TSTP Solution File: NUM926+5 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n007.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 : 600s
% DateTime : Mon Jul 18 11:03:31 EDT 2022
% Result : Theorem 248.10s 248.36s
% Output : CNFRefutation 248.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 147
% Syntax : Number of formulae : 1165 ( 315 unt; 0 def)
% Number of atoms : 2452 ( 629 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2284 ( 997 ~;1012 |; 67 &)
% ( 80 <=>; 128 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 16 con; 0-3 aty)
% Number of variables : 2347 ( 16 sgn 847 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X6,X7] : power_power(int,plus_plus(int,X6,X7),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X6,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))),X7)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X6),power_power(int,X7,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X7,number_number_of(nat,bit1(bit1(pls))))),
file('<stdin>',fact_8_zadd__power3) ).
fof(c_0_1,axiom,
! [X6,X7] : power_power(int,plus_plus(int,X6,X7),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(int,power_power(int,X6,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X6),X7)),power_power(int,X7,number_number_of(nat,bit0(bit1(pls))))),
file('<stdin>',fact_7_zadd__power2) ).
fof(c_0_2,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X8,X9] : power_power(X1,plus_plus(X1,X8,X9),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X1,plus_plus(X1,power_power(X1,X8,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X9,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X8),X9)) ),
file('<stdin>',fact_9_power2__sum) ).
fof(c_0_3,axiom,
twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
file('<stdin>',fact_6_qf1pt) ).
fof(c_0_4,axiom,
~ ! [X14] : 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)),X14),
file('<stdin>',fact_19__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
fof(c_0_5,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('<stdin>',fact_5_t) ).
fof(c_0_6,axiom,
( ord_less(int,one_one(int),t)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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('<stdin>',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_7,axiom,
( t = one_one(int)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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('<stdin>',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(c_0_8,axiom,
ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('<stdin>',fact_3_t__l__p) ).
fof(c_0_9,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('<stdin>',fact_4_p) ).
fof(c_0_10,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,X33,times_times(X1,X34,times_times(X1,X35,X36))) ),
file('<stdin>',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(c_0_11,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,X35,times_times(X1,times_times(X1,X33,X34),X36)) ),
file('<stdin>',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(c_0_12,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37,X38] : plus_plus(X1,plus_plus(X1,X6,X7),plus_plus(X1,X37,X38)) = plus_plus(X1,plus_plus(X1,X6,X37),plus_plus(X1,X7,X38)) ),
file('<stdin>',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_13,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,times_times(X1,X33,X35),times_times(X1,X34,X36)) ),
file('<stdin>',fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(c_0_14,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X12] : power_power(X1,X8,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X12)) = times_times(X1,power_power(X1,X8,X12),power_power(X1,X8,X12)) ),
file('<stdin>',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(c_0_15,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X21,X22] : times_times(X1,power_power(X1,X8,X21),power_power(X1,X8,X22)) = power_power(X1,X8,plus_plus(nat,X21,X22)) ),
file('<stdin>',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(c_0_16,axiom,
! [X26,X15,X27,X11] :
( ord_less(int,X27,X11)
=> ( ord_less_eq(int,X26,X15)
=> ord_less(int,plus_plus(int,X27,X26),plus_plus(int,X11,X15)) ) ),
file('<stdin>',fact_32_zadd__zless__mono) ).
fof(c_0_17,axiom,
! [X8,X9,X15] : power_power(int,X8,plus_plus(nat,X9,X15)) = times_times(int,power_power(int,X8,X9),power_power(int,X8,X15)),
file('<stdin>',fact_34_zpower__zadd__distrib) ).
fof(c_0_18,axiom,
! [X6] : times_times(int,X6,power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X6,number_number_of(nat,bit1(bit1(pls)))),
file('<stdin>',fact_11_cube__square) ).
fof(c_0_19,axiom,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X23,X17] :
( ord_less_eq(X1,number_number_of(X1,X23),number_number_of(X1,X17))
<=> ~ ord_less(X1,number_number_of(X1,X17),number_number_of(X1,X23)) ) ),
file('<stdin>',fact_29_le__number__of__eq__not__less) ).
fof(c_0_20,axiom,
! [X18,X19,X20] :
( ord_less_eq(int,X19,X20)
=> ord_less_eq(int,plus_plus(int,X18,X19),plus_plus(int,X18,X20)) ),
file('<stdin>',fact_51_zadd__left__mono) ).
fof(c_0_21,axiom,
! [X18,X19,X20] :
( ord_less(int,X19,X20)
=> ord_less(int,plus_plus(int,X19,X18),plus_plus(int,X20,X18)) ),
file('<stdin>',fact_50_zadd__strict__right__mono) ).
fof(c_0_22,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37,X38] : plus_plus(X1,X6,plus_plus(X1,X37,X38)) = plus_plus(X1,X37,plus_plus(X1,X6,X38)) ),
file('<stdin>',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_23,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37,X38] : plus_plus(X1,X6,plus_plus(X1,X37,X38)) = plus_plus(X1,plus_plus(X1,X6,X37),X38) ),
file('<stdin>',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_24,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37] : plus_plus(X1,plus_plus(X1,X6,X7),X37) = plus_plus(X1,X6,plus_plus(X1,X7,X37)) ),
file('<stdin>',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_25,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37] : plus_plus(X1,plus_plus(X1,X6,X7),X37) = plus_plus(X1,plus_plus(X1,X6,X37),X7) ),
file('<stdin>',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_26,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X35,X36] : times_times(X1,X33,times_times(X1,X35,X36)) = times_times(X1,X35,times_times(X1,X33,X36)) ),
file('<stdin>',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(c_0_27,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X35,X36] : times_times(X1,X33,times_times(X1,X35,X36)) = times_times(X1,times_times(X1,X33,X35),X36) ),
file('<stdin>',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(c_0_28,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35] : times_times(X1,times_times(X1,X33,X34),X35) = times_times(X1,X33,times_times(X1,X34,X35)) ),
file('<stdin>',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(c_0_29,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35] : times_times(X1,times_times(X1,X33,X34),X35) = times_times(X1,times_times(X1,X33,X35),X34) ),
file('<stdin>',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(c_0_30,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X21,X22] : power_power(X1,power_power(X1,X8,X21),X22) = power_power(X1,X8,times_times(nat,X21,X22)) ),
file('<stdin>',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(c_0_31,axiom,
! [X32,X13] :
( ( ord_less(int,X13,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X32) )
& ( ~ ord_less(int,X13,pls)
=> ( ( ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X13) )
& ( ~ ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,plus_plus(int,X13,X32)) ) ) ) ),
file('<stdin>',fact_52_add__nat__number__of) ).
fof(c_0_32,axiom,
! [X8,X9,X15] : plus_plus(int,X8,plus_plus(int,X9,X15)) = plus_plus(int,X9,plus_plus(int,X8,X15)),
file('<stdin>',fact_88_zadd__left__commute) ).
fof(c_0_33,axiom,
! [X39,X40,X41] : plus_plus(int,plus_plus(int,X39,X40),X41) = plus_plus(int,X39,plus_plus(int,X40,X41)),
file('<stdin>',fact_87_zadd__assoc) ).
fof(c_0_34,axiom,
! [X39,X40,X41] : times_times(int,times_times(int,X39,X40),X41) = times_times(int,X39,times_times(int,X40,X41)),
file('<stdin>',fact_84_zmult__assoc) ).
fof(c_0_35,axiom,
! [X8,X9,X15] : power_power(int,power_power(int,X8,X9),X15) = power_power(int,X8,times_times(nat,X9,X15)),
file('<stdin>',fact_28_zpower__zpower) ).
fof(c_0_36,axiom,
! [X17,X16] :
( ord_less(int,X17,plus_plus(int,X16,one_one(int)))
<=> ord_less_eq(int,X17,X16) ),
file('<stdin>',fact_63_zle__add1__eq__le) ).
fof(c_0_37,axiom,
! [X17,X16] :
( ord_less_eq(int,plus_plus(int,X17,one_one(int)),X16)
<=> ord_less(int,X17,X16) ),
file('<stdin>',fact_62_add1__zle__eq) ).
fof(c_0_38,axiom,
! [X10] :
( ( monoid_mult(X10)
& number(X10) )
=> ! [X11] : power_power(X10,number_number_of(X10,X11),number_number_of(nat,bit0(bit1(pls)))) = times_times(X10,number_number_of(X10,X11),number_number_of(X10,X11)) ),
file('<stdin>',fact_10_power2__eq__square__number__of) ).
fof(c_0_39,axiom,
! [X11,X15] :
( ord_less(int,X11,X15)
=> ord_less_eq(int,plus_plus(int,X11,one_one(int)),X15) ),
file('<stdin>',fact_61_zless__imp__add1__zle) ).
fof(c_0_40,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X24,X25] :
( ord_less_eq(X1,number_number_of(X1,X24),number_number_of(X1,X25))
<=> ord_less_eq(int,X24,X25) ) ),
file('<stdin>',fact_31_le__number__of) ).
fof(c_0_41,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X24,X25] :
( ord_less(X1,number_number_of(X1,X24),number_number_of(X1,X25))
<=> ord_less(int,X24,X25) ) ),
file('<stdin>',fact_30_less__number__of) ).
fof(c_0_42,axiom,
! [X18,X19,X20] :
( ord_less_eq(int,X19,X20)
=> ( ord_less_eq(int,X20,X18)
=> ord_less_eq(int,X19,X18) ) ),
file('<stdin>',fact_24_zle__trans) ).
fof(c_0_43,axiom,
! [X1] :
( number_ring(X1)
=> ! [X13] : plus_plus(X1,number_number_of(X1,X13),one_one(X1)) = number_number_of(X1,plus_plus(int,X13,bit1(pls))) ),
file('<stdin>',fact_17_add__special_I3_J) ).
fof(c_0_44,axiom,
! [X1] :
( number_ring(X1)
=> ! [X11] : plus_plus(X1,one_one(X1),number_number_of(X1,X11)) = number_number_of(X1,plus_plus(int,bit1(pls),X11)) ),
file('<stdin>',fact_16_add__special_I2_J) ).
fof(c_0_45,axiom,
! [X30,X31] :
( ord_less_eq(int,number_number_of(int,X30),number_number_of(int,X31))
<=> ord_less_eq(int,X30,X31) ),
file('<stdin>',fact_49_less__eq__number__of__int__code) ).
fof(c_0_46,axiom,
! [X30,X31] :
( ord_less(int,number_number_of(int,X30),number_number_of(int,X31))
<=> ord_less(int,X30,X31) ),
file('<stdin>',fact_48_less__number__of__int__code) ).
fof(c_0_47,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less_eq(X1,X2,ti(X1,X3))
<=> ord_less_eq(X1,X2,X3) ) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless__eq_arg2) ).
fof(c_0_48,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less_eq(X1,ti(X1,X2),X3)
<=> ord_less_eq(X1,X2,X3) ) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless__eq_arg1) ).
fof(c_0_49,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less(X1,X2,ti(X1,X3))
<=> ord_less(X1,X2,X3) ) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless_arg2) ).
fof(c_0_50,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less(X1,ti(X1,X2),X3)
<=> ord_less(X1,X2,X3) ) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless_arg1) ).
fof(c_0_51,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3) ),
file('<stdin>',tsy_c_Power_Opower__class_Opower_res) ).
fof(c_0_52,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_res) ).
fof(c_0_53,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_res) ).
fof(c_0_54,axiom,
! [X15,X11] :
( ord_less_eq(int,X15,X11)
=> ( ord_less_eq(int,X11,X15)
=> X15 = X11 ) ),
file('<stdin>',fact_25_zle__antisym) ).
fof(c_0_55,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X6] : power_power(X1,X6,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X6,X6) ),
file('<stdin>',fact_14_power2__eq__square) ).
fof(c_0_56,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8] : times_times(X1,X8,X8) = power_power(X1,X8,number_number_of(nat,bit0(bit1(pls)))) ),
file('<stdin>',fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(c_0_57,axiom,
! [X30,X31] :
( ord_less_eq(int,bit0(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
file('<stdin>',fact_97_rel__simps_I32_J) ).
fof(c_0_58,axiom,
! [X28,X29] :
( ord_less_eq(int,bit0(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
file('<stdin>',fact_96_less__eq__int__code_I14_J) ).
fof(c_0_59,axiom,
! [X30,X31] :
( ord_less(int,bit1(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
file('<stdin>',fact_92_rel__simps_I16_J) ).
fof(c_0_60,axiom,
! [X28,X29] :
( ord_less(int,bit1(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
file('<stdin>',fact_91_less__int__code_I15_J) ).
fof(c_0_61,axiom,
! [X30,X31] :
( ord_less(int,bit0(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
file('<stdin>',fact_60_rel__simps_I15_J) ).
fof(c_0_62,axiom,
! [X28,X29] :
( ord_less(int,bit0(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
file('<stdin>',fact_59_less__int__code_I14_J) ).
fof(c_0_63,axiom,
! [X30,X31] :
( ord_less_eq(int,bit1(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
file('<stdin>',fact_58_rel__simps_I33_J) ).
fof(c_0_64,axiom,
! [X28,X29] :
( ord_less_eq(int,bit1(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
file('<stdin>',fact_57_less__eq__int__code_I15_J) ).
fof(c_0_65,axiom,
! [X30,X31] :
( ord_less_eq(int,bit0(X30),bit0(X31))
<=> ord_less_eq(int,X30,X31) ),
file('<stdin>',fact_47_rel__simps_I31_J) ).
fof(c_0_66,axiom,
! [X28,X29] :
( ord_less_eq(int,bit0(X28),bit0(X29))
<=> ord_less_eq(int,X28,X29) ),
file('<stdin>',fact_46_less__eq__int__code_I13_J) ).
fof(c_0_67,axiom,
! [X30,X31] :
( ord_less(int,bit0(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
file('<stdin>',fact_44_rel__simps_I14_J) ).
fof(c_0_68,axiom,
! [X28,X29] :
( ord_less(int,bit0(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
file('<stdin>',fact_43_less__int__code_I13_J) ).
fof(c_0_69,axiom,
! [X30,X31] :
( ord_less_eq(int,bit1(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
file('<stdin>',fact_41_rel__simps_I34_J) ).
fof(c_0_70,axiom,
! [X28,X29] :
( ord_less_eq(int,bit1(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
file('<stdin>',fact_40_less__eq__int__code_I16_J) ).
fof(c_0_71,axiom,
! [X30,X31] :
( ord_less(int,bit1(X30),bit1(X31))
<=> ord_less(int,X30,X31) ),
file('<stdin>',fact_39_rel__simps_I17_J) ).
fof(c_0_72,axiom,
! [X28,X29] :
( ord_less(int,bit1(X28),bit1(X29))
<=> ord_less(int,X28,X29) ),
file('<stdin>',fact_38_less__int__code_I16_J) ).
fof(c_0_73,axiom,
! [X15] : times_times(nat,X15,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X15,X15),
file('<stdin>',fact_36_nat__mult__2__right) ).
fof(c_0_74,axiom,
! [X15] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),X15) = plus_plus(nat,X15,X15),
file('<stdin>',fact_35_nat__mult__2) ).
fof(c_0_75,axiom,
! [X30] :
( ord_less_eq(int,pls,bit1(X30))
<=> ord_less_eq(int,pls,X30) ),
file('<stdin>',fact_95_rel__simps_I22_J) ).
fof(c_0_76,axiom,
! [X30] :
( ord_less(int,pls,bit0(X30))
<=> ord_less(int,pls,X30) ),
file('<stdin>',fact_94_rel__simps_I4_J) ).
fof(c_0_77,axiom,
! [X30] :
( ord_less(int,bit0(X30),pls)
<=> ord_less(int,X30,pls) ),
file('<stdin>',fact_93_rel__simps_I10_J) ).
fof(c_0_78,axiom,
! [X30] :
( ord_less(int,bit1(X30),pls)
<=> ord_less(int,X30,pls) ),
file('<stdin>',fact_90_rel__simps_I12_J) ).
fof(c_0_79,axiom,
! [X30] :
( ord_less(int,pls,bit1(X30))
<=> ord_less_eq(int,pls,X30) ),
file('<stdin>',fact_56_rel__simps_I5_J) ).
fof(c_0_80,axiom,
! [X30] :
( ord_less_eq(int,bit1(X30),pls)
<=> ord_less(int,X30,pls) ),
file('<stdin>',fact_55_rel__simps_I29_J) ).
fof(c_0_81,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3) ),
file('<stdin>',tsy_c_Power_Opower__class_Opower_arg1) ).
fof(c_0_82,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_arg2) ).
fof(c_0_83,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_arg1) ).
fof(c_0_84,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_arg2) ).
fof(c_0_85,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_arg1) ).
fof(c_0_86,axiom,
! [X16,X17] :
( ord_less(int,X16,X17)
<=> ( ord_less_eq(int,X16,X17)
& X16 != X17 ) ),
file('<stdin>',fact_22_zless__le) ).
fof(c_0_87,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3) ),
file('<stdin>',tsy_c_Power_Opower__class_Opower_arg2) ).
fof(c_0_88,axiom,
! [X9,X8] :
( twoSqu33214720sum2sq(X8)
=> ( twoSqu33214720sum2sq(X9)
=> twoSqu33214720sum2sq(times_times(int,X8,X9)) ) ),
file('<stdin>',fact_65_is__mult__sum2sq) ).
fof(c_0_89,axiom,
! [X1] :
( semiring_1(X1)
=> power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1) ),
file('<stdin>',fact_12_one__power2) ).
fof(c_0_90,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37] : plus_plus(X1,X6,X37) = plus_plus(X1,X37,X6) ),
file('<stdin>',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_91,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7] : times_times(X1,X6,X7) = times_times(X1,X7,X6) ),
file('<stdin>',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(c_0_92,axiom,
! [X8,X9] :
( ord_less(int,X8,X9)
| X8 = X9
| ord_less(int,X9,X8) ),
file('<stdin>',fact_23_zless__linear) ).
fof(c_0_93,axiom,
! [X15,X11] :
( ord_less_eq(int,X15,X11)
| ord_less_eq(int,X11,X15) ),
file('<stdin>',fact_21_zle__linear) ).
fof(c_0_94,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
file('<stdin>',fact_89_zadd__commute) ).
fof(c_0_95,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('<stdin>',fact_85_zmult__commute) ).
fof(c_0_96,axiom,
! [X1] :
( number_ring(X1)
=> plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls))) ),
file('<stdin>',fact_18_one__add__one__is__two) ).
fof(c_0_97,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('<stdin>',fact_37_nat__1__add__1) ).
fof(c_0_98,axiom,
! [X1] :
( number(X1)
=> ! [X17,X24] :
( number_number_of(X1,X17) = ti(X1,X24)
<=> ti(X1,X24) = number_number_of(X1,X17) ) ),
file('<stdin>',fact_81_number__of__reorient) ).
fof(c_0_99,axiom,
~ ord_less(int,pls,pls),
file('<stdin>',fact_42_rel__simps_I2_J) ).
fof(c_0_100,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8] : power_power(X1,X8,one_one(nat)) = ti(X1,X8) ),
file('<stdin>',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(c_0_101,axiom,
! [X2,X1] :
( number(X1)
=> ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
file('<stdin>',tsy_c_Int_Onumber__class_Onumber__of_res) ).
fof(c_0_102,axiom,
! [X1] :
( ( number_ring(X1)
& ring_char_0(X1) )
=> ! [X24,X25] :
( number_number_of(X1,X24) = number_number_of(X1,X25)
<=> X24 = X25 ) ),
file('<stdin>',fact_80_eq__number__of) ).
fof(c_0_103,axiom,
! [X2,X1] :
( number(X1)
=> number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2) ),
file('<stdin>',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
fof(c_0_104,axiom,
ord_less_eq(int,one_one(int),t),
file('<stdin>',fact_0_tpos) ).
fof(c_0_105,axiom,
! [X42,X43] : ti(X42,ti(X42,X43)) = ti(X42,X43),
file('<stdin>',help_ti_idem) ).
fof(c_0_106,axiom,
! [X11] : ord_less_eq(int,X11,X11),
file('<stdin>',fact_20_zle__refl) ).
fof(c_0_107,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))),
file('<stdin>',fact_64_zprime__2) ).
fof(c_0_108,axiom,
ord_less_eq(int,pls,pls),
file('<stdin>',fact_45_rel__simps_I19_J) ).
fof(c_0_109,axiom,
! [X2] :
( twoSqu33214720sum2sq(ti(int,X2))
<=> twoSqu33214720sum2sq(X2) ),
file('<stdin>',tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1) ).
fof(c_0_110,axiom,
! [X2] :
( zprime(ti(int,X2))
<=> zprime(X2) ),
file('<stdin>',tsy_c_IntPrimes_Ozprime_arg1) ).
fof(c_0_111,axiom,
! [X1] :
( semiring_1(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
file('<stdin>',tsy_c_Groups_Oone__class_Oone_res) ).
fof(c_0_112,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
file('<stdin>',tsy_c_HOL_Oundefined_res) ).
fof(c_0_113,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
file('<stdin>',fact_54_Numeral1__eq1__nat) ).
fof(c_0_114,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
file('<stdin>',fact_53_nat__numeral__1__eq__1) ).
fof(c_0_115,axiom,
! [X30,X31] :
( bit0(X30) = bit0(X31)
<=> X30 = X31 ),
file('<stdin>',fact_83_rel__simps_I48_J) ).
fof(c_0_116,axiom,
! [X30,X31] :
( bit1(X30) = bit1(X31)
<=> X30 = X31 ),
file('<stdin>',fact_82_rel__simps_I51_J) ).
fof(c_0_117,axiom,
! [X18] : number_number_of(int,X18) = X18,
file('<stdin>',fact_86_number__of__is__id) ).
fof(c_0_118,axiom,
ti(int,t) = t,
file('<stdin>',tsy_v_t_____res) ).
fof(c_0_119,axiom,
ti(int,s) = s,
file('<stdin>',tsy_v_s_____res) ).
fof(c_0_120,axiom,
number(nat),
file('<stdin>',arity_Nat_Onat___Int_Onumber) ).
fof(c_0_121,axiom,
semiring_1(nat),
file('<stdin>',arity_Nat_Onat___Rings_Osemiring__1) ).
fof(c_0_122,axiom,
monoid_mult(nat),
file('<stdin>',arity_Nat_Onat___Groups_Omonoid__mult) ).
fof(c_0_123,axiom,
linorder(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Olinorder) ).
fof(c_0_124,axiom,
number_semiring(nat),
file('<stdin>',arity_Nat_Onat___Int_Onumber__semiring) ).
fof(c_0_125,axiom,
comm_semiring_1(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
fof(c_0_126,axiom,
number(int),
file('<stdin>',arity_Int_Oint___Int_Onumber) ).
fof(c_0_127,axiom,
number_ring(int),
file('<stdin>',arity_Int_Oint___Int_Onumber__ring) ).
fof(c_0_128,axiom,
ring_char_0(int),
file('<stdin>',arity_Int_Oint___Int_Oring__char__0) ).
