TSTP Solution File: NUM924+6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 0.96s 1.09s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 90
% Syntax : Number of formulae : 140 ( 57 unt; 70 typ; 0 def)
% Number of atoms : 83 ( 53 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 80 ( 56 >; 24 *; 0 +; 0 <<)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 14 con; 0-3 aty)
% Number of variables : 78 ( 1 sgn; 47 !; 0 ?; 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,
legendre: ( $i * $i ) > $i ).
tff(decl_52,type,
quadRes: ( $i * $i ) > $o ).
tff(decl_53,type,
dvd_dvd: ( $i * $i * $i ) > $o ).
tff(decl_54,type,
twoSqu420862341sum2sq: $i > $o ).
tff(decl_55,type,
m: $i ).
tff(decl_56,type,
s1: $i ).
tff(decl_57,type,
s: $i ).
tff(decl_58,type,
t: $i ).
tff(decl_59,type,
linordered_idom: $i > $o ).
tff(decl_60,type,
semiring_1: $i > $o ).
tff(decl_61,type,
ring_11004092258visors: $i > $o ).
tff(decl_62,type,
number_ring: $i > $o ).
tff(decl_63,type,
number_semiring: $i > $o ).
tff(decl_64,type,
linord581940658strict: $i > $o ).
tff(decl_65,type,
linordered_ring: $i > $o ).
tff(decl_66,type,
linorder: $i > $o ).
tff(decl_67,type,
ring_char_0: $i > $o ).
tff(decl_68,type,
linordered_semidom: $i > $o ).
tff(decl_69,type,
monoid_mult: $i > $o ).
tff(decl_70,type,
comm_semiring_1: $i > $o ).
tff(decl_71,type,
semiri456707255roduct: $i > $o ).
tff(decl_72,type,
semiring_0: $i > $o ).
tff(decl_73,type,
real: $i ).
tff(decl_74,type,
ring: $i > $o ).
tff(decl_75,type,
ring_1: $i > $o ).
tff(decl_76,type,
comm_monoid_mult: $i > $o ).
tff(decl_77,type,
linord626643107strict: $i > $o ).
tff(decl_78,type,
ring_n68954251visors: $i > $o ).
tff(decl_79,type,
comm_semiring: $i > $o ).
tff(decl_80,type,
comm_ring_1: $i > $o ).
tff(decl_81,type,
ordere453448008miring: $i > $o ).
tff(decl_82,type,
ordered_ring: $i > $o ).
tff(decl_83,type,
bool: $i ).
tff(decl_84,type,
esk1_0: $i ).
tff(decl_85,type,
esk2_0: $i ).
tff(decl_86,type,
esk3_0: $i ).
tff(decl_87,type,
esk4_1: $i > $i ).
tff(decl_88,type,
esk5_0: $i ).
tff(decl_89,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk8_2: ( $i * $i ) > $i ).
fof(fact_130_Bit0__def,axiom,
! [X14] : bit0(X14) = plus_plus(int,X14,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Bit0__def) ).
fof(fact_162_Bit1__def,axiom,
! [X14] : bit1(X14) = plus_plus(int,plus_plus(int,one_one(int),X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Bit1__def) ).
fof(fact_127_add__Pls__right,axiom,
! [X14] : plus_plus(int,X14,pls) = ti(int,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add__Pls__right) ).
fof(fact_22_number__of__is__id,axiom,
! [X14] : number_number_of(int,X14) = ti(int,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(fact_61_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__1__add__1) ).
fof(fact_96_zadd__commute,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
fof(fact_3_t,axiom,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
fof(fact_140_power2__eq__square,axiom,
! [X3] :
( monoid_mult(X3)
=> ! [X9] : power_power(X3,X9,number_number_of(nat,bit0(bit1(pls)))) = times_times(X3,X9,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_power2__eq__square) ).
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,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
fof(fact_94_zadd__assoc,axiom,
! [X18,X19,X20] : plus_plus(int,plus_plus(int,X18,X19),X20) = plus_plus(int,X18,plus_plus(int,X19,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zadd__assoc) ).
fof(fact_95_zadd__left__commute,axiom,
! [X5,X6,X15] : plus_plus(int,X5,plus_plus(int,X6,X15)) = plus_plus(int,X6,plus_plus(int,X5,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__left__commute) ).
fof(fact_106_not__sum__squares__lt__zero,axiom,
! [X3] :
( linordered_ring(X3)
=> ! [X5,X6] : ~ ord_less(X3,plus_plus(X3,times_times(X3,X5,X5),times_times(X3,X6,X6)),zero_zero(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_not__sum__squares__lt__zero) ).
fof(fact_65_zmult__1__right,axiom,
! [X15] : times_times(int,X15,one_one(int)) = ti(int,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zmult__1__right) ).
