%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:01:01 AM UTC 2026
% Result : Theorem 21.62s 3.84s
% Output : CNFRefutation 21.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 168
% Syntax : Number of formulae : 1312 ( 939 unt; 0 typ; 0 def)
% Number of atoms : 5828 (3083 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 12657 (1644 ~;1286 |; 9 &;9493 @)
% ( 96 <=>; 129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 103 ( 100 usr; 13 con; 0-3 aty)
% Number of variables : 2556 ( 0 ^;2545 !; 11 ?;2556 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Complex_Oii,type,
c_Complex_Oii: $i ).
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
thf(tp_c_Groups_Oabs__class_Oabs,type,
c_Groups_Oabs__class_Oabs: $i > $i > $i ).
thf(tp_c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tp_c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(tp_c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(tp_c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tp_c_Int_OBit0,type,
c_Int_OBit0: $i > $i ).
thf(tp_c_Int_OBit1,type,
c_Int_OBit1: $i > $i ).
thf(tp_c_Int_OMin,type,
c_Int_OMin: $i ).
thf(tp_c_Int_OPls,type,
c_Int_OPls: $i ).
thf(tp_c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(tp_c_Nat_OSuc,type,
c_Nat_OSuc: $i > $i ).
thf(tp_c_NthRoot_Osqrt,type,
c_NthRoot_Osqrt: $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(tp_c_Parity_Oeven__odd__class_Oeven,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tp_c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(tp_c_RealVector_Oof__real,type,
c_RealVector_Oof__real: $i > $i > $i ).
thf(tp_c_Rings_Oinverse__class_Odivide,type,
c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(tp_c_Transcendental_Oarctan,type,
c_Transcendental_Oarctan: $i > $i ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
thf(tp_class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(tp_class_Fields_Olinordered__field,type,
class_Fields_Olinordered__field: $i > $o ).
thf(tp_class_Fields_Olinordered__field__inverse__zero,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(tp_class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
thf(tp_class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(tp_class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add__abs,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(tp_class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
thf(tp_class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_RealVector_Oreal__algebra__1,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
thf(tp_class_RealVector_Oreal__field,type,
class_RealVector_Oreal__field: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Rings_Odivision__ring,type,
class_Rings_Odivision__ring: $i > $o ).
thf(tp_class_Rings_Odivision__ring__inverse__zero,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(tp_class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(tp_class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(tp_class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(tp_class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
thf(tp_class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
thf(tp_class_Rings_Oordered__ring__abs,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(tp_class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(tp_class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
thf(tp_class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
thf(tp_class_Rings_Osemiring__1,type,
class_Rings_Osemiring__1: $i > $o ).
thf(tp_class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(tp_class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_sK1_SY288,type,
sK1_SY288: $i > $i ).
thf(tp_sK2_SY321,type,
sK2_SY321: $i > $i ).
thf(tp_tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
thf(tp_tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
thf(tp_tc_Int_Oint,type,
tc_Int_Oint: $i ).
thf(tp_tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
thf(tp_tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_v_b,type,
v_b: $i ).
thf(tp_v_n,type,
v_n: $i ).
thf(tp_v_na____,type,
v_na____: $i ).
thf(102,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(103,axiom,
class_Int_Onumber @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
thf(104,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(105,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(106,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(107,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(108,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(109,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(110,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(111,axiom,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(112,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(113,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(114,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(115,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(116,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(117,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(118,axiom,
class_Divides_Osemiring__div @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(119,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(120,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(121,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(122,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(123,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(124,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(125,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(126,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(127,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(128,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(129,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(130,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(131,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(132,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(133,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(134,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(135,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(136,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(137,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(138,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(410,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
thf(411,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
thf(490,axiom,
! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ V_n )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(491,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) )
<=> ( ( V_m_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( V_nb_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(492,axiom,
! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(493,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( V_m_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( V_nb_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(690,axiom,
! [V_z3: $i,V_z2: $i,V_z1: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z1 @ V_z2 ) @ V_z3 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z1 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z2 @ V_z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(691,axiom,
! [V_w: $i,V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z @ V_w )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_w @ V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(700,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Groups_Oab__semigroup__mult @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ V_b ) @ V_c )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_b @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(716,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m = V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(717,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(729,axiom,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(730,axiom,
! [V_t: $i,V_s: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
=> ( V_s != V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(731,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m != V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(732,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(733,axiom,
! [V_y: $i,V_x: $i] :
( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(736,axiom,
! [V_nb_2: $i,V_k_2: $i,V_m_2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m_2 @ V_k_2 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_nb_2 @ V_k_2 ) )
<=> ( V_m_2 = V_nb_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(737,axiom,
! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( V_m_2 = V_nb_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(739,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(740,axiom,
! [V_z: $i,V_y: $i,V_x: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_x @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(747,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(749,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(751,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( V_m_2 != V_nb_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ V_m_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(755,axiom,
! [V_n: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(758,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(779,axiom,
! [V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_z )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_z @ V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).
thf(780,axiom,
! [V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_z @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_z @ V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
thf(781,axiom,
! [V_n: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_n )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
thf(782,axiom,
! [V_n: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
thf(789,axiom,
! [V_n: $i] :
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
thf(816,axiom,
! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(817,axiom,
! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(831,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(832,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(907,axiom,
! [V_l: $i,V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_k @ V_l )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_l ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(908,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_i ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_j ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(909,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(910,axiom,
! [V_m: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
thf(911,axiom,
! [V_m: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
thf(916,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(917,axiom,
! [V_n: $i,V_m: $i,V_k: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_m ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(918,axiom,
! [V_k: $i,V_j: $i,V_u: $i,V_i: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_u ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_u ) @ V_k ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_u ) @ V_k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(923,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(924,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_m
= ( c_Nat_OSuc @ V_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(925,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(926,axiom,
! [V_m_2: $i,V_nb_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_nb_2 ) @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_nb_2 @ V_m_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(927,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( V_m_2
= ( c_Nat_OSuc @ V_nb_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(928,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_nb_2 ) @ V_m_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(929,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_n ) @ V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(932,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ ( c_Nat_OSuc @ V_n ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(933,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(934,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_m = V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(935,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_i ) @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(936,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( ( c_Nat_OSuc @ V_m )
!= V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(937,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(938,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_m ) )
=> ( V_m = V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(939,axiom,
! [V_m_2: $i,V_nb_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ V_m_2 )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( V_nb_2 = V_m_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(940,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m_2 ) @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(941,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( V_m_2 = V_nb_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(942,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ ( c_Nat_OSuc @ V_m_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(958,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(959,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(960,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(971,axiom,
! [V_k: $i] :
( ( c_Int_OBit0 @ V_k )
!= c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
thf(972,axiom,
! [V_l: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ V_l ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
thf(973,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
thf(974,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
thf(975,axiom,
! [V_k_2: $i] :
( ( ( c_Int_OBit1 @ V_k_2 )
= c_Int_OMin )
<=> ( V_k_2 = c_Int_OMin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
thf(976,axiom,
! [V_l_2: $i] :
( ( c_Int_OMin
= ( c_Int_OBit1 @ V_l_2 ) )
<=> ( c_Int_OMin = V_l_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
thf(977,axiom,
( ( c_Int_OBit1 @ c_Int_OMin )
= c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__Min) ).
thf(1065,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ ( c_Nat_OSuc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1066,axiom,
! [V_n: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(1091,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ V_b )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_b @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1092,axiom,
! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1093,axiom,
! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ V_ry ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1094,axiom,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_rx )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ V_rx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1095,axiom,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_rx )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ V_ly ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1096,axiom,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1097,axiom,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1098,axiom,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ V_ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1099,axiom,
! [V_k: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_k )
= V_k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
thf(1122,axiom,
! [V_z3: $i,V_z2: $i,V_z1: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z1 @ V_z2 ) @ V_z3 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z1 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z2 @ V_z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(1123,axiom,
! [V_w: $i,V_v: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_v ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_w ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_v @ V_w ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(1124,axiom,
! [V_w: $i,V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z @ V_w )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_w @ V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(1130,axiom,
! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( V_m_2 = V_nb_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(1132,axiom,
! [V_x_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_x_2 ) )
<=> ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__Suc) ).
thf(1133,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) )
<=> ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_x_2 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__product__nat) ).
thf(1136,axiom,
! [V_nb_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_nb_2 )
<=> ? [B_m: $i] :
( V_nb_2
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__mult__two__ex) ).
thf(1137,axiom,
! [V_nb_2: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_nb_2 )
<=> ? [B_m: $i] :
( V_nb_2
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
thf(1141,axiom,
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
thf(1142,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
thf(1143,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(1144,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(1145,axiom,
! [V_l_2: $i,V_k_2: $i] :
( ( ( c_Int_OBit0 @ V_k_2 )
= ( c_Int_OBit0 @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
thf(1146,axiom,
! [V_n: $i] :
( V_n
!= ( c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1147,axiom,
! [V_n: $i] :
( ( c_Nat_OSuc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(1148,axiom,
! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( c_Nat_OSuc @ V_nat_2 )
= ( c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1149,axiom,
! [V_y: $i,V_x: $i] :
( ( ( c_Nat_OSuc @ V_x )
= ( c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(1150,axiom,
! [V_l_2: $i,V_k_2: $i] :
( ( ( c_Int_OBit1 @ V_k_2 )
= ( c_Int_OBit1 @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
thf(1151,axiom,
! [V_x_2: $i,V_w_2: $i,T_a: $i] :
( ( class_Int_Onumber @ T_a )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ T_a @ V_w_2 )
= V_x_2 )
<=> ( V_x_2
= ( c_Int_Onumber__class_Onumber__of @ T_a @ V_w_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__reorient) ).
thf(1153,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
thf(1154,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
thf(1155,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( V_m_2
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( V_nb_2
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(1156,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
thf(1157,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
thf(1160,axiom,
! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(1161,axiom,
! [V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(1162,axiom,
! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( V_m_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( V_nb_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(1163,axiom,
! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( ( V_m_2 = V_nb_2 )
| ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(1164,axiom,
! [V_nb_2: $i,V_k_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_k_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_nb_2 @ V_k_2 ) )
<=> ( ( V_m_2 = V_nb_2 )
| ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(1165,axiom,
! [V_m: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1166,axiom,
! [V_nat_H: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(1167,axiom,
! [V_m: $i] :
( ( c_Nat_OSuc @ V_m )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1168,axiom,
! [V_nat_H_1: $i] :
( ( c_Nat_OSuc @ V_nat_H_1 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1169,axiom,
! [V_m: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1170,axiom,
! [V_m: $i] :
( ( c_Nat_OSuc @ V_m )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(1171,axiom,
! [V_l: $i,V_k: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ V_k ) @ V_l )
= ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_k @ V_l ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).
thf(1172,axiom,
! [V_w: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls @ V_w )
= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).
thf(1173,axiom,
! [V_k: $i] :
( ( c_Int_OBit1 @ V_k )
!= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
thf(1174,axiom,
! [V_l: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ V_l ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
thf(1175,axiom,
! [V_l: $i,V_k: $i] :
( ( c_Int_OBit1 @ V_k )
!= ( c_Int_OBit0 @ V_l ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
thf(1176,axiom,
! [V_l: $i,V_k: $i] :
( ( c_Int_OBit0 @ V_k )
!= ( c_Int_OBit1 @ V_l ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
thf(1177,axiom,
! [V_k_2: $i] :
( ( ( c_Int_OBit0 @ V_k_2 )
= c_Int_OPls )
<=> ( V_k_2 = c_Int_OPls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
thf(1178,axiom,
! [V_l_2: $i] :
( ( c_Int_OPls
= ( c_Int_OBit0 @ V_l_2 ) )
<=> ( c_Int_OPls = V_l_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
thf(1179,axiom,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
thf(1180,axiom,
! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( V_m_2 = V_nb_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(1181,axiom,
! [V_a: $i,T_a: $i] :
( ( class_Int_Onumber__ring @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Int_Onumber__class_Onumber__of @ T_a @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
thf(1182,axiom,
! [V_a: $i,T_a: $i] :
( ( class_Int_Onumber__ring @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ ( c_Int_Onumber__class_Onumber__of @ T_a @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
thf(1184,axiom,
( v_na____
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n) ).