fof(c_0_129,axiom,
semiring_1(int),
file('<stdin>',arity_Int_Oint___Rings_Osemiring__1) ).
fof(c_0_130,axiom,
monoid_mult(int),
file('<stdin>',arity_Int_Oint___Groups_Omonoid__mult) ).
fof(c_0_131,axiom,
linorder(int),
file('<stdin>',arity_Int_Oint___Orderings_Olinorder) ).
fof(c_0_132,axiom,
number_semiring(int),
file('<stdin>',arity_Int_Oint___Int_Onumber__semiring) ).
fof(c_0_133,axiom,
comm_semiring_1(int),
file('<stdin>',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
fof(c_0_134,axiom,
linordered_idom(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(c_0_135,axiom,
! [X6,X7] : power_power(int,plus_plus(int,X6,X7),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X6,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))),X7)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X6),power_power(int,X7,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X7,number_number_of(nat,bit1(bit1(pls))))),
c_0_0 ).
fof(c_0_136,axiom,
! [X6,X7] : power_power(int,plus_plus(int,X6,X7),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(int,power_power(int,X6,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X6),X7)),power_power(int,X7,number_number_of(nat,bit0(bit1(pls))))),
c_0_1 ).
fof(c_0_137,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X8,X9] : power_power(X1,plus_plus(X1,X8,X9),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X1,plus_plus(X1,power_power(X1,X8,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X9,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X8),X9)) ),
c_0_2 ).
fof(c_0_138,axiom,
twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
c_0_3 ).
fof(c_0_139,axiom,
~ ! [X14] : 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)),X14),
c_0_4 ).
fof(c_0_140,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),
c_0_5 ).
fof(c_0_141,axiom,
( ord_less(int,one_one(int),t)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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)) ),
c_0_6 ).
fof(c_0_142,axiom,
( t = one_one(int)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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)) ),
c_0_7 ).
fof(c_0_143,axiom,
ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
c_0_8 ).
fof(c_0_144,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
c_0_9 ).
fof(c_0_145,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,X33,times_times(X1,X34,times_times(X1,X35,X36))) ),
c_0_10 ).
fof(c_0_146,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,X35,times_times(X1,times_times(X1,X33,X34),X36)) ),
c_0_11 ).
fof(c_0_147,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37,X38] : plus_plus(X1,plus_plus(X1,X6,X7),plus_plus(X1,X37,X38)) = plus_plus(X1,plus_plus(X1,X6,X37),plus_plus(X1,X7,X38)) ),
c_0_12 ).
fof(c_0_148,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,times_times(X1,X33,X35),times_times(X1,X34,X36)) ),
c_0_13 ).
fof(c_0_149,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X12] : power_power(X1,X8,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X12)) = times_times(X1,power_power(X1,X8,X12),power_power(X1,X8,X12)) ),
c_0_14 ).
fof(c_0_150,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X21,X22] : times_times(X1,power_power(X1,X8,X21),power_power(X1,X8,X22)) = power_power(X1,X8,plus_plus(nat,X21,X22)) ),
c_0_15 ).
fof(c_0_151,axiom,
! [X26,X15,X27,X11] :
( ord_less(int,X27,X11)
=> ( ord_less_eq(int,X26,X15)
=> ord_less(int,plus_plus(int,X27,X26),plus_plus(int,X11,X15)) ) ),
c_0_16 ).
fof(c_0_152,axiom,
! [X8,X9,X15] : power_power(int,X8,plus_plus(nat,X9,X15)) = times_times(int,power_power(int,X8,X9),power_power(int,X8,X15)),
c_0_17 ).
fof(c_0_153,axiom,
! [X6] : times_times(int,X6,power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X6,number_number_of(nat,bit1(bit1(pls)))),
c_0_18 ).
fof(c_0_154,plain,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X23,X17] :
( ord_less_eq(X1,number_number_of(X1,X23),number_number_of(X1,X17))
<=> ~ ord_less(X1,number_number_of(X1,X17),number_number_of(X1,X23)) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_155,axiom,
! [X18,X19,X20] :
( ord_less_eq(int,X19,X20)
=> ord_less_eq(int,plus_plus(int,X18,X19),plus_plus(int,X18,X20)) ),
c_0_20 ).
fof(c_0_156,axiom,
! [X18,X19,X20] :
( ord_less(int,X19,X20)
=> ord_less(int,plus_plus(int,X19,X18),plus_plus(int,X20,X18)) ),
c_0_21 ).
fof(c_0_157,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37,X38] : plus_plus(X1,X6,plus_plus(X1,X37,X38)) = plus_plus(X1,X37,plus_plus(X1,X6,X38)) ),
c_0_22 ).
fof(c_0_158,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37,X38] : plus_plus(X1,X6,plus_plus(X1,X37,X38)) = plus_plus(X1,plus_plus(X1,X6,X37),X38) ),
c_0_23 ).
fof(c_0_159,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37] : plus_plus(X1,plus_plus(X1,X6,X7),X37) = plus_plus(X1,X6,plus_plus(X1,X7,X37)) ),
c_0_24 ).
fof(c_0_160,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37] : plus_plus(X1,plus_plus(X1,X6,X7),X37) = plus_plus(X1,plus_plus(X1,X6,X37),X7) ),
c_0_25 ).
fof(c_0_161,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X35,X36] : times_times(X1,X33,times_times(X1,X35,X36)) = times_times(X1,X35,times_times(X1,X33,X36)) ),
c_0_26 ).
fof(c_0_162,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X35,X36] : times_times(X1,X33,times_times(X1,X35,X36)) = times_times(X1,times_times(X1,X33,X35),X36) ),
c_0_27 ).
fof(c_0_163,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35] : times_times(X1,times_times(X1,X33,X34),X35) = times_times(X1,X33,times_times(X1,X34,X35)) ),
c_0_28 ).
fof(c_0_164,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35] : times_times(X1,times_times(X1,X33,X34),X35) = times_times(X1,times_times(X1,X33,X35),X34) ),
c_0_29 ).
fof(c_0_165,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X21,X22] : power_power(X1,power_power(X1,X8,X21),X22) = power_power(X1,X8,times_times(nat,X21,X22)) ),
c_0_30 ).
fof(c_0_166,plain,
! [X32,X13] :
( ( ord_less(int,X13,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X32) )
& ( ~ ord_less(int,X13,pls)
=> ( ( ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X13) )
& ( ~ ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,plus_plus(int,X13,X32)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_167,axiom,
! [X8,X9,X15] : plus_plus(int,X8,plus_plus(int,X9,X15)) = plus_plus(int,X9,plus_plus(int,X8,X15)),
c_0_32 ).
fof(c_0_168,axiom,
! [X39,X40,X41] : plus_plus(int,plus_plus(int,X39,X40),X41) = plus_plus(int,X39,plus_plus(int,X40,X41)),
c_0_33 ).
fof(c_0_169,axiom,
! [X39,X40,X41] : times_times(int,times_times(int,X39,X40),X41) = times_times(int,X39,times_times(int,X40,X41)),
c_0_34 ).
fof(c_0_170,axiom,
! [X8,X9,X15] : power_power(int,power_power(int,X8,X9),X15) = power_power(int,X8,times_times(nat,X9,X15)),
c_0_35 ).
fof(c_0_171,axiom,
! [X17,X16] :
( ord_less(int,X17,plus_plus(int,X16,one_one(int)))
<=> ord_less_eq(int,X17,X16) ),
c_0_36 ).
fof(c_0_172,axiom,
! [X17,X16] :
( ord_less_eq(int,plus_plus(int,X17,one_one(int)),X16)
<=> ord_less(int,X17,X16) ),
c_0_37 ).
fof(c_0_173,axiom,
! [X10] :
( ( monoid_mult(X10)
& number(X10) )
=> ! [X11] : power_power(X10,number_number_of(X10,X11),number_number_of(nat,bit0(bit1(pls)))) = times_times(X10,number_number_of(X10,X11),number_number_of(X10,X11)) ),
c_0_38 ).
fof(c_0_174,axiom,
! [X11,X15] :
( ord_less(int,X11,X15)
=> ord_less_eq(int,plus_plus(int,X11,one_one(int)),X15) ),
c_0_39 ).
fof(c_0_175,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X24,X25] :
( ord_less_eq(X1,number_number_of(X1,X24),number_number_of(X1,X25))
<=> ord_less_eq(int,X24,X25) ) ),
c_0_40 ).
fof(c_0_176,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X24,X25] :
( ord_less(X1,number_number_of(X1,X24),number_number_of(X1,X25))
<=> ord_less(int,X24,X25) ) ),
c_0_41 ).
fof(c_0_177,axiom,
! [X18,X19,X20] :
( ord_less_eq(int,X19,X20)
=> ( ord_less_eq(int,X20,X18)
=> ord_less_eq(int,X19,X18) ) ),
c_0_42 ).
fof(c_0_178,axiom,
! [X1] :
( number_ring(X1)
=> ! [X13] : plus_plus(X1,number_number_of(X1,X13),one_one(X1)) = number_number_of(X1,plus_plus(int,X13,bit1(pls))) ),
c_0_43 ).
fof(c_0_179,axiom,
! [X1] :
( number_ring(X1)
=> ! [X11] : plus_plus(X1,one_one(X1),number_number_of(X1,X11)) = number_number_of(X1,plus_plus(int,bit1(pls),X11)) ),
c_0_44 ).
fof(c_0_180,axiom,
! [X30,X31] :
( ord_less_eq(int,number_number_of(int,X30),number_number_of(int,X31))
<=> ord_less_eq(int,X30,X31) ),
c_0_45 ).
fof(c_0_181,axiom,
! [X30,X31] :
( ord_less(int,number_number_of(int,X30),number_number_of(int,X31))
<=> ord_less(int,X30,X31) ),
c_0_46 ).
fof(c_0_182,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less_eq(X1,X2,ti(X1,X3))
<=> ord_less_eq(X1,X2,X3) ) ),
c_0_47 ).
fof(c_0_183,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less_eq(X1,ti(X1,X2),X3)
<=> ord_less_eq(X1,X2,X3) ) ),
c_0_48 ).
fof(c_0_184,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less(X1,X2,ti(X1,X3))
<=> ord_less(X1,X2,X3) ) ),
c_0_49 ).
fof(c_0_185,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less(X1,ti(X1,X2),X3)
<=> ord_less(X1,X2,X3) ) ),
c_0_50 ).
fof(c_0_186,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3) ),
c_0_51 ).
fof(c_0_187,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3) ),
c_0_52 ).
fof(c_0_188,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3) ),
c_0_53 ).
fof(c_0_189,axiom,
! [X15,X11] :
( ord_less_eq(int,X15,X11)
=> ( ord_less_eq(int,X11,X15)
=> X15 = X11 ) ),
c_0_54 ).
fof(c_0_190,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X6] : power_power(X1,X6,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X6,X6) ),
c_0_55 ).
fof(c_0_191,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8] : times_times(X1,X8,X8) = power_power(X1,X8,number_number_of(nat,bit0(bit1(pls)))) ),
c_0_56 ).
fof(c_0_192,axiom,
! [X30,X31] :
( ord_less_eq(int,bit0(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
c_0_57 ).
fof(c_0_193,axiom,
! [X28,X29] :
( ord_less_eq(int,bit0(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
c_0_58 ).
fof(c_0_194,axiom,
! [X30,X31] :
( ord_less(int,bit1(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
c_0_59 ).
fof(c_0_195,axiom,
! [X28,X29] :
( ord_less(int,bit1(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
c_0_60 ).
fof(c_0_196,axiom,
! [X30,X31] :
( ord_less(int,bit0(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
c_0_61 ).
fof(c_0_197,axiom,
! [X28,X29] :
( ord_less(int,bit0(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
c_0_62 ).
fof(c_0_198,axiom,
! [X30,X31] :
( ord_less_eq(int,bit1(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
c_0_63 ).
fof(c_0_199,axiom,
! [X28,X29] :
( ord_less_eq(int,bit1(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
c_0_64 ).
fof(c_0_200,axiom,
! [X30,X31] :
( ord_less_eq(int,bit0(X30),bit0(X31))
<=> ord_less_eq(int,X30,X31) ),
c_0_65 ).
fof(c_0_201,axiom,
! [X28,X29] :
( ord_less_eq(int,bit0(X28),bit0(X29))
<=> ord_less_eq(int,X28,X29) ),
c_0_66 ).
fof(c_0_202,axiom,
! [X30,X31] :
( ord_less(int,bit0(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
c_0_67 ).
fof(c_0_203,axiom,
! [X28,X29] :
( ord_less(int,bit0(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
c_0_68 ).
fof(c_0_204,axiom,
! [X30,X31] :
( ord_less_eq(int,bit1(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
c_0_69 ).
fof(c_0_205,axiom,
! [X28,X29] :
( ord_less_eq(int,bit1(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
c_0_70 ).
fof(c_0_206,axiom,
! [X30,X31] :
( ord_less(int,bit1(X30),bit1(X31))
<=> ord_less(int,X30,X31) ),
c_0_71 ).
fof(c_0_207,axiom,
! [X28,X29] :
( ord_less(int,bit1(X28),bit1(X29))
<=> ord_less(int,X28,X29) ),
c_0_72 ).
fof(c_0_208,axiom,
! [X15] : times_times(nat,X15,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X15,X15),
c_0_73 ).
fof(c_0_209,axiom,
! [X15] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),X15) = plus_plus(nat,X15,X15),
c_0_74 ).
fof(c_0_210,axiom,
! [X30] :
( ord_less_eq(int,pls,bit1(X30))
<=> ord_less_eq(int,pls,X30) ),
c_0_75 ).
fof(c_0_211,axiom,
! [X30] :
( ord_less(int,pls,bit0(X30))
<=> ord_less(int,pls,X30) ),
c_0_76 ).
fof(c_0_212,axiom,
! [X30] :
( ord_less(int,bit0(X30),pls)
<=> ord_less(int,X30,pls) ),
c_0_77 ).
fof(c_0_213,axiom,
! [X30] :
( ord_less(int,bit1(X30),pls)
<=> ord_less(int,X30,pls) ),
c_0_78 ).
fof(c_0_214,axiom,
! [X30] :
( ord_less(int,pls,bit1(X30))
<=> ord_less_eq(int,pls,X30) ),
c_0_79 ).
fof(c_0_215,axiom,
! [X30] :
( ord_less_eq(int,bit1(X30),pls)
<=> ord_less(int,X30,pls) ),
c_0_80 ).
fof(c_0_216,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3) ),
c_0_81 ).
fof(c_0_217,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3) ),
c_0_82 ).
fof(c_0_218,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3) ),
c_0_83 ).
fof(c_0_219,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3) ),
c_0_84 ).
fof(c_0_220,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3) ),
c_0_85 ).
fof(c_0_221,axiom,
! [X16,X17] :
( ord_less(int,X16,X17)
<=> ( ord_less_eq(int,X16,X17)
& X16 != X17 ) ),
c_0_86 ).
fof(c_0_222,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3) ),
c_0_87 ).
fof(c_0_223,axiom,
! [X9,X8] :
( twoSqu33214720sum2sq(X8)
=> ( twoSqu33214720sum2sq(X9)
=> twoSqu33214720sum2sq(times_times(int,X8,X9)) ) ),
c_0_88 ).
fof(c_0_224,axiom,
! [X1] :
( semiring_1(X1)
=> power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1) ),
c_0_89 ).
fof(c_0_225,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37] : plus_plus(X1,X6,X37) = plus_plus(X1,X37,X6) ),
c_0_90 ).
fof(c_0_226,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7] : times_times(X1,X6,X7) = times_times(X1,X7,X6) ),
c_0_91 ).
fof(c_0_227,axiom,
! [X8,X9] :
( ord_less(int,X8,X9)
| X8 = X9
| ord_less(int,X9,X8) ),
c_0_92 ).
fof(c_0_228,axiom,
! [X15,X11] :
( ord_less_eq(int,X15,X11)
| ord_less_eq(int,X11,X15) ),
c_0_93 ).
fof(c_0_229,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
c_0_94 ).
fof(c_0_230,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
c_0_95 ).
fof(c_0_231,axiom,
! [X1] :
( number_ring(X1)
=> plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls))) ),
c_0_96 ).
fof(c_0_232,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
c_0_97 ).
fof(c_0_233,axiom,
! [X1] :
( number(X1)
=> ! [X17,X24] :
( number_number_of(X1,X17) = ti(X1,X24)
<=> ti(X1,X24) = number_number_of(X1,X17) ) ),
c_0_98 ).
fof(c_0_234,plain,
~ ord_less(int,pls,pls),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_235,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8] : power_power(X1,X8,one_one(nat)) = ti(X1,X8) ),
c_0_100 ).
fof(c_0_236,axiom,
! [X2,X1] :
( number(X1)
=> ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
c_0_101 ).
fof(c_0_237,axiom,
! [X1] :
( ( number_ring(X1)
& ring_char_0(X1) )
=> ! [X24,X25] :
( number_number_of(X1,X24) = number_number_of(X1,X25)
<=> X24 = X25 ) ),
c_0_102 ).
fof(c_0_238,axiom,
! [X2,X1] :
( number(X1)
=> number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2) ),
c_0_103 ).
fof(c_0_239,axiom,
ord_less_eq(int,one_one(int),t),
c_0_104 ).
fof(c_0_240,axiom,
! [X42,X43] : ti(X42,ti(X42,X43)) = ti(X42,X43),
c_0_105 ).
fof(c_0_241,axiom,
! [X11] : ord_less_eq(int,X11,X11),
c_0_106 ).
fof(c_0_242,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))),
c_0_107 ).
fof(c_0_243,axiom,
ord_less_eq(int,pls,pls),
c_0_108 ).
fof(c_0_244,axiom,
! [X2] :
( twoSqu33214720sum2sq(ti(int,X2))
<=> twoSqu33214720sum2sq(X2) ),
c_0_109 ).
fof(c_0_245,axiom,
! [X2] :
( zprime(ti(int,X2))
<=> zprime(X2) ),
c_0_110 ).
fof(c_0_246,axiom,
! [X1] :
( semiring_1(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
c_0_111 ).
fof(c_0_247,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
c_0_112 ).
fof(c_0_248,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
c_0_113 ).
fof(c_0_249,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
c_0_114 ).
fof(c_0_250,axiom,
! [X30,X31] :
( bit0(X30) = bit0(X31)
<=> X30 = X31 ),
c_0_115 ).
fof(c_0_251,axiom,
! [X30,X31] :
( bit1(X30) = bit1(X31)
<=> X30 = X31 ),
c_0_116 ).
fof(c_0_252,axiom,
! [X18] : number_number_of(int,X18) = X18,
c_0_117 ).
fof(c_0_253,axiom,
ti(int,t) = t,
c_0_118 ).
fof(c_0_254,axiom,
ti(int,s) = s,
c_0_119 ).
fof(c_0_255,axiom,
number(nat),
c_0_120 ).
fof(c_0_256,axiom,
semiring_1(nat),
c_0_121 ).
fof(c_0_257,axiom,
monoid_mult(nat),
c_0_122 ).
fof(c_0_258,axiom,
linorder(nat),
c_0_123 ).
fof(c_0_259,axiom,
number_semiring(nat),
c_0_124 ).
fof(c_0_260,axiom,
comm_semiring_1(nat),
c_0_125 ).
fof(c_0_261,axiom,
number(int),
c_0_126 ).
fof(c_0_262,axiom,
number_ring(int),
c_0_127 ).
fof(c_0_263,axiom,
ring_char_0(int),
c_0_128 ).
fof(c_0_264,axiom,
semiring_1(int),
c_0_129 ).
fof(c_0_265,axiom,
monoid_mult(int),
c_0_130 ).
fof(c_0_266,axiom,
linorder(int),
c_0_131 ).
fof(c_0_267,axiom,
number_semiring(int),
c_0_132 ).
fof(c_0_268,axiom,
comm_semiring_1(int),
c_0_133 ).
fof(c_0_269,axiom,
linordered_idom(int),
c_0_134 ).
fof(c_0_270,plain,
! [X8,X9] : power_power(int,plus_plus(int,X8,X9),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X8,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X8,number_number_of(nat,bit0(bit1(pls))))),X9)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X8),power_power(int,X9,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X9,number_number_of(nat,bit1(bit1(pls))))),
inference(variable_rename,[status(thm)],[c_0_135]) ).
fof(c_0_271,plain,
! [X8,X9] : power_power(int,plus_plus(int,X8,X9),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(int,power_power(int,X8,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X8),X9)),power_power(int,X9,number_number_of(nat,bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[c_0_136]) ).
fof(c_0_272,plain,
! [X10,X11,X12] :
( ~ number_semiring(X10)
| power_power(X10,plus_plus(X10,X11,X12),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X10,plus_plus(X10,power_power(X10,X11,number_number_of(nat,bit0(bit1(pls)))),power_power(X10,X12,number_number_of(nat,bit0(bit1(pls))))),times_times(X10,times_times(X10,number_number_of(X10,bit0(bit1(pls))),X11),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])]) ).
fof(c_0_273,axiom,
twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
c_0_138 ).
fof(c_0_274,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)),esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])])]) ).
fof(c_0_275,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),
c_0_140 ).
fof(c_0_276,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)],[c_0_141])])]) ).
fof(c_0_277,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)],[c_0_142])])]) ).
fof(c_0_278,axiom,
ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
c_0_143 ).
fof(c_0_279,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
c_0_144 ).
fof(c_0_280,plain,
! [X37,X38,X39,X40,X41] :
( ~ comm_semiring_1(X37)
| times_times(X37,times_times(X37,X38,X39),times_times(X37,X40,X41)) = times_times(X37,X38,times_times(X37,X39,times_times(X37,X40,X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])])]) ).
fof(c_0_281,plain,
! [X37,X38,X39,X40,X41] :
( ~ comm_semiring_1(X37)
| times_times(X37,times_times(X37,X38,X39),times_times(X37,X40,X41)) = times_times(X37,X40,times_times(X37,times_times(X37,X38,X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])])]) ).
fof(c_0_282,plain,
! [X39,X40,X41,X42,X43] :
( ~ comm_semiring_1(X39)
| plus_plus(X39,plus_plus(X39,X40,X41),plus_plus(X39,X42,X43)) = plus_plus(X39,plus_plus(X39,X40,X42),plus_plus(X39,X41,X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])])]) ).
fof(c_0_283,plain,
! [X37,X38,X39,X40,X41] :
( ~ comm_semiring_1(X37)
| times_times(X37,times_times(X37,X38,X39),times_times(X37,X40,X41)) = times_times(X37,times_times(X37,X38,X40),times_times(X37,X39,X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_148])])]) ).
fof(c_0_284,plain,
! [X13,X14,X15] :
( ~ comm_semiring_1(X13)
| power_power(X13,X14,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X15)) = times_times(X13,power_power(X13,X14,X15),power_power(X13,X14,X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])]) ).
