TSTP Solution File: NUM926+6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM926+6 : 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 : n001.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 10:41:38 EDT 2023
% Result : Theorem 1.04s 1.12s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 96
% Syntax : Number of formulae : 152 ( 48 unt; 76 typ; 0 def)
% Number of atoms : 116 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 35 ~; 31 |; 1 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 58 >; 28 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 1 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 18 con; 0-4 aty)
% Number of variables : 92 ( 8 sgn; 48 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ab_group_add: $i > $o ).
tff(decl_23,type,
ti: ( $i * $i ) > $i ).
tff(decl_24,type,
minus_minus: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
nat: $i ).
tff(decl_26,type,
zero_neq_one: $i > $o ).
tff(decl_27,type,
one_one: $i > $i ).
tff(decl_28,type,
power: $i > $o ).
tff(decl_29,type,
semiring: $i > $o ).
tff(decl_30,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
dvd: $i > $o ).
tff(decl_32,type,
times_times: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
no_zero_divisors: $i > $o ).
tff(decl_34,type,
mult_zero: $i > $o ).
tff(decl_35,type,
zero_zero: $i > $i ).
tff(decl_36,type,
linord219039673up_add: $i > $o ).
tff(decl_37,type,
undefined: $i > $i ).
tff(decl_38,type,
int: $i ).
tff(decl_39,type,
zcong: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
zprime: $i > $o ).
tff(decl_41,type,
bit0: $i > $i ).
tff(decl_42,type,
bit1: $i > $i ).
tff(decl_43,type,
min: $i ).
tff(decl_44,type,
pls: $i ).
tff(decl_45,type,
number: $i > $o ).
tff(decl_46,type,
number_number_of: ( $i * $i ) > $i ).
tff(decl_47,type,
order: $i > $o ).
tff(decl_48,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
power_power: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
product_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_52,type,
product_prod: ( $i * $i ) > $i ).
tff(decl_53,type,
legendre: ( $i * $i ) > $i ).
tff(decl_54,type,
quadRes: ( $i * $i ) > $o ).
tff(decl_55,type,
dvd_dvd: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
twoSqu420862341sum2sq: $i > $o ).
tff(decl_57,type,
twoSqu579703163sum2sq: $i > $i ).
tff(decl_58,type,
m: $i ).
tff(decl_59,type,
s1: $i ).
tff(decl_60,type,
s: $i ).
tff(decl_61,type,
t: $i ).
tff(decl_62,type,
number_semiring: $i > $o ).
tff(decl_63,type,
monoid_mult: $i > $o ).
tff(decl_64,type,
semiring_1: $i > $o ).
tff(decl_65,type,
comm_semiring_1: $i > $o ).
tff(decl_66,type,
number_ring: $i > $o ).
tff(decl_67,type,
linorder: $i > $o ).
tff(decl_68,type,
linordered_idom: $i > $o ).
tff(decl_69,type,
ring_char_0: $i > $o ).
tff(decl_70,type,
semiri456707255roduct: $i > $o ).
tff(decl_71,type,
real: $i ).
tff(decl_72,type,
linordered_semidom: $i > $o ).
tff(decl_73,type,
ring_11004092258visors: $i > $o ).
tff(decl_74,type,
semiring_0: $i > $o ).
tff(decl_75,type,
linord581940658strict: $i > $o ).
tff(decl_76,type,
linordered_ring: $i > $o ).
tff(decl_77,type,
comm_monoid_mult: $i > $o ).
tff(decl_78,type,
ring: $i > $o ).
tff(decl_79,type,
ring_1: $i > $o ).
tff(decl_80,type,
linord626643107strict: $i > $o ).
tff(decl_81,type,
ring_n68954251visors: $i > $o ).
tff(decl_82,type,
comm_semiring: $i > $o ).
tff(decl_83,type,
comm_ring_1: $i > $o ).
tff(decl_84,type,
ordere453448008miring: $i > $o ).