thf(1185,axiom,
~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ v_na____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o) ).
thf(1186,conjecture,
? [B_m: $i] :
( v_na____
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1187,negated_conjecture,
( ( ? [B_m: $i] :
( v_na____
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1186]) ).
thf(1188,plain,
( ( ? [B_m: $i] :
( v_na____
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[1187]) ).
thf(1189,plain,
( ( class_Groups_Oone @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(1190,plain,
( ( class_Int_Onumber @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(1191,plain,
( ( class_Groups_Ozero @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(1192,plain,
( ( class_Power_Opower @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(1193,plain,
( ( class_Orderings_Oord @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(1194,plain,
( ( class_Rings_Osemiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(1195,plain,
( ( class_Orderings_Oorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(1196,plain,
( ( class_Rings_Omult__zero @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(1197,plain,
( ( class_Rings_Osemiring__0 @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(1198,plain,
( ( class_Rings_Osemiring__1 @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(1199,plain,
( ( class_Groups_Omonoid__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(1200,plain,
( ( class_Groups_Omonoid__mult @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(1201,plain,
( ( class_Orderings_Olinorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(1202,plain,
( ( class_Orderings_Opreorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(1203,plain,
( ( class_Rings_Ozero__neq__one @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(1204,plain,
( ( class_Rings_Ocomm__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(1205,plain,
( ( class_Divides_Osemiring__div @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(1206,plain,
( ( class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(1207,plain,
( ( class_Groups_Ocomm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(1208,plain,
( ( class_Rings_Ono__zero__divisors @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(1209,plain,
( ( class_Rings_Oordered__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(1210,plain,
( ( class_Groups_Oab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(1211,plain,
( ( class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(1212,plain,
( ( class_Groups_Oab__semigroup__mult @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(1213,plain,
( ( class_Rings_Olinordered__semidom @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(1214,plain,
( ( class_Rings_Olinordered__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(1215,plain,
( ( class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(1216,plain,
( ( class_Rings_Oordered__comm__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(1217,plain,
( ( class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(1218,plain,
( ( class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(1219,plain,
( ( class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(1220,plain,
( ( class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(1221,plain,
( ( class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(1222,plain,
( ( class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(1223,plain,
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(1224,plain,
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(1225,plain,
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(1226,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1227,plain,
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1228,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ V_n )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1229,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) )
<=> ( ( V_m_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( V_nb_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1230,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1231,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( V_m_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( V_nb_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1232,plain,
( ( ! [V_z3: $i,V_z2: $i,V_z1: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z1 @ V_z2 ) @ V_z3 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z1 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z2 @ V_z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(1233,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z @ V_w )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_w @ V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(1234,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Groups_Oab__semigroup__mult @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ V_b ) @ V_c )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_b @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(1235,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[716]) ).
thf(1236,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[717]) ).
thf(1237,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[729]) ).
thf(1238,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
=> ( V_s != V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[730]) ).
thf(1239,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m != V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(1240,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(1241,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[733]) ).
thf(1242,plain,
( ( ! [V_nb_2: $i,V_k_2: $i,V_m_2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m_2 @ V_k_2 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_nb_2 @ V_k_2 ) )
<=> ( V_m_2 = V_nb_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(1243,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( V_m_2 = V_nb_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[737]) ).
thf(1244,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(1245,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_x @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[740]) ).
thf(1246,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[747]) ).
thf(1247,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(1248,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( V_m_2 != V_nb_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ V_m_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(1249,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(1250,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[758]) ).
thf(1251,plain,
( ( ! [V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_z )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_z @ V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(1252,plain,
( ( ! [V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_z @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_z @ V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(1253,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_n )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(1254,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(1255,plain,
( ( ! [V_n: $i] :
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[789]) ).
thf(1256,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[816]) ).
thf(1257,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[817]) ).
thf(1258,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[831]) ).
thf(1259,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[832]) ).
thf(1260,plain,
( ( ! [V_l: $i,V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_k @ V_l )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_l ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1261,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_i ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_j ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1262,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(1263,plain,
( ( ! [V_m: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[910]) ).
thf(1264,plain,
( ( ! [V_m: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(1265,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[916]) ).
thf(1266,plain,
( ( ! [V_n: $i,V_m: $i,V_k: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_m ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(1267,plain,
( ( ! [V_k: $i,V_j: $i,V_u: $i,V_i: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_u ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_u ) @ V_k ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_u ) @ V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[918]) ).
thf(1268,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[923]) ).
thf(1269,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_m
= ( c_Nat_OSuc @ V_n ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[924]) ).
thf(1270,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[925]) ).
thf(1271,plain,
( ( ! [V_m_2: $i,V_nb_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_nb_2 ) @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_nb_2 @ V_m_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[926]) ).
thf(1272,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( V_m_2
= ( c_Nat_OSuc @ V_nb_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(1273,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_nb_2 ) @ V_m_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(1274,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_n ) @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(1275,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ ( c_Nat_OSuc @ V_n ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1276,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[933]) ).
thf(1277,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[934]) ).
thf(1278,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_i ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[935]) ).
thf(1279,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( ( c_Nat_OSuc @ V_m )
!= V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[936]) ).
thf(1280,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[937]) ).
thf(1281,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_m ) )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[938]) ).
thf(1282,plain,
( ( ! [V_m_2: $i,V_nb_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ V_m_2 )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( V_nb_2 = V_m_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(1283,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m_2 ) @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(1284,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( V_m_2 = V_nb_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(1285,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ ( c_Nat_OSuc @ V_m_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(1286,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[958]) ).
thf(1287,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[959]) ).
thf(1288,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[960]) ).
thf(1289,plain,
( ( ! [V_k: $i] :
( ( c_Int_OBit0 @ V_k )
!= c_Int_OMin ) )
= $true ),
inference(unfold_def,[status(thm)],[971]) ).
thf(1290,plain,
( ( ! [V_l: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ V_l ) ) )
= $true ),
inference(unfold_def,[status(thm)],[972]) ).
thf(1291,plain,
( ( c_Int_OPls != c_Int_OMin )
= $true ),
inference(unfold_def,[status(thm)],[973]) ).
thf(1292,plain,
( ( c_Int_OMin != c_Int_OPls )
= $true ),
inference(unfold_def,[status(thm)],[974]) ).
thf(1293,plain,
( ( ! [V_k_2: $i] :
( ( ( c_Int_OBit1 @ V_k_2 )
= c_Int_OMin )
<=> ( V_k_2 = c_Int_OMin ) ) )
= $true ),
inference(unfold_def,[status(thm)],[975]) ).
thf(1294,plain,
( ( ! [V_l_2: $i] :
( ( c_Int_OMin
= ( c_Int_OBit1 @ V_l_2 ) )
<=> ( c_Int_OMin = V_l_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[976]) ).
thf(1295,plain,
( ( ( c_Int_OBit1 @ c_Int_OMin )
= c_Int_OMin )
= $true ),
inference(unfold_def,[status(thm)],[977]) ).
thf(1296,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1065]) ).
thf(1297,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1066]) ).
thf(1298,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ V_b )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_b @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1091]) ).
thf(1299,plain,
( ( ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1092]) ).
thf(1300,plain,
( ( ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ V_ry ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1093]) ).
thf(1301,plain,
( ( ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_rx )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ V_rx ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1094]) ).
thf(1302,plain,
( ( ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_rx )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ V_ly ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1095]) ).
thf(1303,plain,
( ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1096]) ).
thf(1304,plain,
( ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1097]) ).
thf(1305,plain,
( ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ V_ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1098]) ).
thf(1306,plain,
( ( ! [V_k: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_k )
= V_k ) )
= $true ),
inference(unfold_def,[status(thm)],[1099]) ).
thf(1307,plain,
( ( ! [V_z3: $i,V_z2: $i,V_z1: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z1 @ V_z2 ) @ V_z3 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z1 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z2 @ V_z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1122]) ).
thf(1308,plain,
( ( ! [V_w: $i,V_v: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_v ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_w ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_v @ V_w ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1123]) ).
thf(1309,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z @ V_w )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_w @ V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1124]) ).
thf(1310,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( V_m_2 = V_nb_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1130]) ).
thf(1311,plain,
( ( ! [V_x_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_x_2 ) )
<=> ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1132]) ).
thf(1312,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) )
<=> ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_x_2 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1133]) ).
thf(1313,plain,
( ( ! [V_nb_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_nb_2 )
<=> ? [B_m: $i] :
( V_nb_2
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1136]) ).
thf(1314,plain,
( ( ! [V_nb_2: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_nb_2 )
<=> ? [B_m: $i] :
( V_nb_2
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1137]) ).
thf(1315,plain,
( ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1141]) ).
thf(1316,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1142]) ).
thf(1317,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1143]) ).
thf(1318,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1144]) ).
thf(1319,plain,
( ( ! [V_l_2: $i,V_k_2: $i] :
( ( ( c_Int_OBit0 @ V_k_2 )
= ( c_Int_OBit0 @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1145]) ).
thf(1320,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1146]) ).
thf(1321,plain,
( ( ! [V_n: $i] :
( ( c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[1147]) ).
thf(1322,plain,
( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( c_Nat_OSuc @ V_nat_2 )
= ( c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1148]) ).
thf(1323,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( ( c_Nat_OSuc @ V_x )
= ( c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1149]) ).
thf(1324,plain,
( ( ! [V_l_2: $i,V_k_2: $i] :
( ( ( c_Int_OBit1 @ V_k_2 )
= ( c_Int_OBit1 @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1150]) ).
thf(1325,plain,
( ( ! [V_x_2: $i,V_w_2: $i,T_a: $i] :
( ( class_Int_Onumber @ T_a )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ T_a @ V_w_2 )
= V_x_2 )
<=> ( V_x_2
= ( c_Int_Onumber__class_Onumber__of @ T_a @ V_w_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1151]) ).
thf(1326,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1153]) ).
thf(1327,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1154]) ).
thf(1328,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( V_m_2
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( V_nb_2
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1155]) ).
thf(1329,plain,
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) )
= $true ),
inference(unfold_def,[status(thm)],[1156]) ).
thf(1330,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(unfold_def,[status(thm)],[1157]) ).
thf(1331,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1160]) ).
thf(1332,plain,
( ( ! [V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1161]) ).
thf(1333,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( V_m_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( V_nb_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1162]) ).
thf(1334,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( ( V_m_2 = V_nb_2 )
| ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1163]) ).
thf(1335,plain,
( ( ! [V_nb_2: $i,V_k_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_k_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_nb_2 @ V_k_2 ) )
<=> ( ( V_m_2 = V_nb_2 )
| ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1164]) ).
thf(1336,plain,
( ( ! [V_m: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1165]) ).
thf(1337,plain,
( ( ! [V_nat_H: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1166]) ).
thf(1338,plain,
( ( ! [V_m: $i] :
( ( c_Nat_OSuc @ V_m )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1167]) ).
thf(1339,plain,
( ( ! [V_nat_H_1: $i] :
( ( c_Nat_OSuc @ V_nat_H_1 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1168]) ).
thf(1340,plain,
( ( ! [V_m: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1169]) ).
thf(1341,plain,
( ( ! [V_m: $i] :
( ( c_Nat_OSuc @ V_m )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1170]) ).
thf(1342,plain,
( ( ! [V_l: $i,V_k: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ V_k ) @ V_l )
= ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_k @ V_l ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1171]) ).
thf(1343,plain,
( ( ! [V_w: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls @ V_w )
= c_Int_OPls ) )
= $true ),
inference(unfold_def,[status(thm)],[1172]) ).
thf(1344,plain,
( ( ! [V_k: $i] :
( ( c_Int_OBit1 @ V_k )
!= c_Int_OPls ) )
= $true ),
inference(unfold_def,[status(thm)],[1173]) ).
thf(1345,plain,
( ( ! [V_l: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ V_l ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1174]) ).
thf(1346,plain,
( ( ! [V_l: $i,V_k: $i] :
( ( c_Int_OBit1 @ V_k )
!= ( c_Int_OBit0 @ V_l ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1175]) ).