fof(c_0_285,plain,
! [X23,X24,X25,X26] :
( ~ comm_semiring_1(X23)
| times_times(X23,power_power(X23,X24,X25),power_power(X23,X24,X26)) = power_power(X23,X24,plus_plus(nat,X25,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])]) ).
fof(c_0_286,plain,
! [X28,X29,X30,X31] :
( ~ ord_less(int,X30,X31)
| ~ ord_less_eq(int,X28,X29)
| ord_less(int,plus_plus(int,X30,X28),plus_plus(int,X31,X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])]) ).
fof(c_0_287,plain,
! [X16,X17,X18] : power_power(int,X16,plus_plus(nat,X17,X18)) = times_times(int,power_power(int,X16,X17),power_power(int,X16,X18)),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_288,plain,
! [X7] : times_times(int,X7,power_power(int,X7,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X7,number_number_of(nat,bit1(bit1(pls)))),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_289,plain,
! [X24,X25,X26,X27,X28] :
( ( ~ ord_less_eq(X24,number_number_of(X24,X25),number_number_of(X24,X26))
| ~ ord_less(X24,number_number_of(X24,X26),number_number_of(X24,X25))
| ~ number(X24)
| ~ linorder(X24) )
& ( ord_less(X24,number_number_of(X24,X28),number_number_of(X24,X27))
| ord_less_eq(X24,number_number_of(X24,X27),number_number_of(X24,X28))
| ~ number(X24)
| ~ linorder(X24) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_154])])])])]) ).
fof(c_0_290,plain,
! [X21,X22,X23] :
( ~ ord_less_eq(int,X22,X23)
| ord_less_eq(int,plus_plus(int,X21,X22),plus_plus(int,X21,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])]) ).
fof(c_0_291,plain,
! [X21,X22,X23] :
( ~ ord_less(int,X22,X23)
| ord_less(int,plus_plus(int,X22,X21),plus_plus(int,X23,X21)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])]) ).
fof(c_0_292,plain,
! [X39,X40,X41,X42] :
( ~ comm_semiring_1(X39)
| plus_plus(X39,X40,plus_plus(X39,X41,X42)) = plus_plus(X39,X41,plus_plus(X39,X40,X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_157])])]) ).
fof(c_0_293,plain,
! [X39,X40,X41,X42] :
( ~ comm_semiring_1(X39)
| plus_plus(X39,X40,plus_plus(X39,X41,X42)) = plus_plus(X39,plus_plus(X39,X40,X41),X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])])]) ).
fof(c_0_294,plain,
! [X38,X39,X40,X41] :
( ~ comm_semiring_1(X38)
| plus_plus(X38,plus_plus(X38,X39,X40),X41) = plus_plus(X38,X39,plus_plus(X38,X40,X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_159])])]) ).
fof(c_0_295,plain,
! [X38,X39,X40,X41] :
( ~ comm_semiring_1(X38)
| plus_plus(X38,plus_plus(X38,X39,X40),X41) = plus_plus(X38,plus_plus(X38,X39,X41),X40) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_160])])]) ).
fof(c_0_296,plain,
! [X37,X38,X39,X40] :
( ~ comm_semiring_1(X37)
| times_times(X37,X38,times_times(X37,X39,X40)) = times_times(X37,X39,times_times(X37,X38,X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])])]) ).
fof(c_0_297,plain,
! [X37,X38,X39,X40] :
( ~ comm_semiring_1(X37)
| times_times(X37,X38,times_times(X37,X39,X40)) = times_times(X37,times_times(X37,X38,X39),X40) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])])]) ).
fof(c_0_298,plain,
! [X36,X37,X38,X39] :
( ~ comm_semiring_1(X36)
| times_times(X36,times_times(X36,X37,X38),X39) = times_times(X36,X37,times_times(X36,X38,X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])]) ).
fof(c_0_299,plain,
! [X36,X37,X38,X39] :
( ~ comm_semiring_1(X36)
| times_times(X36,times_times(X36,X37,X38),X39) = times_times(X36,times_times(X36,X37,X39),X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_164])])]) ).
fof(c_0_300,plain,
! [X23,X24,X25,X26] :
( ~ comm_semiring_1(X23)
| power_power(X23,power_power(X23,X24,X25),X26) = power_power(X23,X24,times_times(nat,X25,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_165])])]) ).
fof(c_0_301,plain,
! [X33,X34,X35,X36] :
( ( ~ ord_less(int,X34,pls)
| plus_plus(nat,number_number_of(nat,X34),number_number_of(nat,X33)) = number_number_of(nat,X33) )
& ( ~ ord_less(int,X35,pls)
| plus_plus(nat,number_number_of(nat,X36),number_number_of(nat,X35)) = number_number_of(nat,X36)
| ord_less(int,X36,pls) )
& ( ord_less(int,X35,pls)
| plus_plus(nat,number_number_of(nat,X36),number_number_of(nat,X35)) = number_number_of(nat,plus_plus(int,X36,X35))
| ord_less(int,X36,pls) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_166])])])])]) ).
fof(c_0_302,plain,
! [X16,X17,X18] : plus_plus(int,X16,plus_plus(int,X17,X18)) = plus_plus(int,X17,plus_plus(int,X16,X18)),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_303,plain,
! [X42,X43,X44] : plus_plus(int,plus_plus(int,X42,X43),X44) = plus_plus(int,X42,plus_plus(int,X43,X44)),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_304,plain,
! [X42,X43,X44] : times_times(int,times_times(int,X42,X43),X44) = times_times(int,X42,times_times(int,X43,X44)),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_305,plain,
! [X16,X17,X18] : power_power(int,power_power(int,X16,X17),X18) = power_power(int,X16,times_times(nat,X17,X18)),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_306,plain,
! [X18,X19,X20,X21] :
( ( ~ ord_less(int,X18,plus_plus(int,X19,one_one(int)))
| ord_less_eq(int,X18,X19) )
& ( ~ ord_less_eq(int,X20,X21)
| ord_less(int,X20,plus_plus(int,X21,one_one(int))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_171])])])]) ).
fof(c_0_307,plain,
! [X18,X19,X20,X21] :
( ( ~ ord_less_eq(int,plus_plus(int,X18,one_one(int)),X19)
| ord_less(int,X18,X19) )
& ( ~ ord_less(int,X20,X21)
| ord_less_eq(int,plus_plus(int,X20,one_one(int)),X21) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_172])])])]) ).
fof(c_0_308,plain,
! [X12,X13] :
( ~ monoid_mult(X12)
| ~ number(X12)
| power_power(X12,number_number_of(X12,X13),number_number_of(nat,bit0(bit1(pls)))) = times_times(X12,number_number_of(X12,X13),number_number_of(X12,X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_173])])]) ).
fof(c_0_309,plain,
! [X16,X17] :
( ~ ord_less(int,X16,X17)
| ord_less_eq(int,plus_plus(int,X16,one_one(int)),X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_174])]) ).
fof(c_0_310,plain,
! [X26,X27,X28,X29,X30] :
( ( ~ ord_less_eq(X26,number_number_of(X26,X27),number_number_of(X26,X28))
| ord_less_eq(int,X27,X28)
| ~ number_ring(X26)
| ~ linordered_idom(X26) )
& ( ~ ord_less_eq(int,X29,X30)
| ord_less_eq(X26,number_number_of(X26,X29),number_number_of(X26,X30))
| ~ number_ring(X26)
| ~ linordered_idom(X26) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_175])])])])]) ).
fof(c_0_311,plain,
! [X26,X27,X28,X29,X30] :
( ( ~ ord_less(X26,number_number_of(X26,X27),number_number_of(X26,X28))
| ord_less(int,X27,X28)
| ~ number_ring(X26)
| ~ linordered_idom(X26) )
& ( ~ ord_less(int,X29,X30)
| ord_less(X26,number_number_of(X26,X29),number_number_of(X26,X30))
| ~ number_ring(X26)
| ~ linordered_idom(X26) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_176])])])])]) ).
fof(c_0_312,plain,
! [X21,X22,X23] :
( ~ ord_less_eq(int,X22,X23)
| ~ ord_less_eq(int,X23,X21)
| ord_less_eq(int,X22,X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_177])]) ).
fof(c_0_313,plain,
! [X14,X15] :
( ~ number_ring(X14)
| plus_plus(X14,number_number_of(X14,X15),one_one(X14)) = number_number_of(X14,plus_plus(int,X15,bit1(pls))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_178])])]) ).
fof(c_0_314,plain,
! [X12,X13] :
( ~ number_ring(X12)
| plus_plus(X12,one_one(X12),number_number_of(X12,X13)) = number_number_of(X12,plus_plus(int,bit1(pls),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_179])])]) ).
fof(c_0_315,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less_eq(int,number_number_of(int,X32),number_number_of(int,X33))
| ord_less_eq(int,X32,X33) )
& ( ~ ord_less_eq(int,X34,X35)
| ord_less_eq(int,number_number_of(int,X34),number_number_of(int,X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_180])])])]) ).
fof(c_0_316,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less(int,number_number_of(int,X32),number_number_of(int,X33))
| ord_less(int,X32,X33) )
& ( ~ ord_less(int,X34,X35)
| ord_less(int,number_number_of(int,X34),number_number_of(int,X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])])])]) ).
fof(c_0_317,plain,
! [X4,X5,X6] :
( ( ~ ord_less_eq(X6,X4,ti(X6,X5))
| ord_less_eq(X6,X4,X5)
| ~ number(X6)
| ~ linorder(X6) )
& ( ~ ord_less_eq(X6,X4,X5)
| ord_less_eq(X6,X4,ti(X6,X5))
| ~ number(X6)
| ~ linorder(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_182])])]) ).
fof(c_0_318,plain,
! [X4,X5,X6] :
( ( ~ ord_less_eq(X6,ti(X6,X4),X5)
| ord_less_eq(X6,X4,X5)
| ~ number(X6)
| ~ linorder(X6) )
& ( ~ ord_less_eq(X6,X4,X5)
| ord_less_eq(X6,ti(X6,X4),X5)
| ~ number(X6)
| ~ linorder(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])])]) ).
fof(c_0_319,plain,
! [X4,X5,X6] :
( ( ~ ord_less(X6,X4,ti(X6,X5))
| ord_less(X6,X4,X5)
| ~ number(X6)
| ~ linorder(X6) )
& ( ~ ord_less(X6,X4,X5)
| ord_less(X6,X4,ti(X6,X5))
| ~ number(X6)
| ~ linorder(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_184])])]) ).
fof(c_0_320,plain,
! [X4,X5,X6] :
( ( ~ ord_less(X6,ti(X6,X4),X5)
| ord_less(X6,X4,X5)
| ~ number(X6)
| ~ linorder(X6) )
& ( ~ ord_less(X6,X4,X5)
| ord_less(X6,ti(X6,X4),X5)
| ~ number(X6)
| ~ linorder(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_185])])]) ).
fof(c_0_321,plain,
! [X4,X5,X6] :
( ~ monoid_mult(X6)
| ti(X6,power_power(X6,X4,X5)) = power_power(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])]) ).
fof(c_0_322,plain,
! [X4,X5,X6] :
( ~ monoid_mult(X6)
| ti(X6,times_times(X6,X4,X5)) = times_times(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])]) ).
fof(c_0_323,plain,
! [X4,X5,X6] :
( ~ comm_semiring_1(X6)
| ti(X6,plus_plus(X6,X4,X5)) = plus_plus(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])]) ).
fof(c_0_324,plain,
! [X16,X17] :
( ~ ord_less_eq(int,X16,X17)
| ~ ord_less_eq(int,X17,X16)
| X16 = X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_189])]) ).
fof(c_0_325,plain,
! [X7,X8] :
( ~ monoid_mult(X7)
| power_power(X7,X8,number_number_of(nat,bit0(bit1(pls)))) = times_times(X7,X8,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])])]) ).
fof(c_0_326,plain,
! [X9,X10] :
( ~ comm_semiring_1(X9)
| times_times(X9,X10,X10) = power_power(X9,X10,number_number_of(nat,bit0(bit1(pls)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_191])])]) ).
fof(c_0_327,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less_eq(int,bit0(X32),bit1(X33))
| ord_less_eq(int,X32,X33) )
& ( ~ ord_less_eq(int,X34,X35)
| ord_less_eq(int,bit0(X34),bit1(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_192])])])]) ).
fof(c_0_328,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less_eq(int,bit0(X30),bit1(X31))
| ord_less_eq(int,X30,X31) )
& ( ~ ord_less_eq(int,X32,X33)
| ord_less_eq(int,bit0(X32),bit1(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_193])])])]) ).
fof(c_0_329,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less(int,bit1(X32),bit0(X33))
| ord_less(int,X32,X33) )
& ( ~ ord_less(int,X34,X35)
| ord_less(int,bit1(X34),bit0(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_194])])])]) ).
fof(c_0_330,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less(int,bit1(X30),bit0(X31))
| ord_less(int,X30,X31) )
& ( ~ ord_less(int,X32,X33)
| ord_less(int,bit1(X32),bit0(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_195])])])]) ).
fof(c_0_331,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less(int,bit0(X32),bit1(X33))
| ord_less_eq(int,X32,X33) )
& ( ~ ord_less_eq(int,X34,X35)
| ord_less(int,bit0(X34),bit1(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_196])])])]) ).
fof(c_0_332,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less(int,bit0(X30),bit1(X31))
| ord_less_eq(int,X30,X31) )
& ( ~ ord_less_eq(int,X32,X33)
| ord_less(int,bit0(X32),bit1(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])])])]) ).
fof(c_0_333,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less_eq(int,bit1(X32),bit0(X33))
| ord_less(int,X32,X33) )
& ( ~ ord_less(int,X34,X35)
| ord_less_eq(int,bit1(X34),bit0(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_198])])])]) ).
fof(c_0_334,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less_eq(int,bit1(X30),bit0(X31))
| ord_less(int,X30,X31) )
& ( ~ ord_less(int,X32,X33)
| ord_less_eq(int,bit1(X32),bit0(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_199])])])]) ).
fof(c_0_335,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less_eq(int,bit0(X32),bit0(X33))
| ord_less_eq(int,X32,X33) )
& ( ~ ord_less_eq(int,X34,X35)
| ord_less_eq(int,bit0(X34),bit0(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])])])]) ).
fof(c_0_336,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less_eq(int,bit0(X30),bit0(X31))
| ord_less_eq(int,X30,X31) )
& ( ~ ord_less_eq(int,X32,X33)
| ord_less_eq(int,bit0(X32),bit0(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])])]) ).
fof(c_0_337,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less(int,bit0(X32),bit0(X33))
| ord_less(int,X32,X33) )
& ( ~ ord_less(int,X34,X35)
| ord_less(int,bit0(X34),bit0(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])])])]) ).
fof(c_0_338,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less(int,bit0(X30),bit0(X31))
| ord_less(int,X30,X31) )
& ( ~ ord_less(int,X32,X33)
| ord_less(int,bit0(X32),bit0(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_203])])])]) ).
fof(c_0_339,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less_eq(int,bit1(X32),bit1(X33))
| ord_less_eq(int,X32,X33) )
& ( ~ ord_less_eq(int,X34,X35)
| ord_less_eq(int,bit1(X34),bit1(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_204])])])]) ).
fof(c_0_340,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less_eq(int,bit1(X30),bit1(X31))
| ord_less_eq(int,X30,X31) )
& ( ~ ord_less_eq(int,X32,X33)
| ord_less_eq(int,bit1(X32),bit1(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_205])])])]) ).
fof(c_0_341,plain,
! [X32,X33,X34,X35] :
( ( ~ ord_less(int,bit1(X32),bit1(X33))
| ord_less(int,X32,X33) )
& ( ~ ord_less(int,X34,X35)
| ord_less(int,bit1(X34),bit1(X35)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_206])])])]) ).
fof(c_0_342,plain,
! [X30,X31,X32,X33] :
( ( ~ ord_less(int,bit1(X30),bit1(X31))
| ord_less(int,X30,X31) )
& ( ~ ord_less(int,X32,X33)
| ord_less(int,bit1(X32),bit1(X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_207])])])]) ).
fof(c_0_343,plain,
! [X16] : times_times(nat,X16,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X16,X16),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_344,plain,
! [X16] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),X16) = plus_plus(nat,X16,X16),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_345,plain,
! [X31,X32] :
( ( ~ ord_less_eq(int,pls,bit1(X31))
| ord_less_eq(int,pls,X31) )
& ( ~ ord_less_eq(int,pls,X32)
| ord_less_eq(int,pls,bit1(X32)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_210])])])]) ).
fof(c_0_346,plain,
! [X31,X32] :
( ( ~ ord_less(int,pls,bit0(X31))
| ord_less(int,pls,X31) )
& ( ~ ord_less(int,pls,X32)
| ord_less(int,pls,bit0(X32)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_211])])])]) ).
fof(c_0_347,plain,
! [X31,X32] :
( ( ~ ord_less(int,bit0(X31),pls)
| ord_less(int,X31,pls) )
& ( ~ ord_less(int,X32,pls)
| ord_less(int,bit0(X32),pls) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_212])])])]) ).
fof(c_0_348,plain,
! [X31,X32] :
( ( ~ ord_less(int,bit1(X31),pls)
| ord_less(int,X31,pls) )
& ( ~ ord_less(int,X32,pls)
| ord_less(int,bit1(X32),pls) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_213])])])]) ).
fof(c_0_349,plain,
! [X31,X32] :
( ( ~ ord_less(int,pls,bit1(X31))
| ord_less_eq(int,pls,X31) )
& ( ~ ord_less_eq(int,pls,X32)
| ord_less(int,pls,bit1(X32)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_214])])])]) ).
fof(c_0_350,plain,
! [X31,X32] :
( ( ~ ord_less_eq(int,bit1(X31),pls)
| ord_less(int,X31,pls) )
& ( ~ ord_less(int,X32,pls)
| ord_less_eq(int,bit1(X32),pls) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_215])])])]) ).
fof(c_0_351,plain,
! [X4,X5,X6] :
( ~ monoid_mult(X6)
| power_power(X6,ti(X6,X4),X5) = power_power(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_216])]) ).
fof(c_0_352,plain,
! [X4,X5,X6] :
( ~ monoid_mult(X6)
| times_times(X6,X4,ti(X6,X5)) = times_times(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_217])]) ).
fof(c_0_353,plain,
! [X4,X5,X6] :
( ~ monoid_mult(X6)
| times_times(X6,ti(X6,X4),X5) = times_times(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_218])]) ).
fof(c_0_354,plain,
! [X4,X5,X6] :
( ~ comm_semiring_1(X6)
| plus_plus(X6,X4,ti(X6,X5)) = plus_plus(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_219])]) ).
fof(c_0_355,plain,
! [X4,X5,X6] :
( ~ comm_semiring_1(X6)
| plus_plus(X6,ti(X6,X4),X5) = plus_plus(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_220])]) ).
fof(c_0_356,plain,
! [X18,X19,X20,X21] :
( ( ord_less_eq(int,X18,X19)
| ~ ord_less(int,X18,X19) )
& ( X18 != X19
| ~ ord_less(int,X18,X19) )
& ( ~ ord_less_eq(int,X20,X21)
| X20 = X21
| ord_less(int,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_221])])])])]) ).
fof(c_0_357,plain,
! [X4,X5,X6] :
( ~ monoid_mult(X6)
| power_power(X6,X4,ti(nat,X5)) = power_power(X6,X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_222])]) ).
fof(c_0_358,plain,
! [X10,X11] :
( ~ twoSqu33214720sum2sq(X11)
| ~ twoSqu33214720sum2sq(X10)
| twoSqu33214720sum2sq(times_times(int,X11,X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_223])]) ).
fof(c_0_359,plain,
! [X2] :
( ~ semiring_1(X2)
| power_power(X2,one_one(X2),number_number_of(nat,bit0(bit1(pls)))) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_224])]) ).
fof(c_0_360,plain,
! [X38,X39,X40] :
( ~ comm_semiring_1(X38)
| plus_plus(X38,X39,X40) = plus_plus(X38,X40,X39) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_225])])]) ).
fof(c_0_361,plain,
! [X8,X9,X10] :
( ~ comm_semiring_1(X8)
| times_times(X8,X9,X10) = times_times(X8,X10,X9) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_226])])]) ).
fof(c_0_362,plain,
! [X10,X11] :
( ord_less(int,X10,X11)
| X10 = X11
| ord_less(int,X11,X10) ),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_363,plain,
! [X16,X17] :
( ord_less_eq(int,X16,X17)
| ord_less_eq(int,X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_364,plain,
! [X16,X17] : plus_plus(int,X16,X17) = plus_plus(int,X17,X16),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_365,plain,
! [X16,X17] : times_times(int,X16,X17) = times_times(int,X17,X16),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_366,plain,
! [X2] :
( ~ number_ring(X2)
| plus_plus(X2,one_one(X2),one_one(X2)) = number_number_of(X2,bit0(bit1(pls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_231])]) ).
fof(c_0_367,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
c_0_232 ).
fof(c_0_368,plain,
! [X25,X26,X27,X28,X29] :
( ( number_number_of(X25,X26) != ti(X25,X27)
| ti(X25,X27) = number_number_of(X25,X26)
| ~ number(X25) )
& ( ti(X25,X29) != number_number_of(X25,X28)
| number_number_of(X25,X28) = ti(X25,X29)
| ~ number(X25) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_233])])])])]) ).
fof(c_0_369,plain,
~ ord_less(int,pls,pls),
c_0_234 ).
fof(c_0_370,plain,
! [X9,X10] :
( ~ comm_semiring_1(X9)
| power_power(X9,X10,one_one(nat)) = ti(X9,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_235])])]) ).
fof(c_0_371,plain,
! [X3,X4] :
( ~ number(X4)
| ti(X4,number_number_of(X4,X3)) = number_number_of(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_236])]) ).
fof(c_0_372,plain,
! [X26,X27,X28,X29,X30] :
( ( number_number_of(X26,X27) != number_number_of(X26,X28)
| X27 = X28
| ~ number_ring(X26)
| ~ ring_char_0(X26) )
& ( X29 != X30
| number_number_of(X26,X29) = number_number_of(X26,X30)
| ~ number_ring(X26)
| ~ ring_char_0(X26) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_237])])])])]) ).
fof(c_0_373,plain,
! [X3,X4] :
( ~ number(X4)
| number_number_of(X4,ti(int,X3)) = number_number_of(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_238])]) ).
fof(c_0_374,axiom,
ord_less_eq(int,one_one(int),t),
c_0_239 ).
fof(c_0_375,plain,
! [X44,X45] : ti(X44,ti(X44,X45)) = ti(X44,X45),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_376,plain,
! [X12] : ord_less_eq(int,X12,X12),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_377,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))),
c_0_242 ).
fof(c_0_378,axiom,
ord_less_eq(int,pls,pls),
c_0_243 ).
fof(c_0_379,plain,
! [X3,X4] :
( ( ~ twoSqu33214720sum2sq(ti(int,X3))
| twoSqu33214720sum2sq(X3) )
& ( ~ twoSqu33214720sum2sq(X4)
| twoSqu33214720sum2sq(ti(int,X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_244])])])]) ).