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/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_0_res) ).
fof(fact_120_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Pls__def) ).
fof(fact_23_zmult__commute,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(fact_62_mult__Pls,axiom,
! [X11] : times_times(int,pls,X11) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(arity_Int_Oint___Rings_Olinordered__ring,axiom,
linordered_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
fof(arity_Int_Oint___Groups_Omonoid__mult,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
fof(c_0_20,plain,
! [X438] : bit0(X438) = plus_plus(int,X438,X438),
inference(variable_rename,[status(thm)],[fact_130_Bit0__def]) ).
fof(c_0_21,plain,
! [X493] : bit1(X493) = plus_plus(int,plus_plus(int,one_one(int),X493),X493),
inference(variable_rename,[status(thm)],[fact_162_Bit1__def]) ).
fof(c_0_22,plain,
! [X434] : plus_plus(int,X434,pls) = ti(int,X434),
inference(variable_rename,[status(thm)],[fact_127_add__Pls__right]) ).
fof(c_0_23,plain,
! [X231] : number_number_of(int,X231) = ti(int,X231),
inference(variable_rename,[status(thm)],[fact_22_number__of__is__id]) ).
cnf(c_0_24,plain,
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_25,plain,
bit0(X1) = plus_plus(int,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X380,X381] : plus_plus(int,X380,X381) = plus_plus(int,X381,X380),
inference(variable_rename,[status(thm)],[fact_96_zadd__commute]) ).
cnf(c_0_28,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(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]) ).
cnf(c_0_29,plain,
plus_plus(int,X1,pls) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
number_number_of(int,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = 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))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_26]) ).
cnf(c_0_32,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X456,X457] :
( ~ monoid_mult(X456)
| power_power(X456,X457,number_number_of(nat,bit0(bit1(pls)))) = times_times(X456,X457,X457) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_power2__eq__square])])]) ).
cnf(c_0_34,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(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_35,plain,
plus_plus(int,power_power(int,s,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)))),one_one(int)) = times_times(int,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),
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_28,c_0_25]),c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_36,plain,
number_number_of(int,X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
number_number_of(nat,plus_plus(int,plus_plus(int,pls,plus_plus(int,pls,one_one(int))),plus_plus(int,pls,plus_plus(int,pls,one_one(int))))) = 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_31,c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_38,plain,
( power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X2,X2)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,plain,
! [X374,X375,X376] : plus_plus(int,plus_plus(int,X374,X375),X376) = plus_plus(int,X374,plus_plus(int,X375,X376)),
inference(variable_rename,[status(thm)],[fact_94_zadd__assoc]) ).
fof(c_0_40,plain,
! [X377,X378,X379] : plus_plus(int,X377,plus_plus(int,X378,X379)) = plus_plus(int,X378,plus_plus(int,X377,X379)),
inference(variable_rename,[status(thm)],[fact_95_zadd__left__commute]) ).
fof(c_0_41,plain,
! [X3] :
( linordered_ring(X3)
=> ! [X5,X6] : ~ ord_less(X3,plus_plus(X3,times_times(X3,X5,X5),times_times(X3,X6,X6)),zero_zero(X3)) ),
inference(fof_simplification,[status(thm)],[fact_106_not__sum__squares__lt__zero]) ).
fof(c_0_42,plain,
! [X316] : times_times(int,X316,one_one(int)) = ti(int,X316),
inference(variable_rename,[status(thm)],[fact_65_zmult__1__right]) ).
fof(c_0_43,plain,
! [X82] :
( ~ zero_neq_one(X82)
| ti(X82,one_one(X82)) = one_one(X82) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_0_res])]) ).