thf(1347,plain,
( ( ! [V_l: $i,V_k: $i] :
( ( c_Int_OBit0 @ V_k )
!= ( c_Int_OBit1 @ V_l ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1176]) ).
thf(1348,plain,
( ( ! [V_k_2: $i] :
( ( ( c_Int_OBit0 @ V_k_2 )
= c_Int_OPls )
<=> ( V_k_2 = c_Int_OPls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1177]) ).
thf(1349,plain,
( ( ! [V_l_2: $i] :
( ( c_Int_OPls
= ( c_Int_OBit0 @ V_l_2 ) )
<=> ( c_Int_OPls = V_l_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1178]) ).
thf(1350,plain,
( ( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls )
= $true ),
inference(unfold_def,[status(thm)],[1179]) ).
thf(1351,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( V_m_2 = V_nb_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1180]) ).
thf(1352,plain,
( ( ! [V_a: $i,T_a: $i] :
( ( class_Int_Onumber__ring @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Int_Onumber__class_Onumber__of @ T_a @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1181]) ).
thf(1353,plain,
( ( ! [V_a: $i,T_a: $i] :
( ( class_Int_Onumber__ring @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ ( c_Int_Onumber__class_Onumber__of @ T_a @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1182]) ).
thf(1354,plain,
( ( v_na____
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(unfold_def,[status(thm)],[1184]) ).
thf(1355,plain,
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ v_na____ ) )
= $true ),
inference(unfold_def,[status(thm)],[1185]) ).
thf(1356,plain,
( ( ~ ? [B_m: $i] :
( v_na____
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[1188]) ).
thf(1357,plain,
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ v_na____ ) )
= $true ),
inference(copy,[status(thm)],[1355]) ).
thf(1358,plain,
( ( v_na____
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(copy,[status(thm)],[1354]) ).
thf(1359,plain,
( ( ! [V_a: $i,T_a: $i] :
( ( class_Int_Onumber__ring @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ ( c_Int_Onumber__class_Onumber__of @ T_a @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1353]) ).
thf(1360,plain,
( ( ! [V_a: $i,T_a: $i] :
( ( class_Int_Onumber__ring @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Int_Onumber__class_Onumber__of @ T_a @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1352]) ).
thf(1361,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( V_m_2 = V_nb_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1351]) ).
thf(1362,plain,
( ( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(1363,plain,
( ( ! [V_l_2: $i] :
( ( c_Int_OPls
= ( c_Int_OBit0 @ V_l_2 ) )
<=> ( c_Int_OPls = V_l_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(1364,plain,
( ( ! [V_k_2: $i] :
( ( ( c_Int_OBit0 @ V_k_2 )
= c_Int_OPls )
<=> ( V_k_2 = c_Int_OPls ) ) )
= $true ),
inference(copy,[status(thm)],[1348]) ).
thf(1365,plain,
( ( ! [V_l: $i,V_k: $i] :
( ( c_Int_OBit0 @ V_k )
!= ( c_Int_OBit1 @ V_l ) ) )
= $true ),
inference(copy,[status(thm)],[1347]) ).
thf(1366,plain,
( ( ! [V_l: $i,V_k: $i] :
( ( c_Int_OBit1 @ V_k )
!= ( c_Int_OBit0 @ V_l ) ) )
= $true ),
inference(copy,[status(thm)],[1346]) ).
thf(1367,plain,
( ( ! [V_l: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ V_l ) ) )
= $true ),
inference(copy,[status(thm)],[1345]) ).
thf(1368,plain,
( ( ! [V_k: $i] :
( ( c_Int_OBit1 @ V_k )
!= c_Int_OPls ) )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(1369,plain,
( ( ! [V_w: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls @ V_w )
= c_Int_OPls ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(1370,plain,
( ( ! [V_l: $i,V_k: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ V_k ) @ V_l )
= ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_k @ V_l ) ) ) )
= $true ),
inference(copy,[status(thm)],[1342]) ).
thf(1371,plain,
( ( ! [V_m: $i] :
( ( c_Nat_OSuc @ V_m )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1341]) ).
thf(1372,plain,
( ( ! [V_m: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(1373,plain,
( ( ! [V_nat_H_1: $i] :
( ( c_Nat_OSuc @ V_nat_H_1 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1374,plain,
( ( ! [V_m: $i] :
( ( c_Nat_OSuc @ V_m )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1338]) ).
thf(1375,plain,
( ( ! [V_nat_H: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1337]) ).
thf(1376,plain,
( ( ! [V_m: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1336]) ).
thf(1377,plain,
( ( ! [V_nb_2: $i,V_k_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_k_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_nb_2 @ V_k_2 ) )
<=> ( ( V_m_2 = V_nb_2 )
| ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1335]) ).
thf(1378,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( ( V_m_2 = V_nb_2 )
| ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(1379,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( V_m_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( V_nb_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(1380,plain,
( ( ! [V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(1381,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1331]) ).
thf(1382,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(copy,[status(thm)],[1330]) ).
thf(1383,plain,
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) )
= $true ),
inference(copy,[status(thm)],[1329]) ).
thf(1384,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( V_m_2
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( V_nb_2
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1328]) ).
thf(1385,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1327]) ).
thf(1386,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1326]) ).
thf(1387,plain,
( ( ! [V_x_2: $i,V_w_2: $i,T_a: $i] :
( ( class_Int_Onumber @ T_a )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ T_a @ V_w_2 )
= V_x_2 )
<=> ( V_x_2
= ( c_Int_Onumber__class_Onumber__of @ T_a @ V_w_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1325]) ).
thf(1388,plain,
( ( ! [V_l_2: $i,V_k_2: $i] :
( ( ( c_Int_OBit1 @ V_k_2 )
= ( c_Int_OBit1 @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1324]) ).
thf(1389,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( ( c_Nat_OSuc @ V_x )
= ( c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1323]) ).
thf(1390,plain,
( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( c_Nat_OSuc @ V_nat_2 )
= ( c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1322]) ).
thf(1391,plain,
( ( ! [V_n: $i] :
( ( c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1321]) ).
thf(1392,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1320]) ).
thf(1393,plain,
( ( ! [V_l_2: $i,V_k_2: $i] :
( ( ( c_Int_OBit0 @ V_k_2 )
= ( c_Int_OBit0 @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1319]) ).
thf(1394,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1318]) ).
thf(1395,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1317]) ).
thf(1396,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1316]) ).
thf(1397,plain,
( ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1315]) ).
thf(1398,plain,
( ( ! [V_nb_2: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_nb_2 )
<=> ? [B_m: $i] :
( V_nb_2
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1314]) ).
thf(1399,plain,
( ( ! [V_nb_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_nb_2 )
<=> ? [B_m: $i] :
( V_nb_2
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[1313]) ).
thf(1400,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) )
<=> ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_x_2 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1312]) ).
thf(1401,plain,
( ( ! [V_x_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_x_2 ) )
<=> ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1311]) ).
thf(1402,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( ( V_k_2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( V_m_2 = V_nb_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1310]) ).
thf(1403,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z @ V_w )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_w @ V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1309]) ).
thf(1404,plain,
( ( ! [V_w: $i,V_v: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_v ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_w ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_v @ V_w ) ) ) )
= $true ),
inference(copy,[status(thm)],[1308]) ).
thf(1405,plain,
( ( ! [V_z3: $i,V_z2: $i,V_z1: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z1 @ V_z2 ) @ V_z3 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z1 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ V_z2 @ V_z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1307]) ).
thf(1406,plain,
( ( ! [V_k: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_k )
= V_k ) )
= $true ),
inference(copy,[status(thm)],[1306]) ).
thf(1407,plain,
( ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ V_ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1305]) ).
thf(1408,plain,
( ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1304]) ).
thf(1409,plain,
( ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1303]) ).
thf(1410,plain,
( ( ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_rx )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ V_ly ) ) ) )
= $true ),
inference(copy,[status(thm)],[1302]) ).
thf(1411,plain,
( ( ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ly ) @ V_rx )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_ly @ V_rx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1301]) ).
thf(1412,plain,
( ( ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_rx ) @ V_ry ) ) ) )
= $true ),
inference(copy,[status(thm)],[1300]) ).
thf(1413,plain,
( ( ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ V_ry ) )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_rx @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_lx @ V_ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1299]) ).
thf(1414,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ V_b )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_b @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1298]) ).
thf(1415,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1297]) ).
thf(1416,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1296]) ).
thf(1417,plain,
( ( ( c_Int_OBit1 @ c_Int_OMin )
= c_Int_OMin )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1418,plain,
( ( ! [V_l_2: $i] :
( ( c_Int_OMin
= ( c_Int_OBit1 @ V_l_2 ) )
<=> ( c_Int_OMin = V_l_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1294]) ).
thf(1419,plain,
( ( ! [V_k_2: $i] :
( ( ( c_Int_OBit1 @ V_k_2 )
= c_Int_OMin )
<=> ( V_k_2 = c_Int_OMin ) ) )
= $true ),
inference(copy,[status(thm)],[1293]) ).
thf(1420,plain,
( ( c_Int_OMin != c_Int_OPls )
= $true ),
inference(copy,[status(thm)],[1292]) ).
thf(1421,plain,
( ( c_Int_OPls != c_Int_OMin )
= $true ),
inference(copy,[status(thm)],[1291]) ).
thf(1422,plain,
( ( ! [V_l: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ V_l ) ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(1423,plain,
( ( ! [V_k: $i] :
( ( c_Int_OBit0 @ V_k )
!= c_Int_OMin ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(1424,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(1425,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(1426,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1286]) ).
thf(1427,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ ( c_Nat_OSuc @ V_m_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1285]) ).
thf(1428,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( V_m_2 = V_nb_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1284]) ).
thf(1429,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m_2 ) @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1283]) ).
thf(1430,plain,
( ( ! [V_m_2: $i,V_nb_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ V_m_2 )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( V_nb_2 = V_m_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1282]) ).
thf(1431,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_m ) )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1281]) ).
thf(1432,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1280]) ).
thf(1433,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( ( c_Nat_OSuc @ V_m )
!= V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1279]) ).
thf(1434,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_i ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1278]) ).
thf(1435,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1277]) ).
thf(1436,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(1437,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ ( c_Nat_OSuc @ V_n ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1275]) ).
thf(1438,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_n ) @ V_n ) )
= $true ),
inference(copy,[status(thm)],[1274]) ).
thf(1439,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_nb_2 ) @ V_m_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1273]) ).
thf(1440,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_nb_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( V_m_2
= ( c_Nat_OSuc @ V_nb_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(1441,plain,
( ( ! [V_m_2: $i,V_nb_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_nb_2 ) @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_nb_2 @ V_m_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1271]) ).
thf(1442,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(1443,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_m
= ( c_Nat_OSuc @ V_n ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(1444,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(1445,plain,
( ( ! [V_k: $i,V_j: $i,V_u: $i,V_i: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_u ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_u ) @ V_k ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_u ) @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(1446,plain,
( ( ! [V_n: $i,V_m: $i,V_k: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_m ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(1447,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(1448,plain,
( ( ! [V_m: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(1449,plain,
( ( ! [V_m: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(1450,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(1451,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_i ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_k @ V_j ) ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(1452,plain,
( ( ! [V_l: $i,V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_k @ V_l )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_j @ V_l ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(1453,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ ( c_Nat_OSuc @ V_n ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(1454,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m ) @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(1455,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(1456,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_m_2 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_k_2 ) @ V_nb_2 ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(1457,plain,
( ( ! [V_n: $i] :
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(1458,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(1459,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_n )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(1460,plain,
( ( ! [V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_z @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_z @ V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1252]) ).
thf(1461,plain,
( ( ! [V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ V_z )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_z @ V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1462,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[1250]) ).
thf(1463,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(1464,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( V_m_2 != V_nb_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_nb_2 @ V_m_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1465,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(1466,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(1467,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_x @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1245]) ).
thf(1468,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n ) @ V_k )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1244]) ).
thf(1469,plain,
( ( ! [V_nb_2: $i,V_m_2: $i,V_k_2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k_2 @ V_m_2 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k_2 @ V_nb_2 ) )
<=> ( V_m_2 = V_nb_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1243]) ).