fof(c_0_380,plain,
! [X3,X4] :
( ( ~ zprime(ti(int,X3))
| zprime(X3) )
& ( ~ zprime(X4)
| zprime(ti(int,X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_245])])])]) ).
fof(c_0_381,plain,
! [X2] :
( ~ semiring_1(X2)
| ti(X2,one_one(X2)) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_246])]) ).
fof(c_0_382,plain,
! [X2] : ti(X2,undefined(X2)) = undefined(X2),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_383,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
c_0_248 ).
fof(c_0_384,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
c_0_249 ).
fof(c_0_385,plain,
! [X32,X33,X34,X35] :
( ( bit0(X32) != bit0(X33)
| X32 = X33 )
& ( X34 != X35
| bit0(X34) = bit0(X35) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_250])])])]) ).
fof(c_0_386,plain,
! [X32,X33,X34,X35] :
( ( bit1(X32) != bit1(X33)
| X32 = X33 )
& ( X34 != X35
| bit1(X34) = bit1(X35) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_251])])])]) ).
fof(c_0_387,plain,
! [X19] : number_number_of(int,X19) = X19,
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_388,axiom,
ti(int,t) = t,
c_0_253 ).
fof(c_0_389,axiom,
ti(int,s) = s,
c_0_254 ).
fof(c_0_390,axiom,
number(nat),
c_0_255 ).
fof(c_0_391,axiom,
semiring_1(nat),
c_0_256 ).
fof(c_0_392,axiom,
monoid_mult(nat),
c_0_257 ).
fof(c_0_393,axiom,
linorder(nat),
c_0_258 ).
fof(c_0_394,axiom,
number_semiring(nat),
c_0_259 ).
fof(c_0_395,axiom,
comm_semiring_1(nat),
c_0_260 ).
fof(c_0_396,axiom,
number(int),
c_0_261 ).
fof(c_0_397,axiom,
number_ring(int),
c_0_262 ).
fof(c_0_398,axiom,
ring_char_0(int),
c_0_263 ).
fof(c_0_399,axiom,
semiring_1(int),
c_0_264 ).
fof(c_0_400,axiom,
monoid_mult(int),
c_0_265 ).
fof(c_0_401,axiom,
linorder(int),
c_0_266 ).
fof(c_0_402,axiom,
number_semiring(int),
c_0_267 ).
fof(c_0_403,axiom,
comm_semiring_1(int),
c_0_268 ).
fof(c_0_404,axiom,
linordered_idom(int),
c_0_269 ).
cnf(c_0_405,plain,
power_power(int,plus_plus(int,X1,X2),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X1,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))),X2)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X1),power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X2,number_number_of(nat,bit1(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_406,plain,
power_power(int,plus_plus(int,X1,X2),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X1),X2)),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_407,plain,
( power_power(X1,plus_plus(X1,X2,X3),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X1,plus_plus(X1,power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X3,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X2),X3))
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_408,plain,
twoSqu33214720sum2sq(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)],[c_0_273]) ).
cnf(c_0_409,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)),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_410,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)],[c_0_275]) ).
cnf(c_0_411,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_276]) ).
cnf(c_0_412,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_277]) ).
cnf(c_0_413,plain,
ord_less(int,t,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_278]) ).
cnf(c_0_414,plain,
zprime(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_279]) ).
cnf(c_0_415,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X2,times_times(X1,X3,times_times(X1,X4,X5)))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_416,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X4,times_times(X1,times_times(X1,X2,X3),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_417,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),plus_plus(X1,X4,X5)) = plus_plus(X1,plus_plus(X1,X2,X4),plus_plus(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_418,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,times_times(X1,X2,X4),times_times(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_419,plain,
( power_power(X1,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X3)) = times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X3))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_420,plain,
( times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X4)) = power_power(X1,X2,plus_plus(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_421,plain,
( ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X4))
| ~ ord_less_eq(int,X2,X4)
| ~ ord_less(int,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_422,plain,
power_power(int,X1,plus_plus(nat,X2,X3)) = times_times(int,power_power(int,X1,X2),power_power(int,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_423,plain,
times_times(int,X1,power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X1,number_number_of(nat,bit1(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_424,plain,
( ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less_eq(X1,number_number_of(X1,X3),number_number_of(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_425,plain,
( ord_less_eq(int,plus_plus(int,X1,X2),plus_plus(int,X1,X3))
| ~ ord_less_eq(int,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_426,plain,
( ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X2))
| ~ ord_less(int,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_427,plain,
( plus_plus(X1,X2,plus_plus(X1,X3,X4)) = plus_plus(X1,X3,plus_plus(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_428,plain,
( plus_plus(X1,X2,plus_plus(X1,X3,X4)) = plus_plus(X1,plus_plus(X1,X2,X3),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_429,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_430,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,plus_plus(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_431,plain,
( times_times(X1,X2,times_times(X1,X3,X4)) = times_times(X1,X3,times_times(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_432,plain,
( times_times(X1,X2,times_times(X1,X3,X4)) = times_times(X1,times_times(X1,X2,X3),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_433,plain,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_434,plain,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,times_times(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_435,plain,
( power_power(X1,power_power(X1,X2,X3),X4) = power_power(X1,X2,times_times(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_436,plain,
( ord_less(int,X1,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,plus_plus(int,X1,X2))
| ord_less(int,X2,pls) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_437,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_302]) ).
cnf(c_0_438,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_303]) ).
cnf(c_0_439,plain,
times_times(int,times_times(int,X1,X2),X3) = times_times(int,X1,times_times(int,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_440,plain,
power_power(int,power_power(int,X1,X2),X3) = power_power(int,X1,times_times(nat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_441,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,plus_plus(int,X2,one_one(int))) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_442,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_443,plain,
( power_power(X1,number_number_of(X1,X2),number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,number_number_of(X1,X2),number_number_of(X1,X2))
| ~ number(X1)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_444,plain,
( ord_less(int,X1,plus_plus(int,X2,one_one(int)))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_445,plain,
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_446,plain,
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_447,plain,
( ord_less(int,X1,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X1)
| ~ ord_less(int,X2,pls) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_448,plain,
( ord_less_eq(int,X2,X3)
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_449,plain,
( ord_less(int,X2,X3)
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_450,plain,
( ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ~ linorder(X1)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_451,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,X3,X2)
| ~ ord_less_eq(int,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_452,plain,
( plus_plus(X1,number_number_of(X1,X2),one_one(X1)) = number_number_of(X1,plus_plus(int,X2,bit1(pls)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_453,plain,
( plus_plus(X1,one_one(X1),number_number_of(X1,X2)) = number_number_of(X1,plus_plus(int,bit1(pls),X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_454,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_455,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_456,plain,
( ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less_eq(int,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_457,plain,
( ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less(int,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_458,plain,
( ord_less_eq(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,ti(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_459,plain,
( ord_less_eq(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,ti(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_460,plain,
( ord_less(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,ti(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_461,plain,
( ord_less(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,ti(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_462,plain,
( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X2)
| ~ ord_less(int,X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_463,plain,
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_464,plain,
( ord_less(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_465,plain,
( ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_466,plain,
( ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_467,plain,
( ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_468,plain,
( ord_less_eq(X1,X2,ti(X1,X3))
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_469,plain,
( ord_less_eq(X1,ti(X1,X2),X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_470,plain,
( ord_less(X1,X2,ti(X1,X3))
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_471,plain,
( ord_less(X1,ti(X1,X2),X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_472,plain,
( X1 = X2
| ~ ord_less_eq(int,X2,X1)
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_473,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_325]) ).
cnf(c_0_474,plain,
( times_times(X1,X2,X2) = power_power(X1,X2,number_number_of(nat,bit0(bit1(pls))))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_475,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_476,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_477,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_478,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_479,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_480,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_481,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_482,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_483,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_484,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_485,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_486,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_487,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_488,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_489,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_490,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_491,plain,
times_times(nat,X1,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_492,plain,
times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) = plus_plus(nat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_493,plain,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_494,plain,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_495,plain,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_496,plain,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_497,plain,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_498,plain,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_499,plain,
( ord_less_eq(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_500,plain,
( ord_less_eq(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_501,plain,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_502,plain,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_503,plain,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_504,plain,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_505,plain,
( ord_less_eq(int,bit1(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_506,plain,
( ord_less_eq(int,bit1(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_507,plain,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_508,plain,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_509,plain,
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,bit1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_510,plain,
( ord_less(int,pls,X1)
| ~ ord_less(int,pls,bit0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_511,plain,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit0(X1),pls) ),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_512,plain,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit1(X1),pls) ),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_513,plain,
( ord_less_eq(int,pls,X1)
| ~ ord_less(int,pls,bit1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_514,plain,
( ord_less(int,X1,pls)
| ~ ord_less_eq(int,bit1(X1),pls) ),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_515,plain,
( power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_516,plain,
( times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_517,plain,
( times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_518,plain,
( plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_519,plain,
( plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_520,plain,
( ord_less(int,X1,X2)
| X1 = X2
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_521,plain,
( ord_less_eq(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_522,plain,
( ord_less(int,pls,bit0(X1))
| ~ ord_less(int,pls,X1) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_523,plain,
( ord_less(int,bit0(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_524,plain,
( ord_less(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_525,plain,
( ord_less(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_526,plain,
( ord_less_eq(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_527,plain,
( power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_528,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_529,plain,
( twoSqu33214720sum2sq(times_times(int,X1,X2))
| ~ twoSqu33214720sum2sq(X2)
| ~ twoSqu33214720sum2sq(X1) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_530,plain,
( power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_531,plain,
( plus_plus(X1,X2,X3) = plus_plus(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_532,plain,
( times_times(X1,X2,X3) = times_times(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_533,plain,
( ord_less(int,X1,X2)
| X2 = X1
| ord_less(int,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_534,plain,
( ord_less_eq(int,X1,X2)
| ord_less_eq(int,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_535,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_536,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_537,plain,
( plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_538,plain,
( ~ ord_less(int,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_539,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_540,plain,
( ti(X1,X2) = number_number_of(X1,X3)
| ~ number(X1)
| number_number_of(X1,X3) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_541,plain,
( number_number_of(X1,X2) = ti(X1,X3)
| ~ number(X1)
| ti(X1,X3) != number_number_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_542,plain,
~ ord_less(int,pls,pls),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_543,plain,
( power_power(X1,X2,one_one(nat)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_544,plain,
( ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_545,plain,
( X2 = X3
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_546,plain,
( number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_547,plain,
ord_less_eq(int,one_one(int),t),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_548,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_549,plain,
ord_less_eq(int,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_550,plain,
zprime(number_number_of(int,bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_551,plain,
ord_less_eq(int,pls,pls),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_552,plain,
( twoSqu33214720sum2sq(X1)
| ~ twoSqu33214720sum2sq(ti(int,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_553,plain,
( zprime(X1)
| ~ zprime(ti(int,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_554,plain,
( number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_555,plain,
( twoSqu33214720sum2sq(ti(int,X1))
| ~ twoSqu33214720sum2sq(X1) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_556,plain,
( zprime(ti(int,X1))
| ~ zprime(X1) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_557,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_558,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_559,plain,
one_one(nat) = number_number_of(nat,bit1(pls)),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_560,plain,
number_number_of(nat,bit1(pls)) = one_one(nat),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_561,plain,
( X1 = X2
| bit0(X1) != bit0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_562,plain,
( X1 = X2
| bit1(X1) != bit1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_563,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_564,plain,
( bit0(X1) = bit0(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_565,plain,
( bit1(X1) = bit1(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_566,plain,
ti(int,t) = t,
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_567,plain,
ti(int,s) = s,
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_568,plain,
number(nat),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_569,plain,
semiring_1(nat),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_570,plain,
monoid_mult(nat),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_571,plain,
linorder(nat),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_572,plain,
number_semiring(nat),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_573,plain,
comm_semiring_1(nat),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_574,plain,
number(int),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_575,plain,
number_ring(int),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_576,plain,
ring_char_0(int),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_577,plain,
semiring_1(int),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_578,plain,
monoid_mult(int),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_579,plain,
linorder(int),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_580,plain,
number_semiring(int),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_581,plain,
comm_semiring_1(int),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_582,plain,
linordered_idom(int),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_583,plain,
plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X1,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))),X2)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X1),power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X2,number_number_of(nat,bit1(bit1(pls))))) = power_power(int,plus_plus(int,X1,X2),number_number_of(nat,bit1(bit1(pls)))),
c_0_405,
[final] ).
cnf(c_0_584,plain,
plus_plus(int,plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X1),X2)),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,plus_plus(int,X1,X2),number_number_of(nat,bit0(bit1(pls)))),
c_0_406,
[final] ).
cnf(c_0_585,plain,
( plus_plus(X1,plus_plus(X1,power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X3,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X2),X3)) = power_power(X1,plus_plus(X1,X2,X3),number_number_of(nat,bit0(bit1(pls))))
| ~ number_semiring(X1) ),
c_0_407,
[final] ).
cnf(c_0_586,plain,
twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
c_0_408,
[final] ).
cnf(c_0_587,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),esk5_0) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
c_0_409,
[final] ).
cnf(c_0_588,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
c_0_410,
[final] ).
cnf(c_0_589,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) ),
c_0_411,
[final] ).
cnf(c_0_590,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))
| one_one(int) != t ),
c_0_412,
[final] ).
cnf(c_0_591,plain,
ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
c_0_413,
[final] ).
cnf(c_0_592,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
c_0_414,
[final] ).
cnf(c_0_593,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X2,times_times(X1,X3,times_times(X1,X4,X5)))
| ~ comm_semiring_1(X1) ),
c_0_415,
[final] ).
cnf(c_0_594,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X4,times_times(X1,times_times(X1,X2,X3),X5))
| ~ comm_semiring_1(X1) ),
c_0_416,
[final] ).
cnf(c_0_595,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),plus_plus(X1,X4,X5)) = plus_plus(X1,plus_plus(X1,X2,X4),plus_plus(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
c_0_417,
[final] ).
cnf(c_0_596,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,times_times(X1,X2,X4),times_times(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
c_0_418,
[final] ).
cnf(c_0_597,plain,
( power_power(X1,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X3)) = times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X3))
| ~ comm_semiring_1(X1) ),
c_0_419,
[final] ).
cnf(c_0_598,plain,
( times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X4)) = power_power(X1,X2,plus_plus(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
c_0_420,
[final] ).
cnf(c_0_599,plain,
( ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X4))
| ~ ord_less_eq(int,X2,X4)
| ~ ord_less(int,X1,X3) ),
c_0_421,
[final] ).
cnf(c_0_600,plain,
times_times(int,power_power(int,X1,X2),power_power(int,X1,X3)) = power_power(int,X1,plus_plus(nat,X2,X3)),
c_0_422,
[final] ).
cnf(c_0_601,plain,
times_times(int,X1,power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X1,number_number_of(nat,bit1(bit1(pls)))),
c_0_423,
[final] ).
cnf(c_0_602,plain,
( ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less_eq(X1,number_number_of(X1,X3),number_number_of(X1,X2)) ),
c_0_424,
[final] ).
cnf(c_0_603,plain,
( ord_less_eq(int,plus_plus(int,X1,X2),plus_plus(int,X1,X3))
| ~ ord_less_eq(int,X2,X3) ),
c_0_425,
[final] ).
cnf(c_0_604,plain,
( ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X2))
| ~ ord_less(int,X1,X3) ),
c_0_426,
[final] ).
cnf(c_0_605,plain,
( plus_plus(X1,X2,plus_plus(X1,X3,X4)) = plus_plus(X1,X3,plus_plus(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
c_0_427,
[final] ).
cnf(c_0_606,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
c_0_428,
[final] ).
cnf(c_0_607,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
c_0_429,
[final] ).
cnf(c_0_608,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,plus_plus(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
c_0_430,
[final] ).
cnf(c_0_609,plain,
( times_times(X1,X2,times_times(X1,X3,X4)) = times_times(X1,X3,times_times(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
c_0_431,
[final] ).
cnf(c_0_610,plain,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
c_0_432,
[final] ).
cnf(c_0_611,plain,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
c_0_433,
[final] ).
cnf(c_0_612,plain,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,times_times(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
c_0_434,
[final] ).
cnf(c_0_613,plain,
( power_power(X1,power_power(X1,X2,X3),X4) = power_power(X1,X2,times_times(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
c_0_435,
[final] ).
cnf(c_0_614,plain,
( ord_less(int,X1,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,plus_plus(int,X1,X2))
| ord_less(int,X2,pls) ),
c_0_436,
[final] ).
cnf(c_0_615,plain,
plus_plus(int,X1,plus_plus(int,X2,X3)) = plus_plus(int,X2,plus_plus(int,X1,X3)),
c_0_437,
[final] ).
cnf(c_0_616,plain,
plus_plus(int,plus_plus(int,X1,X2),X3) = plus_plus(int,X1,plus_plus(int,X2,X3)),
c_0_438,
[final] ).
cnf(c_0_617,plain,
times_times(int,times_times(int,X1,X2),X3) = times_times(int,X1,times_times(int,X2,X3)),
c_0_439,
[final] ).
cnf(c_0_618,plain,
power_power(int,power_power(int,X1,X2),X3) = power_power(int,X1,times_times(nat,X2,X3)),
c_0_440,
[final] ).
cnf(c_0_619,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,plus_plus(int,X2,one_one(int))) ),
c_0_441,
[final] ).
cnf(c_0_620,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2) ),
c_0_442,
[final] ).
cnf(c_0_621,plain,
( power_power(X1,number_number_of(X1,X2),number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,number_number_of(X1,X2),number_number_of(X1,X2))
| ~ number(X1)
| ~ monoid_mult(X1) ),
c_0_443,
[final] ).
cnf(c_0_622,plain,
( ord_less(int,X1,plus_plus(int,X2,one_one(int)))
| ~ ord_less_eq(int,X1,X2) ),
c_0_444,
[final] ).
cnf(c_0_623,plain,
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ~ ord_less(int,X1,X2) ),
c_0_445,
[final] ).
cnf(c_0_624,plain,
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ~ ord_less(int,X1,X2) ),
c_0_446,
[final] ).
cnf(c_0_625,plain,
( ord_less(int,X1,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X1)
| ~ ord_less(int,X2,pls) ),
c_0_447,
[final] ).
cnf(c_0_626,plain,
( ord_less_eq(int,X2,X3)
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
c_0_448,
[final] ).
cnf(c_0_627,plain,
( ord_less(int,X2,X3)
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
c_0_449,
[final] ).
cnf(c_0_628,plain,
( ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ~ linorder(X1)
| ~ number(X1) ),
c_0_450,
[final] ).
cnf(c_0_629,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,X3,X2)
| ~ ord_less_eq(int,X1,X3) ),
c_0_451,
[final] ).
cnf(c_0_630,plain,
( plus_plus(X1,number_number_of(X1,X2),one_one(X1)) = number_number_of(X1,plus_plus(int,X2,bit1(pls)))
| ~ number_ring(X1) ),
c_0_452,
[final] ).
cnf(c_0_631,plain,
( plus_plus(X1,one_one(X1),number_number_of(X1,X2)) = number_number_of(X1,plus_plus(int,bit1(pls),X2))
| ~ number_ring(X1) ),
c_0_453,
[final] ).
cnf(c_0_632,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2)) ),
c_0_454,
[final] ).
cnf(c_0_633,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X2)) ),
c_0_455,
[final] ).
cnf(c_0_634,plain,
( ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less_eq(int,X2,X3) ),
c_0_456,
[final] ).
cnf(c_0_635,plain,
( ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less(int,X2,X3) ),
c_0_457,
[final] ).
cnf(c_0_636,plain,
( ord_less_eq(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,ti(X1,X3)) ),
c_0_458,
[final] ).
cnf(c_0_637,plain,
( ord_less_eq(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,ti(X1,X2),X3) ),
c_0_459,
[final] ).
cnf(c_0_638,plain,
( ord_less(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,ti(X1,X3)) ),
c_0_460,
[final] ).
cnf(c_0_639,plain,
( ord_less(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,ti(X1,X2),X3) ),
c_0_461,
[final] ).
cnf(c_0_640,plain,
( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X2)
| ~ ord_less(int,X1,pls) ),
c_0_462,
[final] ).
cnf(c_0_641,plain,
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_463,
[final] ).
cnf(c_0_642,plain,
( ord_less(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less(int,X1,X2) ),
c_0_464,
[final] ).
cnf(c_0_643,plain,
( ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
c_0_465,
[final] ).
cnf(c_0_644,plain,
( ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
c_0_466,
[final] ).
cnf(c_0_645,plain,
( ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
c_0_467,
[final] ).
cnf(c_0_646,plain,
( ord_less_eq(X1,X2,ti(X1,X3))
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
c_0_468,
[final] ).
cnf(c_0_647,plain,
( ord_less_eq(X1,ti(X1,X2),X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
c_0_469,
[final] ).
cnf(c_0_648,plain,
( ord_less(X1,X2,ti(X1,X3))
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
c_0_470,
[final] ).
cnf(c_0_649,plain,
( ord_less(X1,ti(X1,X2),X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
c_0_471,
[final] ).
cnf(c_0_650,plain,
( X1 = X2
| ~ ord_less_eq(int,X2,X1)
| ~ ord_less_eq(int,X1,X2) ),
c_0_472,
[final] ).
cnf(c_0_651,plain,
( power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X2,X2)
| ~ monoid_mult(X1) ),
c_0_473,
[final] ).
cnf(c_0_652,plain,
( times_times(X1,X2,X2) = power_power(X1,X2,number_number_of(nat,bit0(bit1(pls))))
| ~ comm_semiring_1(X1) ),
c_0_474,
[final] ).
cnf(c_0_653,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
c_0_475,
[final] ).
cnf(c_0_654,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
c_0_476,
[final] ).
cnf(c_0_655,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
c_0_477,
[final] ).
cnf(c_0_656,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
c_0_478,
[final] ).
cnf(c_0_657,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
c_0_479,
[final] ).
cnf(c_0_658,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
c_0_480,
[final] ).
cnf(c_0_659,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit0(X2)) ),
c_0_481,
[final] ).
cnf(c_0_660,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit0(X2)) ),
c_0_482,
[final] ).
cnf(c_0_661,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
c_0_483,
[final] ).
cnf(c_0_662,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
c_0_484,
[final] ).
cnf(c_0_663,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
c_0_485,
[final] ).
cnf(c_0_664,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
c_0_486,
[final] ).
cnf(c_0_665,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit1(X2)) ),
c_0_487,
[final] ).
cnf(c_0_666,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit1(X2)) ),
c_0_488,
[final] ).
cnf(c_0_667,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
c_0_489,
[final] ).
cnf(c_0_668,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
c_0_490,
[final] ).
cnf(c_0_669,plain,
times_times(nat,X1,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X1,X1),
c_0_491,
[final] ).