cnf(c_0_44,plain,
ord_less(int,times_times(int,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),times_times(int,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)),zero_zero(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_34,c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_45,plain,
times_times(int,plus_plus(int,one_one(int),times_times(int,plus_plus(int,pls,plus_plus(int,plus_plus(int,plus_plus(int,pls,plus_plus(int,pls,one_one(int))),plus_plus(int,pls,plus_plus(int,pls,one_one(int)))),plus_plus(int,plus_plus(int,pls,plus_plus(int,pls,one_one(int))),plus_plus(int,pls,plus_plus(int,pls,one_one(int)))))),m)),t) = plus_plus(int,one_one(int),power_power(int,s,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)],[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_35,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_36]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_37]) ).
cnf(c_0_46,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_120_Pls__def]) ).
fof(c_0_47,plain,
! [X232,X233] : times_times(int,X232,X233) = times_times(int,X233,X232),
inference(variable_rename,[status(thm)],[fact_23_zmult__commute]) ).
fof(c_0_48,plain,
! [X311] : times_times(int,pls,X311) = pls,
inference(variable_rename,[status(thm)],[fact_62_mult__Pls]) ).
cnf(c_0_49,plain,
( power_power(X1,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)))) = times_times(X1,X2,X2)
| ~ monoid_mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_25]),c_0_26]),c_0_26]) ).
cnf(c_0_50,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_39]) ).
cnf(c_0_51,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_40]) ).
fof(c_0_52,plain,
! [X405,X406,X407] :
( ~ linordered_ring(X405)
| ~ ord_less(X405,plus_plus(X405,times_times(X405,X406,X406),times_times(X405,X407,X407)),zero_zero(X405)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
cnf(c_0_53,plain,
times_times(int,X1,one_one(int)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
zero_neq_one(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ozero__neq__one]) ).
cnf(c_0_56,plain,
ord_less(int,plus_plus(int,one_one(int),power_power(int,s,plus_plus(nat,one_one(nat),one_one(nat)))),times_times(int,plus_plus(int,one_one(int),times_times(int,plus_plus(int,pls,plus_plus(int,plus_plus(int,plus_plus(int,pls,plus_plus(int,pls,one_one(int))),plus_plus(int,pls,plus_plus(int,pls,one_one(int)))),plus_plus(int,plus_plus(int,pls,plus_plus(int,pls,one_one(int))),plus_plus(int,pls,plus_plus(int,pls,one_one(int)))))),m)),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)],[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_44,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_36]),c_0_32]),c_0_32]),c_0_45]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_36]),c_0_32]),c_0_32]),c_0_46]) ).
cnf(c_0_57,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
times_times(int,pls,X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,plain,
( power_power(X1,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)))))))) = times_times(X1,X2,X2)
| ~ monoid_mult(X1) ),
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_49,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_50]),c_0_50]),c_0_51]),c_0_51]) ).
cnf(c_0_60,plain,
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(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_37,c_0_50]),c_0_50]),c_0_51]),c_0_51]) ).
cnf(c_0_61,plain,
( ~ linordered_ring(X1)
| ~ ord_less(X1,plus_plus(X1,times_times(X1,X2,X2),times_times(X1,X3,X3)),zero_zero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
times_times(int,X1,one_one(int)) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_30]),c_0_36]) ).
cnf(c_0_63,plain,
linordered_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__ring]) ).
cnf(c_0_64,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_54,c_0_55]),c_0_30]),c_0_36]),c_0_32]) ).
cnf(c_0_65,plain,
ord_less(int,plus_plus(int,one_one(int),power_power(int,s,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)],[c_0_56,c_0_57]),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_50]),c_0_57]),c_0_58]) ).
cnf(c_0_66,plain,
( power_power(X1,X2,plus_plus(nat,one_one(nat),one_one(nat))) = times_times(X1,X2,X2)
| ~ monoid_mult(X1) ),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,plain,
monoid_mult(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Omonoid__mult]) ).
cnf(c_0_68,plain,
~ ord_less(int,plus_plus(int,one_one(int),times_times(int,X1,X1)),pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_32]),c_0_46])]),c_0_64]),c_0_32]) ).
cnf(c_0_69,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 10:45:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.96/1.09 % Version : CSE_E---1.5
% 0.96/1.09 % Problem : theBenchmark.p
% 0.96/1.09 % Proof found
% 0.96/1.09 % SZS status Theorem for theBenchmark.p
% 0.96/1.09 % SZS output start Proof
% See solution above
% 1.06/1.10 % Total time : 0.516000 s
% 1.06/1.10 % SZS output end Proof
% 1.06/1.10 % Total time : 0.536000 s
%------------------------------------------------------------------------------