thf(1470,plain,
( ( ! [V_nb_2: $i,V_k_2: $i,V_m_2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m_2 @ V_k_2 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_nb_2 @ V_k_2 ) )
<=> ( V_m_2 = V_nb_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(1471,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(1472,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[1240]) ).
thf(1473,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m != V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1239]) ).
thf(1474,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
=> ( V_s != V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(1475,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(1476,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1477,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(1478,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Groups_Oab__semigroup__mult @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ V_b ) @ V_c )
= ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_b @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(1479,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z @ V_w )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_w @ V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(1480,plain,
( ( ! [V_z3: $i,V_z2: $i,V_z1: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z1 @ V_z2 ) @ V_z3 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z1 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z2 @ V_z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1481,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( V_m_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( V_nb_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(1482,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_n @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1230]) ).
thf(1483,plain,
( ( ! [V_nb_2: $i,V_m_2: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ V_m_2 @ V_nb_2 ) )
<=> ( ( V_m_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( V_nb_2
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(1484,plain,
( ( ! [V_n: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ V_n )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1228]) ).
thf(1485,plain,
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(1486,plain,
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ),
inference(copy,[status(thm)],[1226]) ).
thf(1487,plain,
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(1488,plain,
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1224]) ).
thf(1489,plain,
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(1490,plain,
( ( class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(1491,plain,
( ( class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(1492,plain,
( ( class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(1493,plain,
( ( class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1219]) ).
thf(1494,plain,
( ( class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1218]) ).
thf(1495,plain,
( ( class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1217]) ).
thf(1496,plain,
( ( class_Rings_Oordered__comm__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(1497,plain,
( ( class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(1498,plain,
( ( class_Rings_Olinordered__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1499,plain,
( ( class_Rings_Olinordered__semidom @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1500,plain,
( ( class_Groups_Oab__semigroup__mult @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1501,plain,
( ( class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(1502,plain,
( ( class_Groups_Oab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(1503,plain,
( ( class_Rings_Oordered__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1504,plain,
( ( class_Rings_Ono__zero__divisors @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1505,plain,
( ( class_Groups_Ocomm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1506,plain,
( ( class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1507,plain,
( ( class_Divides_Osemiring__div @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1508,plain,
( ( class_Rings_Ocomm__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1509,plain,
( ( class_Rings_Ozero__neq__one @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1510,plain,
( ( class_Orderings_Opreorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1511,plain,
( ( class_Orderings_Olinorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(1512,plain,
( ( class_Groups_Omonoid__mult @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(1513,plain,
( ( class_Groups_Omonoid__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(1514,plain,
( ( class_Rings_Osemiring__1 @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(1515,plain,
( ( class_Rings_Osemiring__0 @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1516,plain,
( ( class_Rings_Omult__zero @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1517,plain,
( ( class_Orderings_Oorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1518,plain,
( ( class_Rings_Osemiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1519,plain,
( ( class_Orderings_Oord @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1520,plain,
( ( class_Power_Opower @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1521,plain,
( ( class_Groups_Ozero @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(1522,plain,
( ( class_Int_Onumber @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1523,plain,
( ( class_Groups_Oone @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1524,plain,
( ( ~ ? [B_m: $i] :
( v_na____
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ B_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1525,plain,
( ( c_Int_OMin != c_Int_OPls )
= $true ),
inference(unfold_def,[status(thm)],[1420]) ).
thf(1526,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1473]) ).
thf(1527,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX1 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX0 ) )
| ( SX2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SX1 = SX0 ) )
| ~ ( ~ ( ( SX2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SX1 = SX0 ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX1 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1402]) ).
thf(1528,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SX1
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SX0
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SX1
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SX0
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1379]) ).
thf(1529,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1436]) ).
thf(1530,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX1 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX0 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX1 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1456]) ).
thf(1531,plain,
( ( ! [SX0: $i] :
( ( c_Nat_OSuc @ SX0 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1373]) ).
thf(1532,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( c_Int_OMin
!= ( c_Int_OBit1 @ SX0 ) )
| ( c_Int_OMin = SX0 ) )
| ~ ( ( c_Int_OMin != SX0 )
| ( c_Int_OMin
= ( c_Int_OBit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1418]) ).
thf(1533,plain,
( ( ! [SX0: $i] :
( ( c_Nat_OSuc @ SX0 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1374]) ).
thf(1534,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ ( c_Nat_OSuc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1416]) ).
thf(1535,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX2 )
| ( ( c_Groups_Otimes__class_Otimes @ SX2 @ SX1 @ SX0 )
= ( c_Groups_Otimes__class_Otimes @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1414]) ).
thf(1536,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX1 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX0 ) )
| ( SX1 = SX0 )
| ( SX2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SX1 = SX0 )
| ( SX2
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX1 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1378]) ).
thf(1537,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ ( c_Nat_OSuc @ SX1 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ ( c_Nat_OSuc @ SX1 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1427]) ).
thf(1538,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( c_Int_OBit1 @ SX0 )
!= c_Int_OMin )
| ( SX0 = c_Int_OMin ) )
| ~ ( ( SX0 != c_Int_OMin )
| ( ( c_Int_OBit1 @ SX0 )
= c_Int_OMin ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1419]) ).
thf(1539,plain,
( ( ~ ~ ! [SX0: $i] :
( v_na____
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1524]) ).
thf(1540,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Int_Onumber__ring @ SX1 )
| ( ( c_Groups_Otimes__class_Otimes @ SX1 @ ( c_Int_Onumber__class_Onumber__of @ SX1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1360]) ).
thf(1541,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1
= ( c_Nat_OSuc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1443]) ).
thf(1542,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX1 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX1 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1455]) ).
thf(1543,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 )
| ~ ! [SX1: $i] :
( SX0
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
( SX0
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SX1 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1399]) ).
thf(1544,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Nat_OSuc @ SX1 )
!= ( c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1389]) ).
thf(1545,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX3 )
| ( ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX1 @ SX0 ) )
= ( c_Groups_Otimes__class_Otimes @ SX3 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1412]) ).
thf(1546,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1435]) ).
thf(1547,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( c_Int_OBit0 @ SX0 )
!= c_Int_OPls )
| ( SX0 = c_Int_OPls ) )
| ~ ( ( SX0 != c_Int_OPls )
| ( ( c_Int_OBit0 @ SX0 )
= c_Int_OPls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1364]) ).
thf(1548,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX2 @ SX1 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX0 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1450]) ).
thf(1549,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Groups_Oab__semigroup__mult @ SX3 )
| ( ( c_Groups_Otimes__class_Otimes @ SX3 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ SX1 ) @ SX0 )
= ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1478]) ).
thf(1550,plain,
( ( ! [SX0: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1422]) ).
thf(1551,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX3 )
| ( ( c_Groups_Otimes__class_Otimes @ SX3 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ SX1 ) @ SX0 )
= ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1411]) ).
thf(1552,plain,
( ( v_na____
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(unfold_def,[status(thm)],[1358]) ).
thf(1553,plain,
( ( ! [SX0: $i] :
( ( c_Nat_OSuc @ SX0 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1371]) ).
thf(1554,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX1 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 ) )
| ~ ( ~ ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX1 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1400]) ).
thf(1555,plain,
( ( c_Int_OPls != c_Int_OMin )
= $true ),
inference(unfold_def,[status(thm)],[1421]) ).
thf(1556,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1430]) ).
thf(1557,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1442]) ).
thf(1558,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1434]) ).
thf(1559,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX2 @ SX1 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1476]) ).
thf(1560,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Nat_OSuc @ SX1 )
!= ( c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Nat_OSuc @ SX1 )
= ( c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1390]) ).
thf(1561,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1474]) ).
thf(1562,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Int_OBit1 @ SX1 )
!= ( c_Int_OBit1 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Int_OBit1 @ SX1 )
= ( c_Int_OBit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1388]) ).
thf(1563,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1392]) ).
thf(1564,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Int_Onumber__ring @ SX1 )
| ( ( c_Groups_Otimes__class_Otimes @ SX1 @ SX0 @ ( c_Int_Onumber__class_Onumber__of @ SX1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1359]) ).
thf(1565,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX3 )
| ( ( c_Groups_Otimes__class_Otimes @ SX3 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ SX1 ) @ SX0 )
= ( c_Groups_Otimes__class_Otimes @ SX3 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1410]) ).
thf(1566,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX4 )
| ( ( c_Groups_Otimes__class_Otimes @ SX4 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX3 @ SX2 ) @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX1 @ SX0 ) )
= ( c_Groups_Otimes__class_Otimes @ SX4 @ SX3 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX2 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1409]) ).
thf(1567,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX0 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 ) )
| ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1401]) ).
thf(1568,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 )
| ~ ! [SX1: $i] :
( SX0
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SX1 ) ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
( SX0
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SX1 ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1398]) ).
thf(1569,plain,
( ( ! [SX0: $i] :
( ( c_Int_OBit1 @ SX0 )
!= c_Int_OPls ) )
= $true ),
inference(unfold_def,[status(thm)],[1368]) ).
thf(1570,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1
= ( c_Nat_OSuc @ SX0 ) ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1
= ( c_Nat_OSuc @ SX0 ) ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1440]) ).
thf(1571,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ ( c_Nat_OSuc @ SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1437]) ).
thf(1572,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Int_Onumber @ SX2 )
| ~ ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SX2 @ SX1 )
!= SX0 )
| ( SX0
= ( c_Int_Onumber__class_Onumber__of @ SX2 @ SX1 ) ) )
| ~ ( ( SX0
!= ( c_Int_Onumber__class_Onumber__of @ SX2 @ SX1 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SX2 @ SX1 )
= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1387]) ).
thf(1573,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1475]) ).
thf(1574,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX1 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX1 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1469]) ).
thf(1575,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX1 != SX0 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1471]) ).
thf(1576,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX3 )
| ( ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX1 @ SX0 ) )
= ( c_Groups_Otimes__class_Otimes @ SX3 @ SX1 @ ( c_Groups_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1413]) ).
thf(1577,plain,
( ( ! [SX0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1372]) ).
thf(1578,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 = SX0 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 = SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1428]) ).
thf(1579,plain,
( ( ! [SX0: $i] :
( ( c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1391]) ).
thf(1580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1444]) ).
thf(1581,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 )
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ( SX1
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SX0
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
| ~ ( ~ ~ ( ( SX1
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SX0
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1384]) ).
thf(1582,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX1 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX1 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1361]) ).
thf(1583,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ ( c_Nat_OSuc @ SX0 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ ( c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1441]) ).
thf(1584,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ~ ( ( ( c_Nat_OSuc @ SX1 )
!= SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1433]) ).
thf(1585,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX4 )
| ( ( c_Groups_Otimes__class_Otimes @ SX4 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX3 @ SX2 ) @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX1 @ SX0 ) )
= ( c_Groups_Otimes__class_Otimes @ SX4 @ SX1 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1408]) ).
thf(1586,plain,
( ( ! [SX0: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1367]) ).
thf(1587,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Int_OBit0 @ SX1 )
!= ( c_Int_OBit0 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Int_OBit0 @ SX1 )
= ( c_Int_OBit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1393]) ).
thf(1588,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ( SX1 != SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ( SX1 != SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1464]) ).
thf(1589,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX3 @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX3 @ SX1 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1452]) ).
thf(1590,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX2 @ SX1 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX0 @ SX2 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1451]) ).
thf(1591,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX0 ) @ SX1 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX0 ) @ SX1 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1439]) ).
thf(1592,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ ( c_Nat_OSuc @ SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ ( c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1429]) ).
thf(1593,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1432]) ).
thf(1594,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Int_OBit1 @ SX1 )
!= ( c_Int_OBit0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1366]) ).
thf(1595,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SX4 )
| ( ( c_Groups_Otimes__class_Otimes @ SX4 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX3 @ SX2 ) @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX1 @ SX0 ) )
= ( c_Groups_Otimes__class_Otimes @ SX4 @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX3 @ SX1 ) @ ( c_Groups_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1407]) ).
thf(1596,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX1 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX1 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1470]) ).