cnf(c_0_670,plain,
times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) = plus_plus(nat,X1,X1),
c_0_492,
[final] ).
cnf(c_0_671,plain,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_493,
[final] ).
cnf(c_0_672,plain,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_494,
[final] ).
cnf(c_0_673,plain,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
c_0_495,
[final] ).
cnf(c_0_674,plain,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
c_0_496,
[final] ).
cnf(c_0_675,plain,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_497,
[final] ).
cnf(c_0_676,plain,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_498,
[final] ).
cnf(c_0_677,plain,
( ord_less_eq(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
c_0_499,
[final] ).
cnf(c_0_678,plain,
( ord_less_eq(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
c_0_500,
[final] ).
cnf(c_0_679,plain,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_501,
[final] ).
cnf(c_0_680,plain,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_502,
[final] ).
cnf(c_0_681,plain,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
c_0_503,
[final] ).
cnf(c_0_682,plain,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
c_0_504,
[final] ).
cnf(c_0_683,plain,
( ord_less_eq(int,bit1(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_505,
[final] ).
cnf(c_0_684,plain,
( ord_less_eq(int,bit1(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
c_0_506,
[final] ).
cnf(c_0_685,plain,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
c_0_507,
[final] ).
cnf(c_0_686,plain,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
c_0_508,
[final] ).
cnf(c_0_687,plain,
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,bit1(X1)) ),
c_0_509,
[final] ).
cnf(c_0_688,plain,
( ord_less(int,pls,X1)
| ~ ord_less(int,pls,bit0(X1)) ),
c_0_510,
[final] ).
cnf(c_0_689,plain,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit0(X1),pls) ),
c_0_511,
[final] ).
cnf(c_0_690,plain,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit1(X1),pls) ),
c_0_512,
[final] ).
cnf(c_0_691,plain,
( ord_less_eq(int,pls,X1)
| ~ ord_less(int,pls,bit1(X1)) ),
c_0_513,
[final] ).
cnf(c_0_692,plain,
( ord_less(int,X1,pls)
| ~ ord_less_eq(int,bit1(X1),pls) ),
c_0_514,
[final] ).
cnf(c_0_693,plain,
( power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
c_0_515,
[final] ).
cnf(c_0_694,plain,
( times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
c_0_516,
[final] ).
cnf(c_0_695,plain,
( times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
c_0_517,
[final] ).
cnf(c_0_696,plain,
( plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
c_0_518,
[final] ).
cnf(c_0_697,plain,
( plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
c_0_519,
[final] ).
cnf(c_0_698,plain,
( ord_less(int,X1,X2)
| X1 = X2
| ~ ord_less_eq(int,X1,X2) ),
c_0_520,
[final] ).
cnf(c_0_699,plain,
( ord_less_eq(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
c_0_521,
[final] ).
cnf(c_0_700,plain,
( ord_less(int,pls,bit0(X1))
| ~ ord_less(int,pls,X1) ),
c_0_522,
[final] ).
cnf(c_0_701,plain,
( ord_less(int,bit0(X1),pls)
| ~ ord_less(int,X1,pls) ),
c_0_523,
[final] ).
cnf(c_0_702,plain,
( ord_less(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
c_0_524,
[final] ).
cnf(c_0_703,plain,
( ord_less(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
c_0_525,
[final] ).
cnf(c_0_704,plain,
( ord_less_eq(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
c_0_526,
[final] ).
cnf(c_0_705,plain,
( power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
c_0_527,
[final] ).
cnf(c_0_706,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,X2) ),
c_0_528,
[final] ).
cnf(c_0_707,plain,
( twoSqu33214720sum2sq(times_times(int,X1,X2))
| ~ twoSqu33214720sum2sq(X2)
| ~ twoSqu33214720sum2sq(X1) ),
c_0_529,
[final] ).
cnf(c_0_708,plain,
( power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1)
| ~ semiring_1(X1) ),
c_0_530,
[final] ).
cnf(c_0_709,plain,
( plus_plus(X1,X2,X3) = plus_plus(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
c_0_531,
[final] ).
cnf(c_0_710,plain,
( times_times(X1,X2,X3) = times_times(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
c_0_532,
[final] ).
cnf(c_0_711,plain,
( ord_less(int,X1,X2)
| X2 = X1
| ord_less(int,X2,X1) ),
c_0_533,
[final] ).
cnf(c_0_712,plain,
( ord_less_eq(int,X1,X2)
| ord_less_eq(int,X2,X1) ),
c_0_534,
[final] ).
cnf(c_0_713,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
c_0_535,
[final] ).
cnf(c_0_714,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
c_0_536,
[final] ).
cnf(c_0_715,plain,
( plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls)))
| ~ number_ring(X1) ),
c_0_537,
[final] ).
cnf(c_0_716,plain,
( ~ ord_less(int,X1,X2)
| X1 != X2 ),
c_0_538,
[final] ).
cnf(c_0_717,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
c_0_539,
[final] ).
cnf(c_0_718,plain,
( ti(X1,X2) = number_number_of(X1,X3)
| ~ number(X1)
| number_number_of(X1,X3) != ti(X1,X2) ),
c_0_540,
[final] ).
cnf(c_0_719,plain,
( number_number_of(X1,X2) = ti(X1,X3)
| ~ number(X1)
| ti(X1,X3) != number_number_of(X1,X2) ),
c_0_541,
[final] ).
cnf(c_0_720,plain,
~ ord_less(int,pls,pls),
c_0_542,
[final] ).
cnf(c_0_721,plain,
( power_power(X1,X2,one_one(nat)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
c_0_543,
[final] ).
cnf(c_0_722,plain,
( ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
c_0_544,
[final] ).
cnf(c_0_723,plain,
( X2 = X3
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
c_0_545,
[final] ).
cnf(c_0_724,plain,
( number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
c_0_546,
[final] ).
cnf(c_0_725,plain,
ord_less_eq(int,one_one(int),t),
c_0_547,
[final] ).
cnf(c_0_726,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
c_0_548,
[final] ).
cnf(c_0_727,plain,
ord_less_eq(int,X1,X1),
c_0_549,
[final] ).
cnf(c_0_728,plain,
zprime(number_number_of(int,bit0(bit1(pls)))),
c_0_550,
[final] ).
cnf(c_0_729,plain,
ord_less_eq(int,pls,pls),
c_0_551,
[final] ).
cnf(c_0_730,plain,
( twoSqu33214720sum2sq(X1)
| ~ twoSqu33214720sum2sq(ti(int,X1)) ),
c_0_552,
[final] ).
cnf(c_0_731,plain,
( zprime(X1)
| ~ zprime(ti(int,X1)) ),
c_0_553,
[final] ).
cnf(c_0_732,plain,
( number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| X2 != X3 ),
c_0_554,
[final] ).
cnf(c_0_733,plain,
( twoSqu33214720sum2sq(ti(int,X1))
| ~ twoSqu33214720sum2sq(X1) ),
c_0_555,
[final] ).
cnf(c_0_734,plain,
( zprime(ti(int,X1))
| ~ zprime(X1) ),
c_0_556,
[final] ).
cnf(c_0_735,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ semiring_1(X1) ),
c_0_557,
[final] ).
cnf(c_0_736,plain,
ti(X1,undefined(X1)) = undefined(X1),
c_0_558,
[final] ).
cnf(c_0_737,plain,
number_number_of(nat,bit1(pls)) = one_one(nat),
c_0_559,
[final] ).
cnf(c_0_738,plain,
number_number_of(nat,bit1(pls)) = one_one(nat),
c_0_560,
[final] ).
cnf(c_0_739,plain,
( X1 = X2
| bit0(X1) != bit0(X2) ),
c_0_561,
[final] ).
cnf(c_0_740,plain,
( X1 = X2
| bit1(X1) != bit1(X2) ),
c_0_562,
[final] ).
cnf(c_0_741,plain,
number_number_of(int,X1) = X1,
c_0_563,
[final] ).
cnf(c_0_742,plain,
( bit0(X1) = bit0(X2)
| X1 != X2 ),
c_0_564,
[final] ).
cnf(c_0_743,plain,
( bit1(X1) = bit1(X2)
| X1 != X2 ),
c_0_565,
[final] ).
cnf(c_0_744,plain,
ti(int,t) = t,
c_0_566,
[final] ).
cnf(c_0_745,plain,
ti(int,s) = s,
c_0_567,
[final] ).
cnf(c_0_746,plain,
number(nat),
c_0_568,
[final] ).
cnf(c_0_747,plain,
semiring_1(nat),
c_0_569,
[final] ).
cnf(c_0_748,plain,
monoid_mult(nat),
c_0_570,
[final] ).
cnf(c_0_749,plain,
linorder(nat),
c_0_571,
[final] ).
cnf(c_0_750,plain,
number_semiring(nat),
c_0_572,
[final] ).
cnf(c_0_751,plain,
comm_semiring_1(nat),
c_0_573,
[final] ).
cnf(c_0_752,plain,
number(int),
c_0_574,
[final] ).
cnf(c_0_753,plain,
number_ring(int),
c_0_575,
[final] ).
cnf(c_0_754,plain,
ring_char_0(int),
c_0_576,
[final] ).
cnf(c_0_755,plain,
semiring_1(int),
c_0_577,
[final] ).
cnf(c_0_756,plain,
monoid_mult(int),
c_0_578,
[final] ).
cnf(c_0_757,plain,
linorder(int),
c_0_579,
[final] ).
cnf(c_0_758,plain,
number_semiring(int),
c_0_580,
[final] ).
cnf(c_0_759,plain,
comm_semiring_1(int),
c_0_581,
[final] ).
cnf(c_0_760,plain,
linordered_idom(int),
c_0_582,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_585_0,axiom,
( plus_plus(X1,plus_plus(X1,power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X3,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X2),X3)) = power_power(X1,plus_plus(X1,X2,X3),number_number_of(nat,bit0(bit1(pls))))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_585_1,axiom,
( ~ number_semiring(X1)
| plus_plus(X1,plus_plus(X1,power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X3,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X2),X3)) = power_power(X1,plus_plus(X1,X2,X3),number_number_of(nat,bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_589_0,axiom,
( plus_plus(int,power_power(int,sk1_esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_1,axiom,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,sk1_esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_590_0,axiom,
( plus_plus(int,power_power(int,sk1_esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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))
| one_one(int) != t ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_1,axiom,
( one_one(int) != t
| plus_plus(int,power_power(int,sk1_esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_593_0,axiom,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X2,times_times(X1,X3,times_times(X1,X4,X5)))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X2,times_times(X1,X3,times_times(X1,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_594_0,axiom,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X4,times_times(X1,times_times(X1,X2,X3),X5))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_594_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X4,times_times(X1,times_times(X1,X2,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_595_0,axiom,
( plus_plus(X1,plus_plus(X1,X2,X3),plus_plus(X1,X4,X5)) = plus_plus(X1,plus_plus(X1,X2,X4),plus_plus(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_595_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,plus_plus(X1,X2,X3),plus_plus(X1,X4,X5)) = plus_plus(X1,plus_plus(X1,X2,X4),plus_plus(X1,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_596_0,axiom,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,times_times(X1,X2,X4),times_times(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_596_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,times_times(X1,X2,X4),times_times(X1,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_597_0,axiom,
( power_power(X1,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X3)) = times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X3))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_1,axiom,
( ~ comm_semiring_1(X1)
| power_power(X1,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X3)) = times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_598_0,axiom,
( times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X4)) = power_power(X1,X2,plus_plus(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_598]) ).
cnf(c_0_598_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X4)) = power_power(X1,X2,plus_plus(nat,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_598]) ).
cnf(c_0_599_0,axiom,
( ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X4))
| ~ ord_less_eq(int,X2,X4)
| ~ ord_less(int,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_599_1,axiom,
( ~ ord_less_eq(int,X2,X4)
| ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X4))
| ~ ord_less(int,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_599_2,axiom,
( ~ ord_less(int,X1,X3)
| ~ ord_less_eq(int,X2,X4)
| ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_602_0,axiom,
( ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less_eq(X1,number_number_of(X1,X3),number_number_of(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_602_1,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less_eq(X1,number_number_of(X1,X3),number_number_of(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_602_2,axiom,
( ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number(X1)
| ~ linorder(X1)
| ~ ord_less_eq(X1,number_number_of(X1,X3),number_number_of(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_602_3,axiom,
( ~ ord_less_eq(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number(X1)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_603_0,axiom,
( ord_less_eq(int,plus_plus(int,X1,X2),plus_plus(int,X1,X3))
| ~ ord_less_eq(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_603_1,axiom,
( ~ ord_less_eq(int,X2,X3)
| ord_less_eq(int,plus_plus(int,X1,X2),plus_plus(int,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_604_0,axiom,
( ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X2))
| ~ ord_less(int,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_604_1,axiom,
( ~ ord_less(int,X1,X3)
| ord_less(int,plus_plus(int,X1,X2),plus_plus(int,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_605_0,axiom,
( plus_plus(X1,X2,plus_plus(X1,X3,X4)) = plus_plus(X1,X3,plus_plus(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_605_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,X2,plus_plus(X1,X3,X4)) = plus_plus(X1,X3,plus_plus(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_606_0,axiom,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_606_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_607_0,axiom,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_607_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_608_0,axiom,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,plus_plus(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_608_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,plus_plus(X1,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_609_0,axiom,
( times_times(X1,X2,times_times(X1,X3,X4)) = times_times(X1,X3,times_times(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_609]) ).
cnf(c_0_609_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,X2,times_times(X1,X3,X4)) = times_times(X1,X3,times_times(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_609]) ).
cnf(c_0_610_0,axiom,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_610]) ).
cnf(c_0_610_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_610]) ).
cnf(c_0_611_0,axiom,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_611_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_612_0,axiom,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,times_times(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,times_times(X1,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_613_0,axiom,
( power_power(X1,power_power(X1,X2,X3),X4) = power_power(X1,X2,times_times(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_613_1,axiom,
( ~ comm_semiring_1(X1)
| power_power(X1,power_power(X1,X2,X3),X4) = power_power(X1,X2,times_times(nat,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_614_0,axiom,
( ord_less(int,X1,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,plus_plus(int,X1,X2))
| ord_less(int,X2,pls) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_1,axiom,
( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,plus_plus(int,X1,X2))
| ord_less(int,X1,pls)
| ord_less(int,X2,pls) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_2,axiom,
( ord_less(int,X2,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,plus_plus(int,X1,X2))
| ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_619_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,plus_plus(int,X2,one_one(int))) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_1,axiom,
( ~ ord_less(int,X1,plus_plus(int,X2,one_one(int)))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_620_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_620_1,axiom,
( ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_621_0,axiom,
( power_power(X1,number_number_of(X1,X2),number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,number_number_of(X1,X2),number_number_of(X1,X2))
| ~ number(X1)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_1,axiom,
( ~ number(X1)
| power_power(X1,number_number_of(X1,X2),number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,number_number_of(X1,X2),number_number_of(X1,X2))
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_2,axiom,
( ~ monoid_mult(X1)
| ~ number(X1)
| power_power(X1,number_number_of(X1,X2),number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,number_number_of(X1,X2),number_number_of(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_622_0,axiom,
( ord_less(int,X1,plus_plus(int,X2,one_one(int)))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less(int,X1,plus_plus(int,X2,one_one(int))) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_623_0,axiom,
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_623_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_624_0,axiom,
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_624_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_625_0,axiom,
( ord_less(int,X1,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X1)
| ~ ord_less(int,X2,pls) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_1,axiom,
( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X1)
| ord_less(int,X1,pls)
| ~ ord_less(int,X2,pls) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_2,axiom,
( ~ ord_less(int,X2,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X1)
| ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_626_0,axiom,
( ord_less_eq(int,X2,X3)
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_1,axiom,
( ~ linordered_idom(X1)
| ord_less_eq(int,X2,X3)
| ~ number_ring(X1)
| ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less_eq(int,X2,X3)
| ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_3,axiom,
( ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less_eq(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_627_0,axiom,
( ord_less(int,X2,X3)
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_1,axiom,
( ~ linordered_idom(X1)
| ord_less(int,X2,X3)
| ~ number_ring(X1)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less(int,X2,X3)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_3,axiom,
( ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_628_0,axiom,
( ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ~ linorder(X1)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_1,axiom,
( ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ linorder(X1)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_2,axiom,
( ~ linorder(X1)
| ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_3,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_629_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,X3,X2)
| ~ ord_less_eq(int,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_629_1,axiom,
( ~ ord_less_eq(int,X3,X2)
| ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_629_2,axiom,
( ~ ord_less_eq(int,X1,X3)
| ~ ord_less_eq(int,X3,X2)
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_630_0,axiom,
( plus_plus(X1,number_number_of(X1,X2),one_one(X1)) = number_number_of(X1,plus_plus(int,X2,bit1(pls)))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_630_1,axiom,
( ~ number_ring(X1)
| plus_plus(X1,number_number_of(X1,X2),one_one(X1)) = number_number_of(X1,plus_plus(int,X2,bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_631_0,axiom,
( plus_plus(X1,one_one(X1),number_number_of(X1,X2)) = number_number_of(X1,plus_plus(int,bit1(pls),X2))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_631_1,axiom,
( ~ number_ring(X1)
| plus_plus(X1,one_one(X1),number_number_of(X1,X2)) = number_number_of(X1,plus_plus(int,bit1(pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_632_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_1,axiom,
( ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_633_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_633_1,axiom,
( ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_634_0,axiom,
( ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less_eq(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_1,axiom,
( ~ linordered_idom(X1)
| ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number_ring(X1)
| ~ ord_less_eq(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less_eq(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_3,axiom,
( ~ ord_less_eq(int,X2,X3)
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_635_0,axiom,
( ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ ord_less(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_1,axiom,
( ~ linordered_idom(X1)
| ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number_ring(X1)
| ~ ord_less(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less(int,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_3,axiom,
( ~ ord_less(int,X2,X3)
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_636_0,axiom,
( ord_less_eq(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_636_1,axiom,
( ~ linorder(X1)
| ord_less_eq(X1,X2,X3)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_636_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,X3)
| ~ ord_less_eq(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_636_3,axiom,
( ~ ord_less_eq(X1,X2,ti(X1,X3))
| ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_637_0,axiom,
( ord_less_eq(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_637_1,axiom,
( ~ linorder(X1)
| ord_less_eq(X1,X2,X3)
| ~ number(X1)
| ~ ord_less_eq(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_637_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,X3)
| ~ ord_less_eq(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_637_3,axiom,
( ~ ord_less_eq(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_638_0,axiom,
( ord_less(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_1,axiom,
( ~ linorder(X1)
| ord_less(X1,X2,X3)
| ~ number(X1)
| ~ ord_less(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,X2,X3)
| ~ ord_less(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_3,axiom,
( ~ ord_less(X1,X2,ti(X1,X3))
| ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_639_0,axiom,
( ord_less(X1,X2,X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_639_1,axiom,
( ~ linorder(X1)
| ord_less(X1,X2,X3)
| ~ number(X1)
| ~ ord_less(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_639_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,X2,X3)
| ~ ord_less(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_639_3,axiom,
( ~ ord_less(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_640_0,axiom,
( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X2)
| ~ ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_640_1,axiom,
( ~ ord_less(int,X1,pls)
| plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X2)) = number_number_of(nat,X2) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_641_0,axiom,
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_641_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_642_0,axiom,
( ord_less(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_643_0,axiom,
( ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_1,axiom,
( ~ monoid_mult(X1)
| ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_644_0,axiom,
( ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_1,axiom,
( ~ monoid_mult(X1)
| ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_645_0,axiom,
( ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_1,axiom,
( ~ comm_semiring_1(X1)
| ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_646_0,axiom,
( ord_less_eq(X1,X2,ti(X1,X3))
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_1,axiom,
( ~ linorder(X1)
| ord_less_eq(X1,X2,ti(X1,X3))
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,ti(X1,X3))
| ~ ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_3,axiom,
( ~ ord_less_eq(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_647_0,axiom,
( ord_less_eq(X1,ti(X1,X2),X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_1,axiom,
( ~ linorder(X1)
| ord_less_eq(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,ti(X1,X2),X3)
| ~ ord_less_eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_3,axiom,
( ~ ord_less_eq(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_648_0,axiom,
( ord_less(X1,X2,ti(X1,X3))
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_1,axiom,
( ~ linorder(X1)
| ord_less(X1,X2,ti(X1,X3))
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,X2,ti(X1,X3))
| ~ ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_3,axiom,
( ~ ord_less(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,X2,ti(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_649_0,axiom,
( ord_less(X1,ti(X1,X2),X3)
| ~ linorder(X1)
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_649_1,axiom,
( ~ linorder(X1)
| ord_less(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_649_2,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,ti(X1,X2),X3)
| ~ ord_less(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_649_3,axiom,
( ~ ord_less(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,ti(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_650_0,axiom,
( X1 = X2
| ~ ord_less_eq(int,X2,X1)
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_1,axiom,
( ~ ord_less_eq(int,X2,X1)
| X1 = X2
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_2,axiom,
( ~ ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_651_0,axiom,
( power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X2,X2)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_651_1,axiom,
( ~ monoid_mult(X1)
| power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_652_0,axiom,
( times_times(X1,X2,X2) = power_power(X1,X2,number_number_of(nat,bit0(bit1(pls))))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_652_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,X2,X2) = power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_653_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_653_1,axiom,
( ~ ord_less_eq(int,bit0(X1),bit1(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_654_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_654_1,axiom,
( ~ ord_less_eq(int,bit0(X1),bit1(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_655_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_655_1,axiom,
( ~ ord_less(int,bit1(X1),bit0(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_656_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_1,axiom,