tff(decl_85,type,
bool: $i ).
tff(decl_86,type,
esk1_0: $i ).
tff(decl_87,type,
esk2_0: $i ).
tff(decl_88,type,
esk3_0: $i ).
tff(decl_89,type,
esk4_0: $i ).
tff(decl_90,type,
esk5_0: $i ).
tff(decl_91,type,
esk6_0: $i ).
tff(decl_92,type,
esk7_0: $i ).
tff(decl_93,type,
esk8_1: $i > $i ).
tff(decl_94,type,
esk9_0: $i ).
tff(decl_95,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_97,type,
esk12_2: ( $i * $i ) > $i ).
fof(conj_0,conjecture,
? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_403_zcong__not__zero,axiom,
! [X43,X9] :
( ord_less(int,zero_zero(int),X9)
=> ( ord_less(int,X9,X43)
=> ~ zcong(X9,zero_zero(int),X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_zcong__not__zero) ).
fof(fact_126_Bit0__def,axiom,
! [X19] : bit0(X19) = plus_plus(int,X19,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Bit0__def) ).
fof(fact_151_Bit1__def,axiom,
! [X19] : bit1(X19) = plus_plus(int,plus_plus(int,one_one(int),X19),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Bit1__def) ).
fof(fact_123_add__Pls__right,axiom,
! [X19] : plus_plus(int,X19,pls) = ti(int,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add__Pls__right) ).
fof(fact_86_number__of__is__id,axiom,
! [X19] : number_number_of(int,X19) = ti(int,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( ord_less(int,one_one(int),t)
=> ? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = one_one(int)
=> ? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_89_zadd__commute,axiom,
! [X16,X12] : plus_plus(int,X16,X12) = plus_plus(int,X12,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
fof(fact_87_zadd__assoc,axiom,
! [X40,X41,X42] : plus_plus(int,plus_plus(int,X40,X41),X42) = plus_plus(int,X40,plus_plus(int,X41,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zadd__assoc) ).
fof(fact_88_zadd__left__commute,axiom,
! [X9,X10,X16] : plus_plus(int,X9,plus_plus(int,X10,X16)) = plus_plus(int,X10,plus_plus(int,X9,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zadd__left__commute) ).
fof(fact_85_zmult__commute,axiom,
! [X16,X12] : times_times(int,X16,X12) = times_times(int,X12,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).
fof(fact_202_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Pls__def) ).
fof(fact_330_zcong__1,axiom,
! [X7,X8] : zcong(X7,X8,one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_zcong__1) ).
fof(fact_23_zless__linear,axiom,
! [X9,X10] :
( ord_less(int,X9,X10)
| ti(int,X9) = ti(int,X10)
| ord_less(int,X10,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zless__linear) ).
fof(tsy_c_Groups_Oone__class_Oone_0_res,axiom,
! [X3] :
( zero_neq_one(X3)
=> ti(X3,one_one(X3)) = one_one(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_0_res) ).
fof(fact_241_int__one__le__iff__zero__less,axiom,
! [X17] :
( ord_less_eq(int,one_one(int),X17)
<=> ord_less(int,zero_zero(int),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_int__one__le__iff__zero__less) ).
fof(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(tsy_v_t_____res,axiom,
ti(int,t) = t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
fof(fact_0_tpos,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(c_0_20,negated_conjecture,
~ ? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_21,plain,
! [X43,X9] :
( ord_less(int,zero_zero(int),X9)
=> ( ord_less(int,X9,X43)
=> ~ zcong(X9,zero_zero(int),X43) ) ),
inference(fof_simplification,[status(thm)],[fact_403_zcong__not__zero]) ).
fof(c_0_22,negated_conjecture,
! [X1371,X1372] : plus_plus(int,power_power(int,X1371,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1372,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
fof(c_0_23,plain,
! [X488] : bit0(X488) = plus_plus(int,X488,X488),
inference(variable_rename,[status(thm)],[fact_126_Bit0__def]) ).