thf(1597,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX1 @ SX0 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1477]) ).
thf(1598,plain,
( ( ! [SX0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1376]) ).
thf(1599,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ~ ( ( SX1
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SX0
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SX1
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SX0
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1481]) ).
thf(1600,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Int_OBit0 @ SX1 )
!= ( c_Int_OBit1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1365]) ).
thf(1601,plain,
( ( ! [SX0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1375]) ).
thf(1602,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( c_Int_OPls
!= ( c_Int_OBit0 @ SX0 ) )
| ( c_Int_OPls = SX0 ) )
| ~ ( ( c_Int_OPls != SX0 )
| ( c_Int_OPls
= ( c_Int_OBit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1363]) ).
thf(1603,plain,
( ( ! [SX0: $i] :
( ( c_Int_OBit0 @ SX0 )
!= c_Int_OMin ) )
= $true ),
inference(unfold_def,[status(thm)],[1423]) ).
thf(1604,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ ( c_Nat_OSuc @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1431]) ).
thf(1605,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SX0
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SX1
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SX0
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1483]) ).
thf(1606,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX1 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( SX1
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( SX1
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX2 @ SX1 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1377]) ).
thf(1607,plain,
( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ v_na____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1608,plain,
! [SV1: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls @ SV1 )
= c_Int_OPls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1609,plain,
! [SV2: $i] :
( ( ! [SY242: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ SY242 ) @ SV2 )
= ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY242 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1610,plain,
! [SV3: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV3 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1611,plain,
! [SV4: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV4 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1612,plain,
! [SV5: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY244 @ SY243 ) @ SV5 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY244 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY243 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1613,plain,
! [SV6: $i] :
( ( ! [SY245: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY245 @ SV6 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV6 @ SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1614,plain,
! [SV7: $i] :
( ( ! [SY246: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY246 @ SV7 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV7 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1615,plain,
! [SV8: $i] :
( ( ! [SY247: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ SY247 ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ SV8 ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY247 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1616,plain,
! [SV9: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY249 @ SY248 ) @ SV9 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY249 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY248 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1617,plain,
! [SV10: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1618,plain,
! [SV11: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV11 @ ( c_Nat_OSuc @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1619,plain,
! [SV12: $i] :
( ( ! [SY250: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY250 @ ( c_Nat_OSuc @ SV12 ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY250 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1620,plain,
! [SV13: $i] :
( ( ! [SY251: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY251 ) @ SV13 )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY251 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1621,plain,
! [SV14: $i] :
( ( ! [SY252: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY252 ) @ SV14 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY252 @ ( c_Nat_OSuc @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1622,plain,
! [SV15: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV15 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1623,plain,
! [SV16: $i] :
( ( ! [SY253: $i,SY254: $i,SY255: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY255 @ SY254 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY253 @ SY254 ) @ SV16 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY255 @ SY253 ) @ SY254 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1624,plain,
! [SV17: $i] :
( ( ! [SY256: $i,SY257: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY257 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY256 @ SV17 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY257 @ SY256 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY257 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1625,plain,
! [SV18: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY259 @ SY258 ) @ SV18 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY259 @ SV18 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY258 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1626,plain,
! [SV19: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV19 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV19 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1627,plain,
! [SV20: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV20 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV20 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV20 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1628,plain,
! [SV21: $i] :
( ( ! [SY260: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY260 @ ( c_Nat_OSuc @ SV21 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY260 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY260 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1629,plain,
! [SV22: $i] :
( ( ! [SY261: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY261 ) @ SV22 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV22 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY261 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1630,plain,
! [SV23: $i] :
( ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ SV23 ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1631,plain,
! [SV24: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV24 @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1632,plain,
! [SV25: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV25 )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1633,plain,
! [SV26: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV26 @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV26 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1634,plain,
! [SV27: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV27 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV27 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1635,plain,
! [SV28: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV28 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1636,plain,
! [SV29: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV29 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1637,plain,
! [SV30: $i] :
( ( ! [SY262: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY262 @ SV30 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV30 @ SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1638,plain,
! [SV31: $i] :
( ( ! [SY263: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY263 @ SV31 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV31 @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1639,plain,
! [SV32: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY265 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY264 @ SV32 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY264 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY265 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1640,plain,
! [SV33: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY267 @ SY266 ) @ SV33 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY267 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY266 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1641,plain,
! [SV34: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV34 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1642,plain,
! [SV35: $i] :
( ( ! [SY268: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SY268 @ SV35 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SV35 @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1643,plain,
! [SV36: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SY270 @ SY269 ) @ SV36 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SY270 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SY269 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1644,plain,
! [SV37: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV37 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1645,plain,
! [SV38: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ SV38 )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1646,plain,
( ( c_Int_OMin = c_Int_OPls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1647,plain,
! [SV39: $i] :
( ( ! [SY271: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY271 @ SV39 )
| ( SV39 != SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1648,plain,
! [SV40: $i] :
( ( ! [SY272: $i,SY273: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY273 @ SY272 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY273 @ SV40 ) )
| ( SY273
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SY272 = SV40 ) )
| ~ ( ~ ( ( SY273
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SY272 = SV40 ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY273 @ SY272 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY273 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1649,plain,
! [SV41: $i] :
( ( ! [SY274: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY274 @ SV41 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SY274
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SY274
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY274 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1650,plain,
! [SV42: $i] :
( ( ! [SY275: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY275 ) @ SV42 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY275 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1651,plain,
! [SV43: $i] :
( ( ! [SY276: $i,SY277: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY277 ) @ SY276 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY277 ) @ SV43 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY276 @ SV43 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY276 @ SV43 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY277 ) @ SY276 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY277 ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1652,plain,
! [SV44: $i] :
( ( ( c_Nat_OSuc @ SV44 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1653,plain,
! [SV45: $i] :
( ( ~ ( ~ ( ( c_Int_OMin
!= ( c_Int_OBit1 @ SV45 ) )
| ( c_Int_OMin = SV45 ) )
| ~ ( ( c_Int_OMin != SV45 )
| ( c_Int_OMin
= ( c_Int_OBit1 @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1654,plain,
! [SV46: $i] :
( ( ( c_Nat_OSuc @ SV46 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1655,plain,
! [SV47: $i] :
( ( ! [SY278: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY278 @ SV47 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY278 ) @ ( c_Nat_OSuc @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1656,plain,
! [SV48: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY280 )
| ( ( c_Groups_Otimes__class_Otimes @ SY280 @ SY279 @ SV48 )
= ( c_Groups_Otimes__class_Otimes @ SY280 @ SV48 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1657,plain,
! [SV49: $i] :
( ( ! [SY281: $i,SY282: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY282 @ SY281 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY282 @ SV49 ) )
| ( SY281 = SV49 )
| ( SY282
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SY281 = SV49 )
| ( SY282
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY282 @ SY281 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY282 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1658,plain,
! [SV50: $i] :
( ( ! [SY283: $i] :
~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY283 @ SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SY283 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SY283 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY283 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1659,plain,
! [SV51: $i] :
( ( ~ ( ~ ( ( ( c_Int_OBit1 @ SV51 )
!= c_Int_OMin )
| ( SV51 = c_Int_OMin ) )
| ~ ( ( SV51 != c_Int_OMin )
| ( ( c_Int_OBit1 @ SV51 )
= c_Int_OMin ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1660,plain,
( ( ~ ! [SX0: $i] :
( v_na____
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1661,plain,
! [SV52: $i] :
( ( ! [SY284: $i] :
( ~ ( class_Int_Onumber__ring @ SY284 )
| ( ( c_Groups_Otimes__class_Otimes @ SY284 @ ( c_Int_Onumber__class_Onumber__of @ SY284 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ SV52 )
= SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1662,plain,
! [SV53: $i] :
( ( ! [SY285: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY285 @ ( c_Nat_OSuc @ SV53 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY285 @ SV53 )
| ( SY285
= ( c_Nat_OSuc @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1663,plain,
! [SV54: $i] :
( ( ! [SY286: $i,SY287: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY287 ) @ SY286 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY287 ) @ SV54 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY286 @ SV54 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY286 @ SV54 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY287 ) @ SY286 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY287 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1664,plain,
! [SV55: $i] :
( ( ~ ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
| ~ ! [SY288: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY288 ) ) )
| ~ ( ~ ~ ! [SY289: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY289 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1665,plain,
! [SV56: $i] :
( ( ! [SY290: $i] :
( ( ( c_Nat_OSuc @ SY290 )
!= ( c_Nat_OSuc @ SV56 ) )
| ( SY290 = SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1666,plain,
! [SV57: $i] :
( ( ! [SY291: $i,SY292: $i,SY293: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY293 )
| ( ( c_Groups_Otimes__class_Otimes @ SY293 @ SY292 @ ( c_Groups_Otimes__class_Otimes @ SY293 @ SY291 @ SV57 ) )
= ( c_Groups_Otimes__class_Otimes @ SY293 @ ( c_Groups_Otimes__class_Otimes @ SY293 @ SY292 @ SY291 ) @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1667,plain,
! [SV58: $i] :
( ( ! [SY294: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY294 @ ( c_Nat_OSuc @ SV58 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY294 @ SV58 )
| ( SY294 = SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1668,plain,
! [SV59: $i] :
( ( ~ ( ~ ( ( ( c_Int_OBit0 @ SV59 )
!= c_Int_OPls )
| ( SV59 = c_Int_OPls ) )
| ~ ( ( SV59 != c_Int_OPls )
| ( ( c_Int_OBit0 @ SV59 )
= c_Int_OPls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1669,plain,
! [SV60: $i] :
( ( ! [SY295: $i,SY296: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY296 @ SY295 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY296 @ SV60 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY295 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1670,plain,