( ~ ord_less(int,bit1(X1),bit0(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_657_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_657_1,axiom,
( ~ ord_less(int,bit0(X1),bit1(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_658_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_1,axiom,
( ~ ord_less(int,bit0(X1),bit1(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_659_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_659_1,axiom,
( ~ ord_less_eq(int,bit1(X1),bit0(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_660_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_660_1,axiom,
( ~ ord_less_eq(int,bit1(X1),bit0(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_661_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_661_1,axiom,
( ~ ord_less_eq(int,bit0(X1),bit0(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_662_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_1,axiom,
( ~ ord_less_eq(int,bit0(X1),bit0(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_663_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_663_1,axiom,
( ~ ord_less(int,bit0(X1),bit0(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_664_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_1,axiom,
( ~ ord_less(int,bit0(X1),bit0(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_665_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_665_1,axiom,
( ~ ord_less_eq(int,bit1(X1),bit1(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_666_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_666_1,axiom,
( ~ ord_less_eq(int,bit1(X1),bit1(X2))
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_667_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_667_1,axiom,
( ~ ord_less(int,bit1(X1),bit1(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_668_0,axiom,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_668_1,axiom,
( ~ ord_less(int,bit1(X1),bit1(X2))
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_671_0,axiom,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_671_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_672_0,axiom,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_672_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_673_0,axiom,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_673_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_674_0,axiom,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_674_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_675_0,axiom,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_675_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_676_0,axiom,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_676_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less(int,bit0(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_677_0,axiom,
( ord_less_eq(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less_eq(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_678_0,axiom,
( ord_less_eq(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less_eq(int,bit1(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_679_0,axiom,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_680_0,axiom,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_681_0,axiom,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_682_0,axiom,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less(int,bit0(X1),bit0(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_683_0,axiom,
( ord_less_eq(int,bit1(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_684_0,axiom,
( ord_less_eq(int,bit1(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_1,axiom,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_685_0,axiom,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_686_0,axiom,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less(int,bit1(X1),bit1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_687_0,axiom,
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,bit1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_1,axiom,
( ~ ord_less_eq(int,pls,bit1(X1))
| ord_less_eq(int,pls,X1) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_688_0,axiom,
( ord_less(int,pls,X1)
| ~ ord_less(int,pls,bit0(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_688_1,axiom,
( ~ ord_less(int,pls,bit0(X1))
| ord_less(int,pls,X1) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_689_0,axiom,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit0(X1),pls) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_1,axiom,
( ~ ord_less(int,bit0(X1),pls)
| ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_690_0,axiom,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit1(X1),pls) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_1,axiom,
( ~ ord_less(int,bit1(X1),pls)
| ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_691_0,axiom,
( ord_less_eq(int,pls,X1)
| ~ ord_less(int,pls,bit1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_1,axiom,
( ~ ord_less(int,pls,bit1(X1))
| ord_less_eq(int,pls,X1) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_692_0,axiom,
( ord_less(int,X1,pls)
| ~ ord_less_eq(int,bit1(X1),pls) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_1,axiom,
( ~ ord_less_eq(int,bit1(X1),pls)
| ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_693_0,axiom,
( power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_1,axiom,
( ~ monoid_mult(X1)
| power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_694_0,axiom,
( times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_1,axiom,
( ~ monoid_mult(X1)
| times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_695_0,axiom,
( times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_1,axiom,
( ~ monoid_mult(X1)
| times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_696_0,axiom,
( plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_696_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_697_0,axiom,
( plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_698_0,axiom,
( ord_less(int,X1,X2)
| X1 = X2
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_1,axiom,
( X1 = X2
| ord_less(int,X1,X2)
| ~ ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_2,axiom,
( ~ ord_less_eq(int,X1,X2)
| X1 = X2
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_699_0,axiom,
( ord_less_eq(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_699_1,axiom,
( ~ ord_less_eq(int,pls,X1)
| ord_less_eq(int,pls,bit1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_700_0,axiom,
( ord_less(int,pls,bit0(X1))
| ~ ord_less(int,pls,X1) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_700_1,axiom,
( ~ ord_less(int,pls,X1)
| ord_less(int,pls,bit0(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_701_0,axiom,
( ord_less(int,bit0(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_701_1,axiom,
( ~ ord_less(int,X1,pls)
| ord_less(int,bit0(X1),pls) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_702_0,axiom,
( ord_less(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_702_1,axiom,
( ~ ord_less(int,X1,pls)
| ord_less(int,bit1(X1),pls) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_703_0,axiom,
( ord_less(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_1,axiom,
( ~ ord_less_eq(int,pls,X1)
| ord_less(int,pls,bit1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_704_0,axiom,
( ord_less_eq(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_704_1,axiom,
( ~ ord_less(int,X1,pls)
| ord_less_eq(int,bit1(X1),pls) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_705_0,axiom,
( power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_705_1,axiom,
( ~ monoid_mult(X1)
| power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_706_0,axiom,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_706_1,axiom,
( ~ ord_less(int,X1,X2)
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_707_0,axiom,
( twoSqu33214720sum2sq(times_times(int,X1,X2))
| ~ twoSqu33214720sum2sq(X2)
| ~ twoSqu33214720sum2sq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_1,axiom,
( ~ twoSqu33214720sum2sq(X2)
| twoSqu33214720sum2sq(times_times(int,X1,X2))
| ~ twoSqu33214720sum2sq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_2,axiom,
( ~ twoSqu33214720sum2sq(X1)
| ~ twoSqu33214720sum2sq(X2)
| twoSqu33214720sum2sq(times_times(int,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_708_0,axiom,
( power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1)
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_1,axiom,
( ~ semiring_1(X1)
| power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_709_0,axiom,
( plus_plus(X1,X2,X3) = plus_plus(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_1,axiom,
( ~ comm_semiring_1(X1)
| plus_plus(X1,X2,X3) = plus_plus(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_710_0,axiom,
( times_times(X1,X2,X3) = times_times(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_1,axiom,
( ~ comm_semiring_1(X1)
| times_times(X1,X2,X3) = times_times(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_711_0,axiom,
( ord_less(int,X1,X2)
| X2 = X1
| ord_less(int,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_1,axiom,
( X2 = X1
| ord_less(int,X1,X2)
| ord_less(int,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_2,axiom,
( ord_less(int,X2,X1)
| X2 = X1
| ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_712_0,axiom,
( ord_less_eq(int,X1,X2)
| ord_less_eq(int,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_1,axiom,
( ord_less_eq(int,X2,X1)
| ord_less_eq(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_715_0,axiom,
( plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls)))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_715_1,axiom,
( ~ number_ring(X1)
| plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_716_0,axiom,
( ~ ord_less(int,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_716_1,axiom,
( X1 != X2
| ~ ord_less(int,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_718_0,axiom,
( ti(X1,X2) = number_number_of(X1,X3)
| ~ number(X1)
| number_number_of(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_718_1,axiom,
( ~ number(X1)
| ti(X1,X2) = number_number_of(X1,X3)
| number_number_of(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_718_2,axiom,
( number_number_of(X1,X3) != ti(X1,X2)
| ~ number(X1)
| ti(X1,X2) = number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_719_0,axiom,
( number_number_of(X1,X2) = ti(X1,X3)
| ~ number(X1)
| ti(X1,X3) != number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_1,axiom,
( ~ number(X1)
| number_number_of(X1,X2) = ti(X1,X3)
| ti(X1,X3) != number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_2,axiom,
( ti(X1,X3) != number_number_of(X1,X2)
| ~ number(X1)
| number_number_of(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_721_0,axiom,
( power_power(X1,X2,one_one(nat)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_721_1,axiom,
( ~ comm_semiring_1(X1)
| power_power(X1,X2,one_one(nat)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_722_0,axiom,
( ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_722_1,axiom,
( ~ number(X1)
| ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_723_0,axiom,
( X2 = X3
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_723_1,axiom,
( ~ ring_char_0(X1)
| X2 = X3
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_723_2,axiom,
( ~ number_ring(X1)
| ~ ring_char_0(X1)
| X2 = X3
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_723_3,axiom,
( number_number_of(X1,X2) != number_number_of(X1,X3)
| ~ number_ring(X1)
| ~ ring_char_0(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_724_0,axiom,
( number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_724_1,axiom,
( ~ number(X1)
| number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_730_0,axiom,
( twoSqu33214720sum2sq(X1)
| ~ twoSqu33214720sum2sq(ti(int,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_730_1,axiom,
( ~ twoSqu33214720sum2sq(ti(int,X1))
| twoSqu33214720sum2sq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_731_0,axiom,
( zprime(X1)
| ~ zprime(ti(int,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_731_1,axiom,
( ~ zprime(ti(int,X1))
| zprime(X1) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_732_0,axiom,
( number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_1,axiom,
( ~ ring_char_0(X1)
| number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ number_ring(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_2,axiom,
( ~ number_ring(X1)
| ~ ring_char_0(X1)
| number_number_of(X1,X2) = number_number_of(X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_3,axiom,
( X2 != X3
| ~ number_ring(X1)
| ~ ring_char_0(X1)
| number_number_of(X1,X2) = number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_733_0,axiom,
( twoSqu33214720sum2sq(ti(int,X1))
| ~ twoSqu33214720sum2sq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_733_1,axiom,
( ~ twoSqu33214720sum2sq(X1)
| twoSqu33214720sum2sq(ti(int,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_734_0,axiom,
( zprime(ti(int,X1))
| ~ zprime(X1) ),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_734_1,axiom,
( ~ zprime(X1)
| zprime(ti(int,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_735_0,axiom,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_735_1,axiom,
( ~ semiring_1(X1)
| ti(X1,one_one(X1)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_739_0,axiom,
( X1 = X2
| bit0(X1) != bit0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_739_1,axiom,
( bit0(X1) != bit0(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_740_0,axiom,
( X1 = X2
| bit1(X1) != bit1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_740_1,axiom,
( bit1(X1) != bit1(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_742_0,axiom,
( bit0(X1) = bit0(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_1,axiom,
( X1 != X2
| bit0(X1) = bit0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_743_0,axiom,
( bit1(X1) = bit1(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_743_1,axiom,
( X1 != X2
| bit1(X1) = bit1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_720_0,axiom,
~ ord_less(int,pls,pls),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_583_0,axiom,
plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X1,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))),X2)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X1),power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X2,number_number_of(nat,bit1(bit1(pls))))) = power_power(int,plus_plus(int,X1,X2),number_number_of(nat,bit1(bit1(pls)))),
inference(literals_permutation,[status(thm)],[c_0_583]) ).
cnf(c_0_584_0,axiom,
plus_plus(int,plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X1),X2)),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,plus_plus(int,X1,X2),number_number_of(nat,bit0(bit1(pls)))),
inference(literals_permutation,[status(thm)],[c_0_584]) ).
cnf(c_0_586_0,axiom,
twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(literals_permutation,[status(thm)],[c_0_586]) ).
cnf(c_0_587_0,axiom,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),sk1_esk5_0) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(literals_permutation,[status(thm)],[c_0_587]) ).
cnf(c_0_588_0,axiom,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_591_0,axiom,
ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_592_0,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_600_0,axiom,
times_times(int,power_power(int,X1,X2),power_power(int,X1,X3)) = power_power(int,X1,plus_plus(nat,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_601_0,axiom,
times_times(int,X1,power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X1,number_number_of(nat,bit1(bit1(pls)))),
inference(literals_permutation,[status(thm)],[c_0_601]) ).
cnf(c_0_615_0,axiom,
plus_plus(int,X1,plus_plus(int,X2,X3)) = plus_plus(int,X2,plus_plus(int,X1,X3)),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_616_0,axiom,
plus_plus(int,plus_plus(int,X1,X2),X3) = plus_plus(int,X1,plus_plus(int,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_616]) ).
cnf(c_0_617_0,axiom,
times_times(int,times_times(int,X1,X2),X3) = times_times(int,X1,times_times(int,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_617]) ).
cnf(c_0_618_0,axiom,
power_power(int,power_power(int,X1,X2),X3) = power_power(int,X1,times_times(nat,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_618]) ).
cnf(c_0_669_0,axiom,
times_times(nat,X1,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_670_0,axiom,
times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) = plus_plus(nat,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_713_0,axiom,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_714_0,axiom,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_717_0,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_725_0,axiom,
ord_less_eq(int,one_one(int),t),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_726_0,axiom,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_727_0,axiom,
ord_less_eq(int,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_728_0,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))),
inference(literals_permutation,[status(thm)],[c_0_728]) ).
cnf(c_0_729_0,axiom,
ord_less_eq(int,pls,pls),
inference(literals_permutation,[status(thm)],[c_0_729]) ).
cnf(c_0_736_0,axiom,
ti(X1,undefined(X1)) = undefined(X1),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_737_0,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
inference(literals_permutation,[status(thm)],[c_0_737]) ).
cnf(c_0_738_0,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_741_0,axiom,
number_number_of(int,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_744_0,axiom,
ti(int,t) = t,
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_745_0,axiom,
ti(int,s) = s,
inference(literals_permutation,[status(thm)],[c_0_745]) ).
cnf(c_0_746_0,axiom,
number(nat),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_747_0,axiom,
semiring_1(nat),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_748_0,axiom,
monoid_mult(nat),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_749_0,axiom,
linorder(nat),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_750_0,axiom,
number_semiring(nat),
inference(literals_permutation,[status(thm)],[c_0_750]) ).
cnf(c_0_751_0,axiom,
comm_semiring_1(nat),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_752_0,axiom,
number(int),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_753_0,axiom,
number_ring(int),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_754_0,axiom,
ring_char_0(int),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_755_0,axiom,
semiring_1(int),
inference(literals_permutation,[status(thm)],[c_0_755]) ).
cnf(c_0_756_0,axiom,
monoid_mult(int),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_757_0,axiom,
linorder(int),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_758_0,axiom,
number_semiring(int),
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_759_0,axiom,
comm_semiring_1(int),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_760_0,axiom,
linordered_idom(int),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
? [X2,X3] : plus_plus(int,power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X3,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('<stdin>',conj_0) ).
fof(c_0_1_002,hypothesis,
! [X1] : bit1(ti(int,X1)) = bit1(X1),
file('<stdin>',tsy_c_Int_OBit1_arg1) ).
fof(c_0_2_003,hypothesis,
! [X1] : bit0(ti(int,X1)) = bit0(X1),
file('<stdin>',tsy_c_Int_OBit0_arg1) ).
fof(c_0_3_004,hypothesis,
! [X1] : ti(int,bit1(X1)) = bit1(X1),
file('<stdin>',tsy_c_Int_OBit1_res) ).
fof(c_0_4_005,hypothesis,
! [X1] : ti(int,bit0(X1)) = bit0(X1),
file('<stdin>',tsy_c_Int_OBit0_res) ).
fof(c_0_5_006,hypothesis,
ti(int,m) = m,
file('<stdin>',tsy_v_m_res) ).
fof(c_0_6_007,hypothesis,
ti(int,pls) = pls,
file('<stdin>',tsy_c_Int_OPls_res) ).
fof(c_0_7_008,negated_conjecture,
~ ? [X2,X3] : plus_plus(int,power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X3,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)],[c_0_0]) ).
fof(c_0_8_009,hypothesis,
! [X1] : bit1(ti(int,X1)) = bit1(X1),
c_0_1 ).
fof(c_0_9_010,hypothesis,
! [X1] : bit0(ti(int,X1)) = bit0(X1),
c_0_2 ).
fof(c_0_10_011,hypothesis,
! [X1] : ti(int,bit1(X1)) = bit1(X1),
c_0_3 ).
fof(c_0_11_012,hypothesis,
! [X1] : ti(int,bit0(X1)) = bit0(X1),
c_0_4 ).
fof(c_0_12_013,hypothesis,
ti(int,m) = m,
c_0_5 ).
fof(c_0_13_014,hypothesis,
ti(int,pls) = pls,
c_0_6 ).
fof(c_0_14_015,negated_conjecture,
! [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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_7])]) ).
fof(c_0_15_016,hypothesis,
! [X2] : bit1(ti(int,X2)) = bit1(X2),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_16_017,hypothesis,
! [X2] : bit0(ti(int,X2)) = bit0(X2),
inference(variable_rename,[status(thm)],[c_0_9]) ).
fof(c_0_17_018,hypothesis,
! [X2] : ti(int,bit1(X2)) = bit1(X2),
inference(variable_rename,[status(thm)],[c_0_10]) ).
fof(c_0_18_019,hypothesis,
! [X2] : ti(int,bit0(X2)) = bit0(X2),
inference(variable_rename,[status(thm)],[c_0_11]) ).
fof(c_0_19_020,hypothesis,
ti(int,m) = m,
c_0_12 ).
fof(c_0_20_021,hypothesis,
ti(int,pls) = pls,
c_0_13 ).
cnf(c_0_21_022,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_14]) ).
cnf(c_0_22_023,hypothesis,
bit1(ti(int,X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23_024,hypothesis,
bit0(ti(int,X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24_025,hypothesis,
ti(int,bit1(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25_026,hypothesis,
ti(int,bit0(X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26_027,hypothesis,
ti(int,m) = m,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27_028,hypothesis,
ti(int,pls) = pls,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28_029,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)),
c_0_21,
[final] ).
cnf(c_0_29_030,hypothesis,
bit1(ti(int,X1)) = bit1(X1),
c_0_22,
[final] ).
cnf(c_0_30_031,hypothesis,
bit0(ti(int,X1)) = bit0(X1),
c_0_23,
[final] ).
cnf(c_0_31_032,hypothesis,
ti(int,bit1(X1)) = bit1(X1),
c_0_24,
[final] ).
cnf(c_0_32_033,hypothesis,
ti(int,bit0(X1)) = bit0(X1),
c_0_25,
[final] ).
cnf(c_0_33_034,hypothesis,
ti(int,m) = m,
c_0_26,
[final] ).
cnf(c_0_34_035,hypothesis,
ti(int,pls) = pls,
c_0_27,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_354,negated_conjecture,
plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,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/sandbox2/tmp/iprover_modulo_847f5e.p',c_0_28) ).
cnf(c_502,negated_conjecture,
plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,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(copy,[status(esa)],[c_354]) ).
cnf(c_506,negated_conjecture,
plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,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(copy,[status(esa)],[c_502]) ).
cnf(c_519,negated_conjecture,
plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,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(copy,[status(esa)],[c_506]) ).
cnf(c_521,negated_conjecture,
plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,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(copy,[status(esa)],[c_519]) ).
cnf(c_882,negated_conjecture,
plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,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(copy,[status(esa)],[c_521]) ).
cnf(c_1141564,plain,
plus_plus(int,power_power(int,sk1_esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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(instantiation,[status(thm)],[c_882]) ).
cnf(c_112919,plain,
plus_plus(int,power_power(int,sk1_esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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(instantiation,[status(thm)],[c_882]) ).
cnf(c_117,plain,
( ord_less(int,X0,X1)
| X0 = X1
| ~ ord_less_eq(int,X0,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_847f5e.p',c_0_698_2) ).
cnf(c_644,plain,
( ord_less(int,X0,X1)
| X0 = X1
| ~ ord_less_eq(int,X0,X1) ),
inference(copy,[status(esa)],[c_117]) ).
cnf(c_51044,plain,
( ~ ord_less_eq(int,one_one(int),t)
| ord_less(int,one_one(int),t)
| one_one(int) = t ),
inference(instantiation,[status(thm)],[c_644]) ).
cnf(c_25,plain,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox2/tmp/iprover_modulo_847f5e.p',c_0_725_0) ).
cnf(c_349,plain,
( one_one(int) != t
| plus_plus(int,power_power(int,sk1_esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_847f5e.p',c_0_590_0) ).
cnf(c_351,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,sk1_esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk1_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)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_847f5e.p',c_0_589_0) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_1141564,c_112919,c_51044,c_25,c_349,c_351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.14/0.35 % Computer : n007.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 : 600
% 0.14/0.35 % DateTime : Thu Jul 7 16:05:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Running in mono-core mode
% 0.21/0.44 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.44 % FOF problem with conjecture
% 0.21/0.44 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_93f61f.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_847f5e.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_892276 | grep -v "SZS"
% 0.21/0.47
% 0.21/0.47 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.47
% 0.21/0.47 %
% 0.21/0.47 % ------ iProver source info
% 0.21/0.47
% 0.21/0.47 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.47 % git: non_committed_changes: true
% 0.21/0.47 % git: last_make_outside_of_git: true
% 0.21/0.47
% 0.21/0.47 %
% 0.21/0.47 % ------ Input Options
% 0.21/0.47
% 0.21/0.47 % --out_options all
% 0.21/0.47 % --tptp_safe_out true
% 0.21/0.47 % --problem_path ""
% 0.21/0.47 % --include_path ""
% 0.21/0.47 % --clausifier .//eprover
% 0.21/0.47 % --clausifier_options --tstp-format
% 0.21/0.47 % --stdin false
% 0.21/0.47 % --dbg_backtrace false
% 0.21/0.47 % --dbg_dump_prop_clauses false
% 0.21/0.47 % --dbg_dump_prop_clauses_file -
% 0.21/0.47 % --dbg_out_stat false
% 0.21/0.47
% 0.21/0.47 % ------ General Options
% 0.21/0.47
% 0.21/0.47 % --fof false
% 0.21/0.47 % --time_out_real 150.
% 0.21/0.47 % --time_out_prep_mult 0.2
% 0.21/0.47 % --time_out_virtual -1.
