0.68/1.49 % SZS output start Proof
% See solution above
% 0.68/1.50 % Total time : 0.846000 s
% 0.68/1.50 % SZS output end Proof
% 0.68/1.50 % Total time : 0.898000 s
%------------------------------------------------------------------------------