! [SV61: $i] :
( ( ! [SY297: $i,SY298: $i,SY299: $i] :
( ~ ( class_Groups_Oab__semigroup__mult @ SY299 )
| ( ( c_Groups_Otimes__class_Otimes @ SY299 @ ( c_Groups_Otimes__class_Otimes @ SY299 @ SY298 @ SY297 ) @ SV61 )
= ( c_Groups_Otimes__class_Otimes @ SY299 @ SY298 @ ( c_Groups_Otimes__class_Otimes @ SY299 @ SY297 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1671,plain,
! [SV62: $i] :
( ( c_Int_OMin
!= ( c_Int_OBit0 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1672,plain,
! [SV63: $i] :
( ( ! [SY300: $i,SY301: $i,SY302: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY302 )
| ( ( c_Groups_Otimes__class_Otimes @ SY302 @ ( c_Groups_Otimes__class_Otimes @ SY302 @ SY301 @ SY300 ) @ SV63 )
= ( c_Groups_Otimes__class_Otimes @ SY302 @ SY301 @ ( c_Groups_Otimes__class_Otimes @ SY302 @ SY300 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1673,plain,
( ( v_na____
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1674,plain,
! [SV64: $i] :
( ( ( c_Nat_OSuc @ SV64 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1675,plain,
! [SV65: $i] :
( ( ! [SY303: $i] :
~ ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY303 @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SY303 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ~ ( ~ ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SY303 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY303 @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1676,plain,
( ( c_Int_OPls = c_Int_OMin )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1677,plain,
! [SV66: $i] :
( ( ! [SY304: $i] :
( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY304 @ SV66 )
| ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY304 @ ( c_Nat_OSuc @ SV66 ) )
| ( SY304 = SV66 ) )
| ~ ( ( SY304 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY304 @ ( c_Nat_OSuc @ SV66 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1678,plain,
! [SV67: $i] :
( ( ! [SY305: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY305 @ SV67 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY305 @ ( c_Nat_OSuc @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1679,plain,
! [SV68: $i] :
( ( ! [SY306: $i,SY307: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY307 @ SY306 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY306 @ SV68 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY307 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1680,plain,
! [SV69: $i] :
( ( ! [SY308: $i,SY309: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY309 @ SY308 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY308 @ SV69 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY309 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1681,plain,
! [SV70: $i] :
( ( ! [SY310: $i] :
~ ( ~ ( ( ( c_Nat_OSuc @ SY310 )
!= ( c_Nat_OSuc @ SV70 ) )
| ( SY310 = SV70 ) )
| ~ ( ( SY310 != SV70 )
| ( ( c_Nat_OSuc @ SY310 )
= ( c_Nat_OSuc @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1682,plain,
! [SV71: $i] :
( ( ! [SY311: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY311 @ SV71 )
| ( SY311 != SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1683,plain,
! [SV72: $i] :
( ( ! [SY312: $i] :
~ ( ~ ( ( ( c_Int_OBit1 @ SY312 )
!= ( c_Int_OBit1 @ SV72 ) )
| ( SY312 = SV72 ) )
| ~ ( ( SY312 != SV72 )
| ( ( c_Int_OBit1 @ SY312 )
= ( c_Int_OBit1 @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1684,plain,
! [SV73: $i] :
( ( SV73
!= ( c_Nat_OSuc @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1685,plain,
! [SV74: $i] :
( ( ! [SY313: $i] :
( ~ ( class_Int_Onumber__ring @ SY313 )
| ( ( c_Groups_Otimes__class_Otimes @ SY313 @ SV74 @ ( c_Int_Onumber__class_Onumber__of @ SY313 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1686,plain,
! [SV75: $i] :
( ( ! [SY314: $i,SY315: $i,SY316: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY316 )
| ( ( c_Groups_Otimes__class_Otimes @ SY316 @ ( c_Groups_Otimes__class_Otimes @ SY316 @ SY315 @ SY314 ) @ SV75 )
= ( c_Groups_Otimes__class_Otimes @ SY316 @ ( c_Groups_Otimes__class_Otimes @ SY316 @ SY315 @ SV75 ) @ SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1687,plain,
! [SV76: $i] :
( ( ! [SY317: $i,SY318: $i,SY319: $i,SY320: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY320 )
| ( ( c_Groups_Otimes__class_Otimes @ SY320 @ ( c_Groups_Otimes__class_Otimes @ SY320 @ SY319 @ SY318 ) @ ( c_Groups_Otimes__class_Otimes @ SY320 @ SY317 @ SV76 ) )
= ( c_Groups_Otimes__class_Otimes @ SY320 @ SY319 @ ( c_Groups_Otimes__class_Otimes @ SY320 @ SY318 @ ( c_Groups_Otimes__class_Otimes @ SY320 @ SY317 @ SV76 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1688,plain,
! [SV77: $i] :
( ( ~ ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) )
| ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1689,plain,
! [SV78: $i] :
( ( ~ ( ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
| ~ ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) )
| ~ ( ~ ~ ! [SY322: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY322 ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1690,plain,
! [SV79: $i] :
( ( ( c_Int_OBit1 @ SV79 )
!= c_Int_OPls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1691,plain,
! [SV80: $i] :
( ( ! [SY323: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY323 @ ( c_Nat_OSuc @ SV80 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY323 @ SV80 )
| ( SY323
= ( c_Nat_OSuc @ SV80 ) ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY323 @ SV80 )
| ( SY323
= ( c_Nat_OSuc @ SV80 ) ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY323 @ ( c_Nat_OSuc @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1692,plain,
! [SV81: $i] :
( ( ! [SY324: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY324 ) @ ( c_Nat_OSuc @ SV81 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY324 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1693,plain,
! [SV82: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ~ ( class_Int_Onumber @ SY326 )
| ~ ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SY326 @ SY325 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SY326 @ SY325 ) ) )
| ~ ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SY326 @ SY325 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SY326 @ SY325 )
= SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1694,plain,
! [SV83: $i] :
( ( ! [SY327: $i] :
( ( SY327 != SV83 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY327 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1695,plain,
! [SV84: $i] :
( ( ! [SY328: $i,SY329: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY329 @ SY328 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY329 @ SV84 ) )
| ( SY328 = SV84 ) )
| ~ ( ( SY328 != SV84 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY329 @ SY328 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY329 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1696,plain,
! [SV85: $i] :
( ( ! [SY330: $i] :
( ~ ( ( SY330 != SV85 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY330 @ SV85 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1697,plain,
! [SV86: $i] :
( ( ! [SY331: $i,SY332: $i,SY333: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY333 )
| ( ( c_Groups_Otimes__class_Otimes @ SY333 @ SY332 @ ( c_Groups_Otimes__class_Otimes @ SY333 @ SY331 @ SV86 ) )
= ( c_Groups_Otimes__class_Otimes @ SY333 @ SY331 @ ( c_Groups_Otimes__class_Otimes @ SY333 @ SY332 @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1698,plain,
! [SV87: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1699,plain,
! [SV88: $i] :
( ( ! [SY334: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY334 @ ( c_Nat_OSuc @ SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY334 @ SV88 )
| ( SY334 = SV88 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY334 @ SV88 )
| ( SY334 = SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY334 @ ( c_Nat_OSuc @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1700,plain,
! [SV89: $i] :
( ( ( c_Nat_OSuc @ SV89 )
!= SV89 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1701,plain,
! [SV90: $i] :
( ( ! [SY335: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY335 ) @ SV90 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY335 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1702,plain,
! [SV91: $i] :
( ( ! [SY336: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY336 @ SV91 )
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ( SY336
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
| ~ ( ~ ~ ( ( SY336
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY336 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1703,plain,
! [SV92: $i] :
( ( ! [SY337: $i,SY338: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY338 ) @ SY337 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY338 ) @ SV92 ) )
| ( SY337 = SV92 ) )
| ~ ( ( SY337 != SV92 )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY338 ) @ SY337 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY338 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1704,plain,
! [SV93: $i] :
( ( ! [SY339: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY339 ) @ ( c_Nat_OSuc @ SV93 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY339 @ SV93 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY339 @ SV93 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY339 ) @ ( c_Nat_OSuc @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1705,plain,
! [SV94: $i] :
( ( ! [SY340: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY340 @ SV94 )
| ~ ( ( ( c_Nat_OSuc @ SY340 )
!= SV94 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY340 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1706,plain,
! [SV95: $i] :
( ( ! [SY341: $i,SY342: $i,SY343: $i,SY344: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY344 )
| ( ( c_Groups_Otimes__class_Otimes @ SY344 @ ( c_Groups_Otimes__class_Otimes @ SY344 @ SY343 @ SY342 ) @ ( c_Groups_Otimes__class_Otimes @ SY344 @ SY341 @ SV95 ) )
= ( c_Groups_Otimes__class_Otimes @ SY344 @ SY341 @ ( c_Groups_Otimes__class_Otimes @ SY344 @ ( c_Groups_Otimes__class_Otimes @ SY344 @ SY343 @ SY342 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1707,plain,
! [SV96: $i] :
( ( c_Int_OPls
!= ( c_Int_OBit1 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1708,plain,
! [SV97: $i] :
( ( ! [SY345: $i] :
~ ( ~ ( ( ( c_Int_OBit0 @ SY345 )
!= ( c_Int_OBit0 @ SV97 ) )
| ( SY345 = SV97 ) )
| ~ ( ( SY345 != SV97 )
| ( ( c_Int_OBit0 @ SY345 )
= ( c_Int_OBit0 @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1709,plain,
! [SV98: $i] :
( ( ! [SY346: $i] :
~ ( ~ ( ~ ( ( SY346 != SV98 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY346 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SY346 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY346 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SY346 ) )
| ( SY346 != SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1710,plain,
! [SV99: $i] :
( ( ! [SY347: $i,SY348: $i,SY349: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY349 @ SY348 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY347 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY349 @ SY347 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY348 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1711,plain,
! [SV100: $i] :
( ( ! [SY350: $i,SY351: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY351 @ SY350 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SY351 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1712,plain,
! [SV101: $i] :
( ( ! [SY352: $i] :
~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY352 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SY352 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SY352 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY352 @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1713,plain,
! [SV102: $i] :
( ( ! [SY353: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY353 ) @ ( c_Nat_OSuc @ SV102 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY353 @ SV102 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY353 @ SV102 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY353 ) @ ( c_Nat_OSuc @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1714,plain,
! [SV103: $i] :
( ( ! [SY354: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY354 @ SV103 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY354 @ ( c_Nat_OSuc @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1715,plain,
! [SV104: $i] :
( ( ! [SY355: $i] :
( ( c_Int_OBit1 @ SY355 )
!= ( c_Int_OBit0 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1716,plain,
! [SV105: $i] :
( ( ! [SY356: $i,SY357: $i,SY358: $i,SY359: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY359 )
| ( ( c_Groups_Otimes__class_Otimes @ SY359 @ ( c_Groups_Otimes__class_Otimes @ SY359 @ SY358 @ SY357 ) @ ( c_Groups_Otimes__class_Otimes @ SY359 @ SY356 @ SV105 ) )
= ( c_Groups_Otimes__class_Otimes @ SY359 @ ( c_Groups_Otimes__class_Otimes @ SY359 @ SY358 @ SY356 ) @ ( c_Groups_Otimes__class_Otimes @ SY359 @ SY357 @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1717,plain,
! [SV106: $i] :
( ( ! [SY360: $i,SY361: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY361 @ SY360 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SY360 ) )
| ( SY361 = SV106 ) )
| ~ ( ( SY361 != SV106 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY361 @ SY360 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SY360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1718,plain,
! [SV107: $i] :
( ( ! [SY362: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY362 @ SV107 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV107 @ SY362 )
| ( SY362 = SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1719,plain,
! [SV108: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1720,plain,
! [SV109: $i] :
( ( ! [SY363: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY363 @ SV109 )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ~ ( ( SY363
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SY363
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY363 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1721,plain,
! [SV110: $i] :
( ( ! [SY364: $i] :
( ( c_Int_OBit0 @ SY364 )
!= ( c_Int_OBit1 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1722,plain,
! [SV111: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1723,plain,
! [SV112: $i] :
( ( ~ ( ~ ( ( c_Int_OPls
!= ( c_Int_OBit0 @ SV112 ) )
| ( c_Int_OPls = SV112 ) )
| ~ ( ( c_Int_OPls != SV112 )
| ( c_Int_OPls
= ( c_Int_OBit0 @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1724,plain,
! [SV113: $i] :
( ( ( c_Int_OBit0 @ SV113 )
!= c_Int_OMin )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1725,plain,
! [SV114: $i] :
( ( ! [SY365: $i] :
( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY365 @ SV114 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY365 @ ( c_Nat_OSuc @ SV114 ) )
| ( SV114 = SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1726,plain,
! [SV115: $i] :
( ( ! [SY366: $i] :
~ ( ~ ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY366 @ SV115 ) )
| ~ ( ( SY366
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SY366
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY366 @ SV115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1727,plain,
! [SV116: $i] :
( ( ! [SY367: $i,SY368: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY368 @ SY367 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SY367 ) )
| ( SY368 = SV116 )
| ( SY367
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SY368 = SV116 )
| ( SY367
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY368 @ SY367 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SY367 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1728,plain,
! [SV2: $i,SV117: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ SV117 ) @ SV2 )
= ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV117 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1729,plain,
! [SV5: $i,SV118: $i] :
( ( ! [SY369: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY369 @ SV118 ) @ SV5 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY369 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV118 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1730,plain,