% 0.21/0.47 % --schedule none
% 0.21/0.47 % --ground_splitting input
% 0.21/0.47 % --splitting_nvd 16
% 0.21/0.47 % --non_eq_to_eq false
% 0.21/0.47 % --prep_gs_sim true
% 0.21/0.47 % --prep_unflatten false
% 0.21/0.47 % --prep_res_sim true
% 0.21/0.47 % --prep_upred true
% 0.21/0.47 % --res_sim_input true
% 0.21/0.47 % --clause_weak_htbl true
% 0.21/0.47 % --gc_record_bc_elim false
% 0.21/0.47 % --symbol_type_check false
% 0.21/0.47 % --clausify_out false
% 0.21/0.47 % --large_theory_mode false
% 0.21/0.47 % --prep_sem_filter none
% 0.21/0.47 % --prep_sem_filter_out false
% 0.21/0.47 % --preprocessed_out false
% 0.21/0.47 % --sub_typing false
% 0.21/0.47 % --brand_transform false
% 0.21/0.47 % --pure_diseq_elim true
% 0.21/0.47 % --min_unsat_core false
% 0.21/0.47 % --pred_elim true
% 0.21/0.47 % --add_important_lit false
% 0.21/0.47 % --soft_assumptions false
% 0.21/0.47 % --reset_solvers false
% 0.21/0.47 % --bc_imp_inh []
% 0.21/0.47 % --conj_cone_tolerance 1.5
% 0.21/0.47 % --prolific_symb_bound 500
% 0.21/0.47 % --lt_threshold 2000
% 0.21/0.47
% 0.21/0.47 % ------ SAT Options
% 0.21/0.47
% 0.21/0.47 % --sat_mode false
% 0.21/0.47 % --sat_fm_restart_options ""
% 0.21/0.47 % --sat_gr_def false
% 0.21/0.47 % --sat_epr_types true
% 0.21/0.47 % --sat_non_cyclic_types false
% 0.21/0.47 % --sat_finite_models false
% 0.21/0.47 % --sat_fm_lemmas false
% 0.21/0.47 % --sat_fm_prep false
% 0.21/0.47 % --sat_fm_uc_incr true
% 0.21/0.47 % --sat_out_model small
% 0.21/0.47 % --sat_out_clauses false
% 0.21/0.47
% 0.21/0.47 % ------ QBF Options
% 0.21/0.47
% 0.21/0.47 % --qbf_mode false
% 0.21/0.47 % --qbf_elim_univ true
% 0.21/0.47 % --qbf_sk_in true
% 0.21/0.47 % --qbf_pred_elim true
% 0.21/0.47 % --qbf_split 32
% 0.21/0.47
% 0.21/0.47 % ------ BMC1 Options
% 0.21/0.47
% 0.21/0.47 % --bmc1_incremental false
% 0.21/0.47 % --bmc1_axioms reachable_all
% 0.21/0.47 % --bmc1_min_bound 0
% 0.21/0.47 % --bmc1_max_bound -1
% 0.21/0.47 % --bmc1_max_bound_default -1
% 0.21/0.47 % --bmc1_symbol_reachability true
% 0.21/0.47 % --bmc1_property_lemmas false
% 0.21/0.47 % --bmc1_k_induction false
% 0.21/0.47 % --bmc1_non_equiv_states false
% 0.21/0.47 % --bmc1_deadlock false
% 0.21/0.47 % --bmc1_ucm false
% 0.21/0.47 % --bmc1_add_unsat_core none
% 0.21/0.47 % --bmc1_unsat_core_children false
% 0.21/0.47 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.47 % --bmc1_out_stat full
% 0.21/0.47 % --bmc1_ground_init false
% 0.21/0.47 % --bmc1_pre_inst_next_state false
% 0.21/0.47 % --bmc1_pre_inst_state false
% 0.21/0.47 % --bmc1_pre_inst_reach_state false
% 0.21/0.47 % --bmc1_out_unsat_core false
% 0.21/0.47 % --bmc1_aig_witness_out false
% 0.21/0.47 % --bmc1_verbose false
% 0.21/0.47 % --bmc1_dump_clauses_tptp false
% 1.18/1.55 % --bmc1_dump_unsat_core_tptp false
% 1.18/1.55 % --bmc1_dump_file -
% 1.18/1.55 % --bmc1_ucm_expand_uc_limit 128
% 1.18/1.55 % --bmc1_ucm_n_expand_iterations 6
% 1.18/1.55 % --bmc1_ucm_extend_mode 1
% 1.18/1.55 % --bmc1_ucm_init_mode 2
% 1.18/1.55 % --bmc1_ucm_cone_mode none
% 1.18/1.55 % --bmc1_ucm_reduced_relation_type 0
% 1.18/1.55 % --bmc1_ucm_relax_model 4
% 1.18/1.55 % --bmc1_ucm_full_tr_after_sat true
% 1.18/1.55 % --bmc1_ucm_expand_neg_assumptions false
% 1.18/1.55 % --bmc1_ucm_layered_model none
% 1.18/1.55 % --bmc1_ucm_max_lemma_size 10
% 1.18/1.55
% 1.18/1.55 % ------ AIG Options
% 1.18/1.55
% 1.18/1.55 % --aig_mode false
% 1.18/1.55
% 1.18/1.55 % ------ Instantiation Options
% 1.18/1.55
% 1.18/1.55 % --instantiation_flag true
% 1.18/1.55 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.18/1.55 % --inst_solver_per_active 750
% 1.18/1.55 % --inst_solver_calls_frac 0.5
% 1.18/1.55 % --inst_passive_queue_type priority_queues
% 1.18/1.55 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.18/1.55 % --inst_passive_queues_freq [25;2]
% 1.18/1.55 % --inst_dismatching true
% 1.18/1.55 % --inst_eager_unprocessed_to_passive true
% 1.18/1.55 % --inst_prop_sim_given true
% 1.18/1.55 % --inst_prop_sim_new false
% 1.18/1.55 % --inst_orphan_elimination true
% 1.18/1.55 % --inst_learning_loop_flag true
% 1.18/1.55 % --inst_learning_start 3000
% 1.18/1.55 % --inst_learning_factor 2
% 1.18/1.55 % --inst_start_prop_sim_after_learn 3
% 1.18/1.55 % --inst_sel_renew solver
% 1.18/1.55 % --inst_lit_activity_flag true
% 1.18/1.55 % --inst_out_proof true
% 1.18/1.55
% 1.18/1.55 % ------ Resolution Options
% 1.18/1.55
% 1.18/1.55 % --resolution_flag true
% 1.18/1.55 % --res_lit_sel kbo_max
% 1.18/1.55 % --res_to_prop_solver none
% 1.18/1.55 % --res_prop_simpl_new false
% 1.18/1.55 % --res_prop_simpl_given false
% 1.18/1.55 % --res_passive_queue_type priority_queues
% 1.18/1.55 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.18/1.55 % --res_passive_queues_freq [15;5]
% 1.18/1.55 % --res_forward_subs full
% 1.18/1.55 % --res_backward_subs full
% 1.18/1.55 % --res_forward_subs_resolution true
% 1.18/1.55 % --res_backward_subs_resolution true
% 1.18/1.55 % --res_orphan_elimination false
% 1.18/1.55 % --res_time_limit 1000.
% 1.18/1.55 % --res_out_proof true
% 1.18/1.55 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_93f61f.s
% 1.18/1.55 % --modulo true
% 1.18/1.55
% 1.18/1.55 % ------ Combination Options
% 1.18/1.55
% 1.18/1.55 % --comb_res_mult 1000
% 1.18/1.55 % --comb_inst_mult 300
% 1.18/1.55 % ------
% 1.18/1.55
% 1.18/1.55 % ------ Parsing...% successful
% 1.18/1.55
% 1.18/1.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 1.18/1.55
% 1.18/1.55 % ------ Proving...
% 1.18/1.55 % ------ Problem Properties
% 1.18/1.55
% 1.18/1.55 %
% 1.18/1.55 % EPR false
% 1.18/1.55 % Horn false
% 1.18/1.55 % Has equality true
% 1.18/1.55
% 1.18/1.55 % % ------ Input Options Time Limit: Unbounded
% 1.18/1.55
% 1.18/1.55
% 1.18/1.55 Compiling...
% 1.18/1.55 Loading plugin: done.
% 1.18/1.55 Compiling...
% 1.18/1.55 Loading plugin: done.
% 1.18/1.55 Compiling...
% 1.18/1.55 Loading plugin: done.
% 1.18/1.55 Compiling...
% 1.18/1.55 Loading plugin: done.
% 1.18/1.55 Compiling...
% 1.18/1.55 Loading plugin: done.
% 1.18/1.55 Compiling...
% 1.18/1.55 Loading plugin: done.
% 1.18/1.55 Compiling...
% 1.18/1.55 Loading plugin: done.
% 1.18/1.55 % % ------ Current options:
% 1.18/1.55
% 1.18/1.55 % ------ Input Options
% 1.18/1.55
% 1.18/1.55 % --out_options all
% 1.18/1.55 % --tptp_safe_out true
% 1.18/1.55 % --problem_path ""
% 1.18/1.55 % --include_path ""
% 1.18/1.55 % --clausifier .//eprover
% 1.18/1.55 % --clausifier_options --tstp-format
% 1.18/1.55 % --stdin false
% 1.18/1.55 % --dbg_backtrace false
% 1.18/1.55 % --dbg_dump_prop_clauses false
% 1.18/1.55 % --dbg_dump_prop_clauses_file -
% 1.18/1.55 % --dbg_out_stat false
% 1.18/1.55
% 1.18/1.55 % ------ General Options
% 1.18/1.55
% 1.18/1.55 % --fof false
% 1.18/1.55 % --time_out_real 150.
% 1.18/1.55 % --time_out_prep_mult 0.2
% 1.18/1.55 % --time_out_virtual -1.
% 1.18/1.55 % --schedule none
% 1.18/1.55 % --ground_splitting input
% 1.18/1.55 % --splitting_nvd 16
% 1.18/1.55 % --non_eq_to_eq false
% 1.18/1.55 % --prep_gs_sim true
% 1.18/1.55 % --prep_unflatten false
% 1.18/1.55 % --prep_res_sim true
% 1.18/1.55 % --prep_upred true
% 1.18/1.55 % --res_sim_input true
% 1.18/1.55 % --clause_weak_htbl true
% 1.18/1.55 % --gc_record_bc_elim false
% 1.18/1.55 % --symbol_type_check false
% 1.18/1.55 % --clausify_out false
% 1.18/1.55 % --large_theory_mode false
% 1.18/1.55 % --prep_sem_filter none
% 1.18/1.55 % --prep_sem_filter_out false
% 1.18/1.55 % --preprocessed_out false
% 1.18/1.55 % --sub_typing false
% 1.18/1.55 % --brand_transform false
% 1.18/1.55 % --pure_diseq_elim true
% 1.18/1.55 % --min_unsat_core false
% 1.18/1.55 % --pred_elim true
% 1.18/1.55 % --add_important_lit false
% 1.18/1.55 % --soft_assumptions false
% 1.18/1.55 % --reset_solvers false
% 1.18/1.55 % --bc_imp_inh []
% 1.18/1.55 % --conj_cone_tolerance 1.5
% 1.18/1.55 % --prolific_symb_bound 500
% 1.18/1.55 % --lt_threshold 2000
% 1.18/1.55
% 1.18/1.55 % ------ SAT Options
% 1.18/1.55
% 1.18/1.55 % --sat_mode false
% 1.18/1.55 % --sat_fm_restart_options ""
% 1.18/1.55 % --sat_gr_def false
% 1.18/1.55 % --sat_epr_types true
% 1.18/1.55 % --sat_non_cyclic_types false
% 1.18/1.55 % --sat_finite_models false
% 1.18/1.55 % --sat_fm_lemmas false
% 1.18/1.55 % --sat_fm_prep false
% 1.18/1.55 % --sat_fm_uc_incr true
% 1.18/1.55 % --sat_out_model small
% 1.18/1.55 % --sat_out_clauses false
% 1.18/1.55
% 1.18/1.55 % ------ QBF Options
% 1.18/1.55
% 1.18/1.55 % --qbf_mode false
% 1.18/1.55 % --qbf_elim_univ true
% 1.18/1.55 % --qbf_sk_in true
% 1.18/1.55 % --qbf_pred_elim true
% 1.18/1.55 % --qbf_split 32
% 1.18/1.55
% 1.18/1.55 % ------ BMC1 Options
% 1.18/1.55
% 1.18/1.55 % --bmc1_incremental false
% 1.18/1.55 % --bmc1_axioms reachable_all
% 1.18/1.55 % --bmc1_min_bound 0
% 1.18/1.55 % --bmc1_max_bound -1
% 1.18/1.55 % --bmc1_max_bound_default -1
% 1.18/1.55 % --bmc1_symbol_reachability true
% 1.18/1.55 % --bmc1_property_lemmas false
% 1.18/1.55 % --bmc1_k_induction false
% 1.18/1.55 % --bmc1_non_equiv_states false
% 1.18/1.55 % --bmc1_deadlock false
% 1.18/1.55 % --bmc1_ucm false
% 1.18/1.55 % --bmc1_add_unsat_core none
% 1.18/1.55 % --bmc1_unsat_core_children false
% 1.18/1.55 % --bmc1_unsat_core_extrapolate_axioms false
% 1.18/1.55 % --bmc1_out_stat full
% 1.18/1.55 % --bmc1_ground_init false
% 1.18/1.55 % --bmc1_pre_inst_next_state false
% 1.18/1.55 % --bmc1_pre_inst_state false
% 1.18/1.55 % --bmc1_pre_inst_reach_state false
% 1.18/1.55 % --bmc1_out_unsat_core false
% 1.18/1.55 % --bmc1_aig_witness_out false
% 1.18/1.55 % --bmc1_verbose false
% 1.18/1.55 % --bmc1_dump_clauses_tptp false
% 1.18/1.55 % --bmc1_dump_unsat_core_tptp false
% 1.18/1.55 % --bmc1_dump_file -
% 1.18/1.55 % --bmc1_ucm_expand_uc_limit 128
% 1.18/1.55 % --bmc1_ucm_n_expand_iterations 6
% 1.18/1.55 % --bmc1_ucm_extend_mode 1
% 1.18/1.55 % --bmc1_ucm_init_mode 2
% 1.18/1.55 % --bmc1_ucm_cone_mode none
% 1.18/1.55 % --bmc1_ucm_reduced_relation_type 0
% 1.18/1.55 % --bmc1_ucm_relax_model 4
% 1.18/1.55 % --bmc1_ucm_full_tr_after_sat true
% 1.18/1.55 % --bmc1_ucm_expand_neg_assumptions false
% 1.18/1.55 % --bmc1_ucm_layered_model none
% 1.18/1.55 % --bmc1_ucm_max_lemma_size 10
% 1.18/1.55
% 1.18/1.55 % ------ AIG Options
% 1.18/1.55
% 1.18/1.55 % --aig_mode false
% 1.18/1.55
% 1.18/1.55 % ------ Instantiation Options
% 1.18/1.55
% 1.18/1.55 % --instantiation_flag true
% 1.18/1.55 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.18/1.55 % --inst_solver_per_active 750
% 1.18/1.55 % --inst_solver_calls_frac 0.5
% 1.18/1.55 % --inst_passive_queue_type priority_queues
% 1.18/1.55 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.21/150.47 % --inst_passive_queues_freq [25;2]
% 150.21/150.47 % --inst_dismatching true
% 150.21/150.47 % --inst_eager_unprocessed_to_passive true
% 150.21/150.47 % --inst_prop_sim_given true
% 150.21/150.47 % --inst_prop_sim_new false
% 150.21/150.47 % --inst_orphan_elimination true
% 150.21/150.47 % --inst_learning_loop_flag true
% 150.21/150.47 % --inst_learning_start 3000
% 150.21/150.47 % --inst_learning_factor 2
% 150.21/150.47 % --inst_start_prop_sim_after_learn 3
% 150.21/150.47 % --inst_sel_renew solver
% 150.21/150.47 % --inst_lit_activity_flag true
% 150.21/150.47 % --inst_out_proof true
% 150.21/150.47
% 150.21/150.47 % ------ Resolution Options
% 150.21/150.47
% 150.21/150.47 % --resolution_flag true
% 150.21/150.47 % --res_lit_sel kbo_max
% 150.21/150.47 % --res_to_prop_solver none
% 150.21/150.47 % --res_prop_simpl_new false
% 150.21/150.47 % --res_prop_simpl_given false
% 150.21/150.47 % --res_passive_queue_type priority_queues
% 150.21/150.47 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.21/150.47 % --res_passive_queues_freq [15;5]
% 150.21/150.47 % --res_forward_subs full
% 150.21/150.47 % --res_backward_subs full
% 150.21/150.47 % --res_forward_subs_resolution true
% 150.21/150.47 % --res_backward_subs_resolution true
% 150.21/150.47 % --res_orphan_elimination false
% 150.21/150.47 % --res_time_limit 1000.
% 150.21/150.47 % --res_out_proof true
% 150.21/150.47 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_93f61f.s
% 150.21/150.47 % --modulo true
% 150.21/150.47
% 150.21/150.47 % ------ Combination Options
% 150.21/150.47
% 150.21/150.47 % --comb_res_mult 1000
% 150.21/150.47 % --comb_inst_mult 300
% 150.21/150.47 % ------
% 150.21/150.47
% 150.21/150.47
% 150.21/150.47
% 150.21/150.47 % ------ Proving...
% 150.21/150.47 %
% 150.21/150.47
% 150.21/150.47
% 150.21/150.47 % Time Out Real
% 150.21/150.47
% 150.21/150.47 % ------ Statistics
% 150.21/150.47
% 150.21/150.47 % ------ General
% 150.21/150.47
% 150.21/150.47 % num_of_input_clauses: 238
% 150.21/150.47 % num_of_input_neg_conjectures: 1
% 150.21/150.47 % num_of_splits: 0
% 150.21/150.47 % num_of_split_atoms: 0
% 150.21/150.47 % num_of_sem_filtered_clauses: 0
% 150.21/150.47 % num_of_subtypes: 0
% 150.21/150.47 % monotx_restored_types: 0
% 150.21/150.47 % sat_num_of_epr_types: 0
% 150.21/150.47 % sat_num_of_non_cyclic_types: 0
% 150.21/150.47 % sat_guarded_non_collapsed_types: 0
% 150.21/150.47 % is_epr: 0
% 150.21/150.47 % is_horn: 0
% 150.21/150.47 % has_eq: 1
% 150.21/150.47 % num_pure_diseq_elim: 0
% 150.21/150.47 % simp_replaced_by: 0
% 150.21/150.47 % res_preprocessed: 8
% 150.21/150.47 % prep_upred: 0
% 150.21/150.47 % prep_unflattend: 0
% 150.21/150.47 % pred_elim_cands: 0
% 150.21/150.47 % pred_elim: 0
% 150.21/150.47 % pred_elim_cl: 0
% 150.21/150.47 % pred_elim_cycles: 0
% 150.21/150.47 % forced_gc_time: 0
% 150.21/150.47 % gc_basic_clause_elim: 0
% 150.21/150.47 % parsing_time: 0.01
% 150.21/150.47 % sem_filter_time: 0.
% 150.21/150.47 % pred_elim_time: 0.
% 150.21/150.47 % out_proof_time: 0.
% 150.21/150.47 % monotx_time: 0.
% 150.21/150.47 % subtype_inf_time: 0.
% 150.21/150.47 % unif_index_cands_time: 0.
% 150.21/150.47 % unif_index_add_time: 0.007
% 150.21/150.47 % total_time: 150.017
% 150.21/150.47 % num_of_symbols: 58
% 150.21/150.47 % num_of_terms: 40932
% 150.21/150.47
% 150.21/150.47 % ------ Propositional Solver
% 150.21/150.47
% 150.21/150.47 % prop_solver_calls: 1
% 150.21/150.47 % prop_fast_solver_calls: 15
% 150.21/150.47 % prop_num_of_clauses: 299
% 150.21/150.47 % prop_preprocess_simplified: 653
% 150.21/150.47 % prop_fo_subsumed: 0
% 150.21/150.47 % prop_solver_time: 0.
% 150.21/150.47 % prop_fast_solver_time: 0.
% 150.21/150.47 % prop_unsat_core_time: 0.
% 150.21/150.47
% 150.21/150.47 % ------ QBF
% 150.21/150.47
% 150.21/150.47 % qbf_q_res: 0
% 150.21/150.47 % qbf_num_tautologies: 0
% 150.21/150.47 % qbf_prep_cycles: 0
% 150.21/150.47
% 150.21/150.47 % ------ BMC1
% 150.21/150.47
% 150.21/150.47 % bmc1_current_bound: -1
% 150.21/150.47 % bmc1_last_solved_bound: -1
% 150.21/150.47 % bmc1_unsat_core_size: -1
% 150.21/150.47 % bmc1_unsat_core_parents_size: -1
% 150.21/150.47 % bmc1_merge_next_fun: 0
% 150.21/150.47 % bmc1_unsat_core_clauses_time: 0.
% 150.21/150.47
% 150.21/150.47 % ------ Instantiation
% 150.21/150.47
% 150.21/150.47 % inst_num_of_clauses: 219
% 150.21/150.47 % inst_num_in_passive: 0
% 150.21/150.47 % inst_num_in_active: 0
% 150.21/150.47 % inst_num_in_unprocessed: 238
% 150.21/150.47 % inst_num_of_loops: 0
% 150.21/150.47 % inst_num_of_learning_restarts: 0
% 150.21/150.47 % inst_num_moves_active_passive: 0
% 150.21/150.47 % inst_lit_activity: 0
% 150.21/150.47 % inst_lit_activity_moves: 0
% 150.21/150.47 % inst_num_tautologies: 0
% 150.21/150.47 % inst_num_prop_implied: 0
% 150.21/150.47 % inst_num_existing_simplified: 0
% 150.21/150.47 % inst_num_eq_res_simplified: 0
% 150.21/150.47 % inst_num_child_elim: 0
% 150.21/150.47 % inst_num_of_dismatching_blockings: 0
% 150.21/150.47 % inst_num_of_non_proper_insts: 0
% 150.21/150.47 % inst_num_of_duplicates: 0
% 150.21/150.47 % inst_inst_num_from_inst_to_res: 0
% 150.21/150.47 % inst_dismatching_checking_time: 0.
% 150.21/150.47
% 150.21/150.47 % ------ Resolution
% 150.21/150.47
% 150.21/150.47 % res_num_of_clauses: 764
% 150.21/150.47 % res_num_in_passive: 214
% 150.21/150.47 % res_num_in_active: 378
% 150.21/150.47 % res_num_of_loops: 414
% 150.21/150.47 % res_forward_subset_subsumed: 162
% 150.21/150.47 % res_backward_subset_subsumed: 1
% 150.21/150.47 % res_forward_subsumed: 170
% 150.21/150.47 % res_backward_subsumed: 4
% 150.21/150.47 % res_forward_subsumption_resolution: 60
% 150.21/150.47 % res_backward_subsumption_resolution: 2
% 150.21/150.47 % res_clause_to_clause_subsumption: 408
% 150.21/150.47 % res_orphan_elimination: 0
% 150.21/150.47 % res_tautology_del: 15
% 150.21/150.47 % res_num_eq_res_simplified: 0
% 150.21/150.47 % res_num_sel_changes: 0
% 150.21/150.47 % res_moves_from_active_to_pass: 0
% 150.21/150.47
% 150.21/150.47 % Status Unknown
% 150.30/150.54 % Orienting using strategy ClausalAll
% 150.30/150.54 % FOF problem with conjecture
% 150.30/150.54 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_93f61f.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_847f5e.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_16f44d | grep -v "SZS"
% 150.30/150.56
% 150.30/150.56 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.30/150.56
% 150.30/150.56 %
% 150.30/150.56 % ------ iProver source info
% 150.30/150.56
% 150.30/150.56 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.30/150.56 % git: non_committed_changes: true
% 150.30/150.56 % git: last_make_outside_of_git: true
% 150.30/150.56
% 150.30/150.56 %
% 150.30/150.56 % ------ Input Options
% 150.30/150.56
% 150.30/150.56 % --out_options all
% 150.30/150.56 % --tptp_safe_out true
% 150.30/150.56 % --problem_path ""
% 150.30/150.56 % --include_path ""
% 150.30/150.56 % --clausifier .//eprover
% 150.30/150.56 % --clausifier_options --tstp-format
% 150.30/150.56 % --stdin false
% 150.30/150.56 % --dbg_backtrace false
% 150.30/150.56 % --dbg_dump_prop_clauses false
% 150.30/150.56 % --dbg_dump_prop_clauses_file -
% 150.30/150.56 % --dbg_out_stat false
% 150.30/150.56
% 150.30/150.56 % ------ General Options
% 150.30/150.56
% 150.30/150.56 % --fof false
% 150.30/150.56 % --time_out_real 150.
% 150.30/150.56 % --time_out_prep_mult 0.2
% 150.30/150.56 % --time_out_virtual -1.