fof(c_0_24,plain,
! [X552] : bit1(X552) = plus_plus(int,plus_plus(int,one_one(int),X552),X552),
inference(variable_rename,[status(thm)],[fact_151_Bit1__def]) ).
fof(c_0_25,plain,
! [X484] : plus_plus(int,X484,pls) = ti(int,X484),
inference(variable_rename,[status(thm)],[fact_123_add__Pls__right]) ).
fof(c_0_26,plain,
! [X407] : number_number_of(int,X407) = ti(int,X407),
inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).
fof(c_0_27,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])]) ).
fof(c_0_28,plain,
! [X1104,X1105] :
( ~ ord_less(int,zero_zero(int),X1105)
| ~ ord_less(int,X1105,X1104)
| ~ zcong(X1105,zero_zero(int),X1104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_29,plain,
( t != one_one(int)
| plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])]) ).
cnf(c_0_30,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
bit0(X1) = plus_plus(int,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X414,X415] : plus_plus(int,X414,X415) = plus_plus(int,X415,X414),
inference(variable_rename,[status(thm)],[fact_89_zadd__commute]) ).
fof(c_0_34,plain,
! [X408,X409,X410] : plus_plus(int,plus_plus(int,X408,X409),X410) = plus_plus(int,X408,plus_plus(int,X409,X410)),
inference(variable_rename,[status(thm)],[fact_87_zadd__assoc]) ).
fof(c_0_35,plain,
! [X411,X412,X413] : plus_plus(int,X411,plus_plus(int,X412,X413)) = plus_plus(int,X412,plus_plus(int,X411,X413)),
inference(variable_rename,[status(thm)],[fact_88_zadd__left__commute]) ).
fof(c_0_36,plain,
! [X405,X406] : times_times(int,X405,X406) = times_times(int,X406,X405),
inference(variable_rename,[status(thm)],[fact_85_zmult__commute]) ).
cnf(c_0_37,plain,
plus_plus(int,X1,pls) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
number_number_of(int,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,plain,
( plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,plain,
( ~ ord_less(int,zero_zero(int),X1)
| ~ ord_less(int,X1,X2)
| ~ zcong(X1,zero_zero(int),X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_202_Pls__def]) ).
fof(c_0_42,plain,
! [X912,X913] : zcong(X912,X913,one_one(int)),
inference(variable_rename,[status(thm)],[fact_330_zcong__1]) ).
fof(c_0_43,plain,
! [X250,X251] :
( ord_less(int,X250,X251)
| ti(int,X250) = ti(int,X251)
| ord_less(int,X251,X250) ),
inference(variable_rename,[status(thm)],[fact_23_zless__linear]) ).
fof(c_0_44,plain,
! [X83] :
( ~ zero_neq_one(X83)
| ti(X83,one_one(X83)) = one_one(X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_0_res])]) ).
fof(c_0_45,plain,
! [X747] :
( ( ~ ord_less_eq(int,one_one(int),X747)
| ord_less(int,zero_zero(int),X747) )
& ( ~ ord_less(int,zero_zero(int),X747)
| ord_less_eq(int,one_one(int),X747) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_241_int__one__le__iff__zero__less])]) ).
cnf(c_0_46,plain,
( plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| t != one_one(int) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_47,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(int,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) != plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),
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_30,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_48,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_49,plain,
plus_plus(int,plus_plus(int,X1,X2),X3) = plus_plus(int,X1,plus_plus(int,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_50,plain,
plus_plus(int,X1,plus_plus(int,X2,X3)) = plus_plus(int,X2,plus_plus(int,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52,plain,
number_number_of(int,X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_53,plain,
( plus_plus(int,power_power(int,esk3_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(int,esk4_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) = plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
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_39,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_54,plain,
( ~ ord_less(int,pls,X1)
| ~ ord_less(int,X1,X2)
| ~ zcong(X1,pls,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]) ).