! [SV6: $i,SV119: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV119 @ SV6 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV6 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1731,plain,
! [SV7: $i,SV120: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV120 @ SV7 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV7 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1732,plain,
! [SV8: $i,SV121: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ SV8 ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV121 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1733,plain,
! [SV9: $i,SV122: $i] :
( ( ! [SY370: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY370 @ SV122 ) @ SV9 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SY370 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV122 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1734,plain,
! [SV12: $i,SV123: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV123 @ ( c_Nat_OSuc @ SV12 ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV123 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1735,plain,
! [SV13: $i,SV124: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV124 ) @ SV13 )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV124 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1736,plain,
! [SV14: $i,SV125: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV125 ) @ SV14 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV125 @ ( c_Nat_OSuc @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1737,plain,
! [SV15: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV15 ) @ SV15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1738,plain,
! [SV16: $i,SV126: $i] :
( ( ! [SY371: $i,SY372: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY372 @ SY371 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV126 @ SY371 ) @ SV16 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY372 @ SV126 ) @ SY371 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1739,plain,
! [SV17: $i,SV127: $i] :
( ( ! [SY373: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY373 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV127 @ SV17 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY373 @ SV127 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY373 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1740,plain,
! [SV18: $i,SV128: $i] :
( ( ! [SY374: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY374 @ SV128 ) @ SV18 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY374 @ SV18 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV128 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1741,plain,
! [SV21: $i,SV129: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV21 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV129 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV129 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1742,plain,
! [SV22: $i,SV130: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV130 ) @ SV22 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV22 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV130 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1743,plain,
! [SV28: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV28 @ SV28 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1744,plain,
! [SV30: $i,SV131: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV131 @ SV30 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV30 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1745,plain,
! [SV31: $i,SV132: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV132 @ SV31 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV31 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1746,plain,
! [SV32: $i,SV133: $i] :
( ( ! [SY375: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY375 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV133 @ SV32 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV133 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY375 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1747,plain,
! [SV33: $i,SV134: $i] :
( ( ! [SY376: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY376 @ SV134 ) @ SV33 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY376 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV134 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1748,plain,
! [SV34: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV34 @ SV34 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1749,plain,
! [SV35: $i,SV135: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SV135 @ SV35 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SV35 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1750,plain,
! [SV36: $i,SV136: $i] :
( ( ! [SY377: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SY377 @ SV136 ) @ SV36 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SY377 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SV136 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1751,plain,
! [SV39: $i,SV137: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV137 @ SV39 )
| ( SV39 != SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1752,plain,
! [SV40: $i,SV138: $i] :
( ( ! [SY378: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY378 @ SV138 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY378 @ SV40 ) )
| ( SY378
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ~ ( ~ ( ( SY378
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY378 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY378 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1753,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1754,plain,
! [SV42: $i,SV140: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV140 ) @ SV42 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV140 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1755,plain,
! [SV43: $i,SV141: $i] :
( ( ! [SY379: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY379 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY379 ) @ SV43 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY379 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY379 ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1756,plain,
! [SV44: $i] :
( ( ( c_Nat_OSuc @ SV44 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1757,plain,
! [SV45: $i] :
( ( ~ ( ( c_Int_OMin
!= ( c_Int_OBit1 @ SV45 ) )
| ( c_Int_OMin = SV45 ) )
| ~ ( ( c_Int_OMin != SV45 )
| ( c_Int_OMin
= ( c_Int_OBit1 @ SV45 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1758,plain,
! [SV46: $i] :
( ( ( c_Nat_OSuc @ SV46 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1759,plain,
! [SV47: $i,SV142: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV47 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV142 ) @ ( c_Nat_OSuc @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1760,plain,
! [SV48: $i,SV143: $i] :
( ( ! [SY380: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY380 )
| ( ( c_Groups_Otimes__class_Otimes @ SY380 @ SV143 @ SV48 )
= ( c_Groups_Otimes__class_Otimes @ SY380 @ SV48 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1761,plain,
! [SV49: $i,SV144: $i] :
( ( ! [SY381: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY381 @ SV144 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY381 @ SV49 ) )
| ( SV144 = SV49 )
| ( SY381
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SV144 = SV49 )
| ( SY381
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY381 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY381 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1762,plain,
! [SV50: $i,SV145: $i] :
( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1763,plain,
! [SV51: $i] :
( ( ~ ( ( ( c_Int_OBit1 @ SV51 )
!= c_Int_OMin )
| ( SV51 = c_Int_OMin ) )
| ~ ( ( SV51 != c_Int_OMin )
| ( ( c_Int_OBit1 @ SV51 )
= c_Int_OMin ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1764,plain,
( ( ! [SX0: $i] :
( v_na____
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1765,plain,
! [SV52: $i,SV146: $i] :
( ( ~ ( class_Int_Onumber__ring @ SV146 )
| ( ( c_Groups_Otimes__class_Otimes @ SV146 @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ SV52 )
= SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1766,plain,
! [SV53: $i,SV147: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ ( c_Nat_OSuc @ SV53 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ SV53 )
| ( SV147
= ( c_Nat_OSuc @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1767,plain,
! [SV54: $i,SV148: $i] :
( ( ! [SY382: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY382 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY382 ) @ SV54 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY382 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY382 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1768,plain,
! [SV55: $i] :
( ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
| ~ ! [SY288: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY288 ) ) )
| ~ ( ~ ~ ! [SY289: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY289 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1769,plain,
! [SV56: $i,SV149: $i] :
( ( ( ( c_Nat_OSuc @ SV149 )
!= ( c_Nat_OSuc @ SV56 ) )
| ( SV149 = SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1770,plain,
! [SV57: $i,SV150: $i] :
( ( ! [SY383: $i,SY384: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY384 )
| ( ( c_Groups_Otimes__class_Otimes @ SY384 @ SY383 @ ( c_Groups_Otimes__class_Otimes @ SY384 @ SV150 @ SV57 ) )
= ( c_Groups_Otimes__class_Otimes @ SY384 @ ( c_Groups_Otimes__class_Otimes @ SY384 @ SY383 @ SV150 ) @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1771,plain,
! [SV58: $i,SV151: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ ( c_Nat_OSuc @ SV58 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ SV58 )
| ( SV151 = SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1772,plain,
! [SV59: $i] :
( ( ~ ( ( ( c_Int_OBit0 @ SV59 )
!= c_Int_OPls )
| ( SV59 = c_Int_OPls ) )
| ~ ( ( SV59 != c_Int_OPls )
| ( ( c_Int_OBit0 @ SV59 )
= c_Int_OPls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1773,plain,
! [SV60: $i,SV152: $i] :
( ( ! [SY385: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY385 @ SV152 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY385 @ SV60 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV152 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1774,plain,
! [SV61: $i,SV153: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ( class_Groups_Oab__semigroup__mult @ SY387 )
| ( ( c_Groups_Otimes__class_Otimes @ SY387 @ ( c_Groups_Otimes__class_Otimes @ SY387 @ SY386 @ SV153 ) @ SV61 )
= ( c_Groups_Otimes__class_Otimes @ SY387 @ SY386 @ ( c_Groups_Otimes__class_Otimes @ SY387 @ SV153 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1775,plain,
! [SV62: $i] :
( ( c_Int_OMin
= ( c_Int_OBit0 @ SV62 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1776,plain,
! [SV63: $i,SV154: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY389 )
| ( ( c_Groups_Otimes__class_Otimes @ SY389 @ ( c_Groups_Otimes__class_Otimes @ SY389 @ SY388 @ SV154 ) @ SV63 )
= ( c_Groups_Otimes__class_Otimes @ SY389 @ SY388 @ ( c_Groups_Otimes__class_Otimes @ SY389 @ SV154 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1777,plain,
! [SV64: $i] :
( ( ( c_Nat_OSuc @ SV64 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1778,plain,
! [SV65: $i,SV155: $i] :
( ( ~ ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ~ ( ~ ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1779,plain,
! [SV66: $i,SV156: $i] :
( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
| ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
| ( SV156 = SV66 ) )
| ~ ( ( SV156 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(1780,plain,
! [SV67: $i,SV157: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV157 @ SV67 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV157 @ ( c_Nat_OSuc @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1781,plain,
! [SV68: $i,SV158: $i] :
( ( ! [SY390: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY390 @ SV158 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV158 @ SV68 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY390 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(1782,plain,
! [SV69: $i,SV159: $i] :
( ( ! [SY391: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY391 @ SV159 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV159 @ SV69 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY391 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1783,plain,
! [SV70: $i,SV160: $i] :
( ( ~ ( ~ ( ( ( c_Nat_OSuc @ SV160 )
!= ( c_Nat_OSuc @ SV70 ) )
| ( SV160 = SV70 ) )
| ~ ( ( SV160 != SV70 )
| ( ( c_Nat_OSuc @ SV160 )
= ( c_Nat_OSuc @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1784,plain,
! [SV71: $i,SV161: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV161 @ SV71 )
| ( SV161 != SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1785,plain,
! [SV72: $i,SV162: $i] :
( ( ~ ( ~ ( ( ( c_Int_OBit1 @ SV162 )
!= ( c_Int_OBit1 @ SV72 ) )
| ( SV162 = SV72 ) )
| ~ ( ( SV162 != SV72 )
| ( ( c_Int_OBit1 @ SV162 )
= ( c_Int_OBit1 @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1786,plain,
! [SV73: $i] :
( ( SV73
= ( c_Nat_OSuc @ SV73 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1787,plain,
! [SV74: $i,SV163: $i] :
( ( ~ ( class_Int_Onumber__ring @ SV163 )
| ( ( c_Groups_Otimes__class_Otimes @ SV163 @ SV74 @ ( c_Int_Onumber__class_Onumber__of @ SV163 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1788,plain,
! [SV75: $i,SV164: $i] :
( ( ! [SY392: $i,SY393: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY393 )
| ( ( c_Groups_Otimes__class_Otimes @ SY393 @ ( c_Groups_Otimes__class_Otimes @ SY393 @ SY392 @ SV164 ) @ SV75 )
= ( c_Groups_Otimes__class_Otimes @ SY393 @ ( c_Groups_Otimes__class_Otimes @ SY393 @ SY392 @ SV75 ) @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1789,plain,
! [SV76: $i,SV165: $i] :
( ( ! [SY394: $i,SY395: $i,SY396: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY396 )
| ( ( c_Groups_Otimes__class_Otimes @ SY396 @ ( c_Groups_Otimes__class_Otimes @ SY396 @ SY395 @ SY394 ) @ ( c_Groups_Otimes__class_Otimes @ SY396 @ SV165 @ SV76 ) )
= ( c_Groups_Otimes__class_Otimes @ SY396 @ SY395 @ ( c_Groups_Otimes__class_Otimes @ SY396 @ SY394 @ ( c_Groups_Otimes__class_Otimes @ SY396 @ SV165 @ SV76 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(1790,plain,
! [SV77: $i] :
( ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) )
| ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1791,plain,
! [SV78: $i] :
( ( ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
| ~ ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) )
| ~ ( ~ ~ ! [SY322: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY322 ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1792,plain,
! [SV79: $i] :
( ( ( c_Int_OBit1 @ SV79 )
= c_Int_OPls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1793,plain,
! [SV80: $i,SV166: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1794,plain,
! [SV81: $i,SV167: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV167 ) @ ( c_Nat_OSuc @ SV81 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV167 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1795,plain,
! [SV82: $i,SV168: $i] :
( ( ! [SY397: $i] :
( ~ ( class_Int_Onumber @ SY397 )
| ~ ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SY397 @ SV168 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SY397 @ SV168 ) ) )
| ~ ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SY397 @ SV168 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SY397 @ SV168 )
= SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1796,plain,
! [SV83: $i,SV169: $i] :
( ( ( SV169 != SV83 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV169 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1797,plain,
! [SV84: $i,SV170: $i] :
( ( ! [SY398: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY398 @ SV170 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY398 @ SV84 ) )
| ( SV170 = SV84 ) )