% 150.30/150.56 % --schedule none
% 150.30/150.56 % --ground_splitting input
% 150.30/150.56 % --splitting_nvd 16
% 150.30/150.56 % --non_eq_to_eq false
% 150.30/150.56 % --prep_gs_sim true
% 150.30/150.56 % --prep_unflatten false
% 150.30/150.56 % --prep_res_sim true
% 150.30/150.56 % --prep_upred true
% 150.30/150.56 % --res_sim_input true
% 150.30/150.56 % --clause_weak_htbl true
% 150.30/150.56 % --gc_record_bc_elim false
% 150.30/150.56 % --symbol_type_check false
% 150.30/150.56 % --clausify_out false
% 150.30/150.56 % --large_theory_mode false
% 150.30/150.56 % --prep_sem_filter none
% 150.30/150.56 % --prep_sem_filter_out false
% 150.30/150.56 % --preprocessed_out false
% 150.30/150.56 % --sub_typing false
% 150.30/150.56 % --brand_transform false
% 150.30/150.56 % --pure_diseq_elim true
% 150.30/150.56 % --min_unsat_core false
% 150.30/150.56 % --pred_elim true
% 150.30/150.56 % --add_important_lit false
% 150.30/150.56 % --soft_assumptions false
% 150.30/150.56 % --reset_solvers false
% 150.30/150.56 % --bc_imp_inh []
% 150.30/150.56 % --conj_cone_tolerance 1.5
% 150.30/150.56 % --prolific_symb_bound 500
% 150.30/150.56 % --lt_threshold 2000
% 150.30/150.56
% 150.30/150.56 % ------ SAT Options
% 150.30/150.56
% 150.30/150.56 % --sat_mode false
% 150.30/150.56 % --sat_fm_restart_options ""
% 150.30/150.56 % --sat_gr_def false
% 150.30/150.56 % --sat_epr_types true
% 150.30/150.56 % --sat_non_cyclic_types false
% 150.30/150.56 % --sat_finite_models false
% 150.30/150.56 % --sat_fm_lemmas false
% 150.30/150.56 % --sat_fm_prep false
% 150.30/150.56 % --sat_fm_uc_incr true
% 150.30/150.56 % --sat_out_model small
% 150.30/150.56 % --sat_out_clauses false
% 150.30/150.56
% 150.30/150.56 % ------ QBF Options
% 150.30/150.56
% 150.30/150.56 % --qbf_mode false
% 150.30/150.56 % --qbf_elim_univ true
% 150.30/150.56 % --qbf_sk_in true
% 150.30/150.56 % --qbf_pred_elim true
% 150.30/150.56 % --qbf_split 32
% 150.30/150.56
% 150.30/150.56 % ------ BMC1 Options
% 150.30/150.56
% 150.30/150.56 % --bmc1_incremental false
% 150.30/150.56 % --bmc1_axioms reachable_all
% 150.30/150.56 % --bmc1_min_bound 0
% 150.30/150.56 % --bmc1_max_bound -1
% 150.30/150.56 % --bmc1_max_bound_default -1
% 150.30/150.56 % --bmc1_symbol_reachability true
% 150.30/150.56 % --bmc1_property_lemmas false
% 150.30/150.56 % --bmc1_k_induction false
% 150.30/150.56 % --bmc1_non_equiv_states false
% 150.30/150.56 % --bmc1_deadlock false
% 150.30/150.56 % --bmc1_ucm false
% 150.30/150.56 % --bmc1_add_unsat_core none
% 150.30/150.56 % --bmc1_unsat_core_children false
% 150.30/150.56 % --bmc1_unsat_core_extrapolate_axioms false
% 150.30/150.56 % --bmc1_out_stat full
% 150.30/150.56 % --bmc1_ground_init false
% 150.30/150.56 % --bmc1_pre_inst_next_state false
% 150.30/150.56 % --bmc1_pre_inst_state false
% 150.30/150.56 % --bmc1_pre_inst_reach_state false
% 150.30/150.56 % --bmc1_out_unsat_core false
% 150.30/150.56 % --bmc1_aig_witness_out false
% 150.30/150.56 % --bmc1_verbose false
% 150.30/150.56 % --bmc1_dump_clauses_tptp false
% 151.41/151.69 % --bmc1_dump_unsat_core_tptp false
% 151.41/151.69 % --bmc1_dump_file -
% 151.41/151.69 % --bmc1_ucm_expand_uc_limit 128
% 151.41/151.69 % --bmc1_ucm_n_expand_iterations 6
% 151.41/151.69 % --bmc1_ucm_extend_mode 1
% 151.41/151.69 % --bmc1_ucm_init_mode 2
% 151.41/151.69 % --bmc1_ucm_cone_mode none
% 151.41/151.69 % --bmc1_ucm_reduced_relation_type 0
% 151.41/151.69 % --bmc1_ucm_relax_model 4
% 151.41/151.69 % --bmc1_ucm_full_tr_after_sat true
% 151.41/151.69 % --bmc1_ucm_expand_neg_assumptions false
% 151.41/151.69 % --bmc1_ucm_layered_model none
% 151.41/151.69 % --bmc1_ucm_max_lemma_size 10
% 151.41/151.69
% 151.41/151.69 % ------ AIG Options
% 151.41/151.69
% 151.41/151.69 % --aig_mode false
% 151.41/151.69
% 151.41/151.69 % ------ Instantiation Options
% 151.41/151.69
% 151.41/151.69 % --instantiation_flag true
% 151.41/151.69 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.41/151.69 % --inst_solver_per_active 750
% 151.41/151.69 % --inst_solver_calls_frac 0.5
% 151.41/151.69 % --inst_passive_queue_type priority_queues
% 151.41/151.69 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.41/151.69 % --inst_passive_queues_freq [25;2]
% 151.41/151.69 % --inst_dismatching true
% 151.41/151.69 % --inst_eager_unprocessed_to_passive true
% 151.41/151.69 % --inst_prop_sim_given true
% 151.41/151.69 % --inst_prop_sim_new false
% 151.41/151.69 % --inst_orphan_elimination true
% 151.41/151.69 % --inst_learning_loop_flag true
% 151.41/151.69 % --inst_learning_start 3000
% 151.41/151.69 % --inst_learning_factor 2
% 151.41/151.69 % --inst_start_prop_sim_after_learn 3
% 151.41/151.69 % --inst_sel_renew solver
% 151.41/151.69 % --inst_lit_activity_flag true
% 151.41/151.69 % --inst_out_proof true
% 151.41/151.69
% 151.41/151.69 % ------ Resolution Options
% 151.41/151.69
% 151.41/151.69 % --resolution_flag true
% 151.41/151.69 % --res_lit_sel kbo_max
% 151.41/151.69 % --res_to_prop_solver none
% 151.41/151.69 % --res_prop_simpl_new false
% 151.41/151.69 % --res_prop_simpl_given false
% 151.41/151.69 % --res_passive_queue_type priority_queues
% 151.41/151.69 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.41/151.69 % --res_passive_queues_freq [15;5]
% 151.41/151.69 % --res_forward_subs full
% 151.41/151.69 % --res_backward_subs full
% 151.41/151.69 % --res_forward_subs_resolution true
% 151.41/151.69 % --res_backward_subs_resolution true
% 151.41/151.69 % --res_orphan_elimination false
% 151.41/151.69 % --res_time_limit 1000.
% 151.41/151.69 % --res_out_proof true
% 151.41/151.69 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_93f61f.s
% 151.41/151.69 % --modulo true
% 151.41/151.69
% 151.41/151.69 % ------ Combination Options
% 151.41/151.69
% 151.41/151.69 % --comb_res_mult 1000
% 151.41/151.69 % --comb_inst_mult 300
% 151.41/151.69 % ------
% 151.41/151.69
% 151.41/151.69 % ------ Parsing...% successful
% 151.41/151.69
% 151.41/151.69 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 151.41/151.69
% 151.41/151.69 % ------ Proving...
% 151.41/151.69 % ------ Problem Properties
% 151.41/151.69
% 151.41/151.69 %
% 151.41/151.69 % EPR false
% 151.41/151.69 % Horn false
% 151.41/151.69 % Has equality true
% 151.41/151.69
% 151.41/151.69 % % ------ Input Options Time Limit: Unbounded
% 151.41/151.69
% 151.41/151.69
% 151.41/151.69 Compiling...
% 151.41/151.69 Loading plugin: done.
% 151.41/151.69 Compiling...
% 151.41/151.69 Loading plugin: done.
% 151.41/151.69 Compiling...
% 151.41/151.69 Loading plugin: done.
% 151.41/151.69 Compiling...
% 151.41/151.69 Loading plugin: done.
% 151.41/151.69 Compiling...
% 151.41/151.69 Loading plugin: done.
% 151.41/151.69 Compiling...
% 151.41/151.69 Loading plugin: done.
% 151.41/151.69 Compiling...
% 151.41/151.69 Loading plugin: done.
% 151.41/151.69 % % ------ Current options:
% 151.41/151.69
% 151.41/151.69 % ------ Input Options
% 151.41/151.69
% 151.41/151.69 % --out_options all
% 151.41/151.69 % --tptp_safe_out true
% 151.41/151.69 % --problem_path ""
% 151.41/151.69 % --include_path ""
% 151.41/151.69 % --clausifier .//eprover
% 151.41/151.69 % --clausifier_options --tstp-format
% 151.41/151.69 % --stdin false
% 151.41/151.69 % --dbg_backtrace false
% 151.41/151.69 % --dbg_dump_prop_clauses false
% 151.41/151.69 % --dbg_dump_prop_clauses_file -
% 151.41/151.69 % --dbg_out_stat false
% 151.41/151.69
% 151.41/151.69 % ------ General Options
% 151.41/151.69
% 151.41/151.69 % --fof false
% 151.41/151.69 % --time_out_real 150.
% 151.41/151.69 % --time_out_prep_mult 0.2
% 151.41/151.69 % --time_out_virtual -1.
% 151.41/151.69 % --schedule none
% 151.41/151.69 % --ground_splitting input
% 151.41/151.69 % --splitting_nvd 16
% 151.41/151.69 % --non_eq_to_eq false
% 151.41/151.69 % --prep_gs_sim true
% 151.41/151.69 % --prep_unflatten false
% 151.41/151.69 % --prep_res_sim true
% 151.41/151.69 % --prep_upred true
% 151.41/151.69 % --res_sim_input true
% 151.41/151.69 % --clause_weak_htbl true
% 151.41/151.69 % --gc_record_bc_elim false
% 151.41/151.69 % --symbol_type_check false
% 151.41/151.69 % --clausify_out false
% 151.41/151.69 % --large_theory_mode false
% 151.41/151.69 % --prep_sem_filter none
% 151.41/151.69 % --prep_sem_filter_out false
% 151.41/151.69 % --preprocessed_out false
% 151.41/151.69 % --sub_typing false
% 151.41/151.69 % --brand_transform false
% 151.41/151.69 % --pure_diseq_elim true
% 151.41/151.69 % --min_unsat_core false
% 151.41/151.69 % --pred_elim true
% 151.41/151.69 % --add_important_lit false
% 151.41/151.69 % --soft_assumptions false
% 151.41/151.69 % --reset_solvers false
% 151.41/151.69 % --bc_imp_inh []
% 151.41/151.69 % --conj_cone_tolerance 1.5
% 151.41/151.69 % --prolific_symb_bound 500
% 151.41/151.69 % --lt_threshold 2000
% 151.41/151.69
% 151.41/151.69 % ------ SAT Options
% 151.41/151.69
% 151.41/151.69 % --sat_mode false
% 151.41/151.69 % --sat_fm_restart_options ""
% 151.41/151.69 % --sat_gr_def false
% 151.41/151.69 % --sat_epr_types true
% 151.41/151.69 % --sat_non_cyclic_types false
% 151.41/151.69 % --sat_finite_models false
% 151.41/151.69 % --sat_fm_lemmas false
% 151.41/151.69 % --sat_fm_prep false
% 151.41/151.69 % --sat_fm_uc_incr true
% 151.41/151.69 % --sat_out_model small
% 151.41/151.69 % --sat_out_clauses false
% 151.41/151.69
% 151.41/151.69 % ------ QBF Options
% 151.41/151.69
% 151.41/151.69 % --qbf_mode false
% 151.41/151.69 % --qbf_elim_univ true
% 151.41/151.69 % --qbf_sk_in true
% 151.41/151.69 % --qbf_pred_elim true
% 151.41/151.69 % --qbf_split 32
% 151.41/151.69
% 151.41/151.69 % ------ BMC1 Options
% 151.41/151.69
% 151.41/151.69 % --bmc1_incremental false
% 151.41/151.69 % --bmc1_axioms reachable_all
% 151.41/151.69 % --bmc1_min_bound 0
% 151.41/151.69 % --bmc1_max_bound -1
% 151.41/151.69 % --bmc1_max_bound_default -1
% 151.41/151.69 % --bmc1_symbol_reachability true
% 151.41/151.69 % --bmc1_property_lemmas false
% 151.41/151.69 % --bmc1_k_induction false
% 151.41/151.69 % --bmc1_non_equiv_states false
% 151.41/151.69 % --bmc1_deadlock false
% 151.41/151.69 % --bmc1_ucm false
% 151.41/151.69 % --bmc1_add_unsat_core none
% 151.41/151.69 % --bmc1_unsat_core_children false
% 151.41/151.69 % --bmc1_unsat_core_extrapolate_axioms false
% 151.41/151.69 % --bmc1_out_stat full
% 151.41/151.69 % --bmc1_ground_init false
% 151.41/151.69 % --bmc1_pre_inst_next_state false
% 151.41/151.69 % --bmc1_pre_inst_state false
% 151.41/151.69 % --bmc1_pre_inst_reach_state false
% 151.41/151.69 % --bmc1_out_unsat_core false
% 151.41/151.69 % --bmc1_aig_witness_out false
% 151.41/151.69 % --bmc1_verbose false
% 151.41/151.69 % --bmc1_dump_clauses_tptp false
% 151.41/151.69 % --bmc1_dump_unsat_core_tptp false
% 151.41/151.69 % --bmc1_dump_file -
% 151.41/151.69 % --bmc1_ucm_expand_uc_limit 128
% 151.41/151.69 % --bmc1_ucm_n_expand_iterations 6
% 151.41/151.69 % --bmc1_ucm_extend_mode 1
% 151.41/151.69 % --bmc1_ucm_init_mode 2
% 151.41/151.69 % --bmc1_ucm_cone_mode none
% 151.41/151.69 % --bmc1_ucm_reduced_relation_type 0
% 151.41/151.69 % --bmc1_ucm_relax_model 4
% 151.41/151.69 % --bmc1_ucm_full_tr_after_sat true
% 151.41/151.69 % --bmc1_ucm_expand_neg_assumptions false
% 151.41/151.69 % --bmc1_ucm_layered_model none
% 151.41/151.69 % --bmc1_ucm_max_lemma_size 10
% 151.41/151.69
% 151.41/151.69 % ------ AIG Options
% 151.41/151.69
% 151.41/151.69 % --aig_mode false
% 151.41/151.69
% 151.41/151.69 % ------ Instantiation Options
% 151.41/151.69
% 151.41/151.69 % --instantiation_flag true
% 151.41/151.69 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.41/151.69 % --inst_solver_per_active 750
% 151.41/151.69 % --inst_solver_calls_frac 0.5
% 151.41/151.69 % --inst_passive_queue_type priority_queues
% 151.41/151.69 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 248.10/248.35 % --inst_passive_queues_freq [25;2]
% 248.10/248.35 % --inst_dismatching true
% 248.10/248.35 % --inst_eager_unprocessed_to_passive true
% 248.10/248.35 % --inst_prop_sim_given true
% 248.10/248.35 % --inst_prop_sim_new false
% 248.10/248.35 % --inst_orphan_elimination true
% 248.10/248.35 % --inst_learning_loop_flag true
% 248.10/248.35 % --inst_learning_start 3000
% 248.10/248.35 % --inst_learning_factor 2
% 248.10/248.35 % --inst_start_prop_sim_after_learn 3
% 248.10/248.35 % --inst_sel_renew solver
% 248.10/248.35 % --inst_lit_activity_flag true
% 248.10/248.35 % --inst_out_proof true
% 248.10/248.35
% 248.10/248.35 % ------ Resolution Options
% 248.10/248.35
% 248.10/248.35 % --resolution_flag true
% 248.10/248.35 % --res_lit_sel kbo_max
% 248.10/248.35 % --res_to_prop_solver none
% 248.10/248.35 % --res_prop_simpl_new false
% 248.10/248.35 % --res_prop_simpl_given false
% 248.10/248.35 % --res_passive_queue_type priority_queues
% 248.10/248.35 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 248.10/248.35 % --res_passive_queues_freq [15;5]
% 248.10/248.35 % --res_forward_subs full
% 248.10/248.35 % --res_backward_subs full
% 248.10/248.35 % --res_forward_subs_resolution true
% 248.10/248.35 % --res_backward_subs_resolution true
% 248.10/248.35 % --res_orphan_elimination false
% 248.10/248.35 % --res_time_limit 1000.
% 248.10/248.35 % --res_out_proof true
% 248.10/248.35 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_93f61f.s
% 248.10/248.35 % --modulo true
% 248.10/248.35
% 248.10/248.35 % ------ Combination Options
% 248.10/248.35
% 248.10/248.35 % --comb_res_mult 1000
% 248.10/248.35 % --comb_inst_mult 300
% 248.10/248.35 % ------
% 248.10/248.35
% 248.10/248.35
% 248.10/248.35
% 248.10/248.35 % ------ Proving...
% 248.10/248.35 %
% 248.10/248.35
% 248.10/248.35
% 248.10/248.35 % ------ Statistics
% 248.10/248.35
% 248.10/248.35 % ------ General
% 248.10/248.35
% 248.10/248.35 % num_of_input_clauses: 361
% 248.10/248.35 % num_of_input_neg_conjectures: 1
% 248.10/248.35 % num_of_splits: 0
% 248.10/248.35 % num_of_split_atoms: 0
% 248.10/248.35 % num_of_sem_filtered_clauses: 0
% 248.10/248.35 % num_of_subtypes: 0
% 248.10/248.35 % monotx_restored_types: 0
% 248.10/248.35 % sat_num_of_epr_types: 0
% 248.10/248.35 % sat_num_of_non_cyclic_types: 0
% 248.10/248.35 % sat_guarded_non_collapsed_types: 0
% 248.10/248.35 % is_epr: 0
% 248.10/248.35 % is_horn: 0
% 248.10/248.35 % has_eq: 1
% 248.10/248.35 % num_pure_diseq_elim: 0
% 248.10/248.35 % simp_replaced_by: 0
% 248.10/248.35 % res_preprocessed: 8
% 248.10/248.35 % prep_upred: 0
% 248.10/248.35 % prep_unflattend: 0
% 248.10/248.35 % pred_elim_cands: 0
% 248.10/248.35 % pred_elim: 0
% 248.10/248.35 % pred_elim_cl: 0
% 248.10/248.35 % pred_elim_cycles: 0
% 248.10/248.35 % forced_gc_time: 0
% 248.10/248.35 % gc_basic_clause_elim: 0
% 248.10/248.35 % parsing_time: 0.015
% 248.10/248.35 % sem_filter_time: 0.
% 248.10/248.35 % pred_elim_time: 0.
% 248.10/248.35 % out_proof_time: 0.001
% 248.10/248.35 % monotx_time: 0.
% 248.10/248.35 % subtype_inf_time: 0.
% 248.10/248.35 % unif_index_cands_time: 0.335
% 248.10/248.35 % unif_index_add_time: 0.061
% 248.10/248.35 % total_time: 97.805
% 248.10/248.35 % num_of_symbols: 58
% 248.10/248.35 % num_of_terms: 176436
% 248.10/248.35
% 248.10/248.35 % ------ Propositional Solver
% 248.10/248.35
% 248.10/248.35 % prop_solver_calls: 13
% 248.10/248.35 % prop_fast_solver_calls: 15
% 248.10/248.35 % prop_num_of_clauses: 13281
% 248.10/248.35 % prop_preprocess_simplified: 13867
% 248.10/248.35 % prop_fo_subsumed: 0
% 248.10/248.35 % prop_solver_time: 0.003
% 248.10/248.35 % prop_fast_solver_time: 0.
% 248.10/248.35 % prop_unsat_core_time: 0.001
% 248.10/248.35
% 248.10/248.35 % ------ QBF
% 248.10/248.35
% 248.10/248.35 % qbf_q_res: 0
% 248.10/248.35 % qbf_num_tautologies: 0
% 248.10/248.35 % qbf_prep_cycles: 0
% 248.10/248.35
% 248.10/248.35 % ------ BMC1
% 248.10/248.35
% 248.10/248.35 % bmc1_current_bound: -1
% 248.10/248.35 % bmc1_last_solved_bound: -1
% 248.10/248.35 % bmc1_unsat_core_size: -1
% 248.10/248.35 % bmc1_unsat_core_parents_size: -1
% 248.10/248.35 % bmc1_merge_next_fun: 0
% 248.10/248.35 % bmc1_unsat_core_clauses_time: 0.
% 248.10/248.36
% 248.10/248.36 % ------ Instantiation
% 248.10/248.36
% 248.10/248.36 % inst_num_of_clauses: 7797
% 248.10/248.36 % inst_num_in_passive: 4325
% 248.10/248.36 % inst_num_in_active: 1455
% 248.10/248.36 % inst_num_in_unprocessed: 2010
% 248.10/248.36 % inst_num_of_loops: 2158
% 248.10/248.36 % inst_num_of_learning_restarts: 0
% 248.10/248.36 % inst_num_moves_active_passive: 697
% 248.10/248.36 % inst_lit_activity: 3226
% 248.10/248.36 % inst_lit_activity_moves: 0
% 248.10/248.36 % inst_num_tautologies: 3
% 248.10/248.36 % inst_num_prop_implied: 0
% 248.10/248.36 % inst_num_existing_simplified: 0
% 248.10/248.36 % inst_num_eq_res_simplified: 0
% 248.10/248.36 % inst_num_child_elim: 0
% 248.10/248.36 % inst_num_of_dismatching_blockings: 2984
% 248.10/248.36 % inst_num_of_non_proper_insts: 7601
% 248.10/248.36 % inst_num_of_duplicates: 14497
% 248.10/248.36 % inst_inst_num_from_inst_to_res: 0
% 248.10/248.36 % inst_dismatching_checking_time: 0.112
% 248.10/248.36
% 248.10/248.36 % ------ Resolution
% 248.10/248.36
% 248.10/248.36 % res_num_of_clauses: 481081
% 248.10/248.36 % res_num_in_passive: 474315
% 248.10/248.36 % res_num_in_active: 6829
% 248.10/248.36 % res_num_of_loops: 8000
% 248.10/248.36 % res_forward_subset_subsumed: 46874
% 248.10/248.36 % res_backward_subset_subsumed: 281
% 248.10/248.36 % res_forward_subsumed: 1174
% 248.10/248.36 % res_backward_subsumed: 22
% 248.10/248.36 % res_forward_subsumption_resolution: 1233
% 248.10/248.36 % res_backward_subsumption_resolution: 3
% 248.10/248.36 % res_clause_to_clause_subsumption: 473515
% 248.10/248.36 % res_orphan_elimination: 0
% 248.10/248.36 % res_tautology_del: 1873
% 248.10/248.36 % res_num_eq_res_simplified: 0
% 248.10/248.36 % res_num_sel_changes: 0
% 248.10/248.36 % res_moves_from_active_to_pass: 0
% 248.10/248.36
% 248.10/248.36 % Status Unsatisfiable
% 248.10/248.36 % SZS status Theorem
% 248.10/248.36 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------