cnf(c_0_55,plain,
zcong(X1,X2,one_one(int)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,plain,
( ord_less(int,X1,X2)
| ti(int,X1) = ti(int,X2)
| ord_less(int,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,plain,
zero_neq_one(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ozero__neq__one]) ).
cnf(c_0_59,plain,
( ord_less(int,zero_zero(int),X1)
| ~ ord_less_eq(int,one_one(int),X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_60,plain,
( plus_plus(int,power_power(int,esk1_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(int,esk2_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) = plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))
| t != one_one(int) ),
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_46,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_61,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int)))))))),power_power(int,X2,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int))))))))) != plus_plus(int,one_one(int),times_times(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,one_one(int),one_one(int))))))))))))))),
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)],[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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_51]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_52]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_48]),c_0_50]),c_0_50]),c_0_50]) ).
cnf(c_0_62,plain,
( plus_plus(int,power_power(int,esk3_0,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int)))))))),power_power(int,esk4_0,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int))))))))) = plus_plus(int,one_one(int),times_times(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,one_one(int),one_one(int)))))))))))))))
| ~ ord_less(int,one_one(int),t) ),
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)],[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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_52]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_48]),c_0_50]),c_0_50]),c_0_50]),c_0_51]) ).
cnf(c_0_63,plain,
( ~ ord_less(int,X1,one_one(int))
| ~ ord_less(int,pls,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_64,plain,
( plus_plus(int,X1,pls) = plus_plus(int,X2,pls)
| ord_less(int,X1,X2)
| ord_less(int,X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_38]),c_0_52]),c_0_38]),c_0_52]) ).
cnf(c_0_65,plain,
plus_plus(int,pls,one_one(int)) = one_one(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_38]),c_0_52]),c_0_48]) ).
cnf(c_0_66,plain,
ti(int,t) = t,
inference(split_conjunct,[status(thm)],[tsy_v_t_____res]) ).
cnf(c_0_67,plain,
( ord_less(int,pls,X1)
| ~ ord_less_eq(int,one_one(int),X1) ),
inference(rw,[status(thm)],[c_0_59,c_0_41]) ).
cnf(c_0_68,plain,
ord_less_eq(int,one_one(int),t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
cnf(c_0_69,plain,
( plus_plus(int,power_power(int,esk1_0,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int)))))))),power_power(int,esk2_0,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int))))))))) = plus_plus(int,one_one(int),times_times(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,one_one(int),one_one(int)))))))))))))))
| one_one(int) != t ),
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)],[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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_52]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_48]),c_0_50]),c_0_50]),c_0_50]),c_0_51]) ).
cnf(c_0_70,negated_conjecture,
~ ord_less(int,one_one(int),t),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,plain,
( plus_plus(int,X1,pls) = one_one(int)
| ord_less(int,one_one(int),X1)
| ~ ord_less(int,pls,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_48]),c_0_65]) ).
cnf(c_0_72,plain,
plus_plus(int,pls,t) = t,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_38]),c_0_52]),c_0_48]) ).
cnf(c_0_73,plain,
ord_less(int,pls,t),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
one_one(int) != t,
inference(spm,[status(thm)],[c_0_61,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_48]),c_0_72]),c_0_73])]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM926+6 : 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
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri Aug 25 17:16:43 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.04/1.12 % Version : CSE_E---1.5
% 1.04/1.12 % Problem : theBenchmark.p
% 1.04/1.12 % Proof found
% 1.04/1.12 % SZS status Theorem for theBenchmark.p
% 1.04/1.12 % SZS output start Proof
% See solution above
% 1.04/1.13 % Total time : 0.529000 s
% 1.04/1.13 % SZS output end Proof
% 1.04/1.13 % Total time : 0.549000 s
%------------------------------------------------------------------------------