| ~ ( ( SV170 != SV84 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY398 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY398 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1798,plain,
! [SV85: $i,SV171: $i] :
( ( ~ ( ( SV171 != SV85 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV171 @ SV85 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1799,plain,
! [SV86: $i,SV172: $i] :
( ( ! [SY399: $i,SY400: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY400 )
| ( ( c_Groups_Otimes__class_Otimes @ SY400 @ SY399 @ ( c_Groups_Otimes__class_Otimes @ SY400 @ SV172 @ SV86 ) )
= ( c_Groups_Otimes__class_Otimes @ SY400 @ SV172 @ ( c_Groups_Otimes__class_Otimes @ SY400 @ SY399 @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1800,plain,
! [SV87: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Nat_OSuc @ SV87 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1801,plain,
! [SV88: $i,SV173: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1802,plain,
! [SV89: $i] :
( ( ( c_Nat_OSuc @ SV89 )
= SV89 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1803,plain,
! [SV90: $i,SV174: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV174 ) @ SV90 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV174 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(1804,plain,
! [SV91: $i,SV175: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
| ~ ( ~ ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1805,plain,
! [SV92: $i,SV176: $i] :
( ( ! [SY401: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY401 ) @ SV176 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY401 ) @ SV92 ) )
| ( SV176 = SV92 ) )
| ~ ( ( SV176 != SV92 )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY401 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY401 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1806,plain,
! [SV93: $i,SV177: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(1807,plain,
! [SV94: $i,SV178: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV178 @ SV94 )
| ~ ( ( ( c_Nat_OSuc @ SV178 )
!= SV94 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV178 ) @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1808,plain,
! [SV95: $i,SV179: $i] :
( ( ! [SY402: $i,SY403: $i,SY404: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY404 )
| ( ( c_Groups_Otimes__class_Otimes @ SY404 @ ( c_Groups_Otimes__class_Otimes @ SY404 @ SY403 @ SY402 ) @ ( c_Groups_Otimes__class_Otimes @ SY404 @ SV179 @ SV95 ) )
= ( c_Groups_Otimes__class_Otimes @ SY404 @ SV179 @ ( c_Groups_Otimes__class_Otimes @ SY404 @ ( c_Groups_Otimes__class_Otimes @ SY404 @ SY403 @ SY402 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1809,plain,
! [SV96: $i] :
( ( c_Int_OPls
= ( c_Int_OBit1 @ SV96 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1810,plain,
! [SV97: $i,SV180: $i] :
( ( ~ ( ~ ( ( ( c_Int_OBit0 @ SV180 )
!= ( c_Int_OBit0 @ SV97 ) )
| ( SV180 = SV97 ) )
| ~ ( ( SV180 != SV97 )
| ( ( c_Int_OBit0 @ SV180 )
= ( c_Int_OBit0 @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1811,plain,
! [SV98: $i,SV181: $i] :
( ( ~ ( ~ ( ~ ( ( SV181 != SV98 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
| ( SV181 != SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1812,plain,
! [SV99: $i,SV182: $i] :
( ( ! [SY405: $i,SY406: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY406 @ SY405 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV182 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY406 @ SV182 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY405 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1813,plain,
! [SV100: $i,SV183: $i] :
( ( ! [SY407: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY407 @ SV183 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SY407 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1814,plain,
! [SV101: $i,SV184: $i] :
( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1815,plain,
! [SV102: $i,SV185: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1816,plain,
! [SV103: $i,SV186: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV186 @ SV103 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV186 @ ( c_Nat_OSuc @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1817,plain,
! [SV104: $i,SV187: $i] :
( ( ( c_Int_OBit1 @ SV187 )
!= ( c_Int_OBit0 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1818,plain,
! [SV105: $i,SV188: $i] :
( ( ! [SY408: $i,SY409: $i,SY410: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY410 )
| ( ( c_Groups_Otimes__class_Otimes @ SY410 @ ( c_Groups_Otimes__class_Otimes @ SY410 @ SY409 @ SY408 ) @ ( c_Groups_Otimes__class_Otimes @ SY410 @ SV188 @ SV105 ) )
= ( c_Groups_Otimes__class_Otimes @ SY410 @ ( c_Groups_Otimes__class_Otimes @ SY410 @ SY409 @ SV188 ) @ ( c_Groups_Otimes__class_Otimes @ SY410 @ SY408 @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1819,plain,
! [SV106: $i,SV189: $i] :
( ( ! [SY411: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY411 @ SV189 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
| ( SY411 = SV106 ) )
| ~ ( ( SY411 != SV106 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY411 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(1820,plain,
! [SV107: $i,SV190: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV190 @ SV107 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV107 @ SV190 )
| ( SV190 = SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1821,plain,
! [SV108: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Nat_OSuc @ SV108 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1822,plain,
! [SV109: $i,SV191: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1823,plain,
! [SV110: $i,SV192: $i] :
( ( ( c_Int_OBit0 @ SV192 )
!= ( c_Int_OBit1 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1824,plain,
! [SV111: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Nat_OSuc @ SV111 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1825,plain,
! [SV112: $i] :
( ( ~ ( ( c_Int_OPls
!= ( c_Int_OBit0 @ SV112 ) )
| ( c_Int_OPls = SV112 ) )
| ~ ( ( c_Int_OPls != SV112 )
| ( c_Int_OPls
= ( c_Int_OBit0 @ SV112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1826,plain,
! [SV113: $i] :
( ( ( c_Int_OBit0 @ SV113 )
= c_Int_OMin )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1827,plain,
! [SV114: $i,SV193: $i] :
( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ SV114 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ ( c_Nat_OSuc @ SV114 ) )
| ( SV114 = SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1828,plain,
! [SV115: $i,SV194: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
| ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1829,plain,
! [SV116: $i,SV195: $i] :
( ( ! [SY412: $i] :
~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY412 @ SV195 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
| ( SY412 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SY412 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY412 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(1830,plain,
! [SV5: $i,SV118: $i,SV196: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV196 @ SV118 ) @ SV5 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV196 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV118 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1831,plain,
! [SV9: $i,SV122: $i,SV197: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV197 @ SV122 ) @ SV9 )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV197 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ SV122 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(1832,plain,
! [SV16: $i,SV126: $i,SV198: $i] :
( ( ! [SY413: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY413 @ SV198 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV126 @ SV198 ) @ SV16 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY413 @ SV126 ) @ SV198 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1833,plain,
! [SV17: $i,SV127: $i,SV199: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV199 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV127 @ SV17 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV199 @ SV127 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV199 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(1834,plain,
! [SV18: $i,SV128: $i,SV200: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV128 ) @ SV18 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV200 @ SV18 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV128 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1835,plain,
! [SV31: $i,SV132: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV132 @ SV31 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV31 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1836,plain,
! [SV32: $i,SV133: $i,SV201: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV201 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV133 @ SV32 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV133 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV201 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1837,plain,
! [SV33: $i,SV134: $i,SV202: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV202 @ SV134 ) @ SV33 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV202 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV134 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1838,plain,
! [SV36: $i,SV136: $i,SV203: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SV203 @ SV136 ) @ SV36 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SV203 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ SV136 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1839,plain,
! [SV39: $i,SV137: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV137 @ SV39 ) )
= $true )
| ( ( SV39 != SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1840,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
| ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ~ ( ~ ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1841,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1842,plain,
! [SV42: $i,SV140: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV140 ) @ SV42 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV140 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1843,plain,
! [SV43: $i,SV141: $i,SV205: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(1844,plain,
! [SV45: $i] :
( ( ~ ( ( c_Int_OMin
!= ( c_Int_OBit1 @ SV45 ) )
| ( c_Int_OMin = SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1845,plain,
! [SV45: $i] :
( ( ~ ( ( c_Int_OMin != SV45 )
| ( c_Int_OMin
= ( c_Int_OBit1 @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1846,plain,
! [SV47: $i,SV142: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV47 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV142 ) @ ( c_Nat_OSuc @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1847,plain,
! [SV48: $i,SV143: $i,SV206: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV206 )
| ( ( c_Groups_Otimes__class_Otimes @ SV206 @ SV143 @ SV48 )
= ( c_Groups_Otimes__class_Otimes @ SV206 @ SV48 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1848,plain,
! [SV49: $i,SV144: $i,SV207: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
| ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1849,plain,
! [SV50: $i,SV145: $i] :
( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1850,plain,
! [SV51: $i] :
( ( ~ ( ( ( c_Int_OBit1 @ SV51 )
!= c_Int_OMin )
| ( SV51 = c_Int_OMin ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1851,plain,
! [SV51: $i] :
( ( ~ ( ( SV51 != c_Int_OMin )
| ( ( c_Int_OBit1 @ SV51 )
= c_Int_OMin ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1852,plain,
! [SV208: $i] :
( ( v_na____
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(1853,plain,
! [SV52: $i,SV146: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV146 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV146 @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ SV52 )
= SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1854,plain,
! [SV53: $i,SV147: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ ( c_Nat_OSuc @ SV53 ) ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ SV53 )
| ( SV147
= ( c_Nat_OSuc @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1855,plain,
! [SV54: $i,SV148: $i,SV209: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(1856,plain,
! [SV55: $i] :
( ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
| ~ ! [SY288: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY288 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1768]) ).
thf(1857,plain,
! [SV55: $i] :
( ( ~ ( ~ ~ ! [SY289: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY289 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1768]) ).
thf(1858,plain,
! [SV56: $i,SV149: $i] :
( ( ( ( c_Nat_OSuc @ SV149 )
!= ( c_Nat_OSuc @ SV56 ) )
= $true )
| ( ( SV149 = SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1859,plain,
! [SV57: $i,SV150: $i,SV210: $i] :
( ( ! [SY414: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY414 )
| ( ( c_Groups_Otimes__class_Otimes @ SY414 @ SV210 @ ( c_Groups_Otimes__class_Otimes @ SY414 @ SV150 @ SV57 ) )
= ( c_Groups_Otimes__class_Otimes @ SY414 @ ( c_Groups_Otimes__class_Otimes @ SY414 @ SV210 @ SV150 ) @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(1860,plain,
! [SV58: $i,SV151: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ ( c_Nat_OSuc @ SV58 ) ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ SV58 )
| ( SV151 = SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1861,plain,
! [SV59: $i] :
( ( ~ ( ( ( c_Int_OBit0 @ SV59 )
!= c_Int_OPls )
| ( SV59 = c_Int_OPls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1772]) ).
thf(1862,plain,
! [SV59: $i] :
( ( ~ ( ( SV59 != c_Int_OPls )
| ( ( c_Int_OBit0 @ SV59 )
= c_Int_OPls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1772]) ).
thf(1863,plain,
! [SV60: $i,SV152: $i,SV211: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV211 @ SV152 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV211 @ SV60 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV152 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(1864,plain,
! [SV61: $i,SV153: $i,SV212: $i] :
( ( ! [SY415: $i] :
( ~ ( class_Groups_Oab__semigroup__mult @ SY415 )
| ( ( c_Groups_Otimes__class_Otimes @ SY415 @ ( c_Groups_Otimes__class_Otimes @ SY415 @ SV212 @ SV153 ) @ SV61 )
= ( c_Groups_Otimes__class_Otimes @ SY415 @ SV212 @ ( c_Groups_Otimes__class_Otimes @ SY415 @ SV153 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(1865,plain,
! [SV63: $i,SV154: $i,SV213: $i] :
( ( ! [SY416: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY416 )
| ( ( c_Groups_Otimes__class_Otimes @ SY416 @ ( c_Groups_Otimes__class_Otimes @ SY416 @ SV213 @ SV154 ) @ SV63 )
= ( c_Groups_Otimes__class_Otimes @ SY416 @ SV213 @ ( c_Groups_Otimes__class_Otimes @ SY416 @ SV154 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(1866,plain,
! [SV65: $i,SV155: $i] :
( ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ~ ( ~ ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1867,plain,
! [SV66: $i,SV156: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
| ( SV156 = SV66 ) )
| ~ ( ( SV156 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1868,plain,
! [SV67: $i,SV157: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV157 @ SV67 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV157 @ ( c_Nat_OSuc @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1869,plain,
! [SV68: $i,SV158: $i,SV214: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV214 @ SV158 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV158 @ SV68 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV214 ) @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(1870,plain,
! [SV69: $i,SV159: $i,SV215: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV159 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV159 @ SV69 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1871,plain,
! [SV70: $i,SV160: $i] :
( ( ~ ( ( ( c_Nat_OSuc @ SV160 )
!= ( c_Nat_OSuc @ SV70 ) )
| ( SV160 = SV70 ) )
| ~ ( ( SV160 != SV70 )
| ( ( c_Nat_OSuc @ SV160 )
= ( c_Nat_OSuc @ SV70 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1872,plain,
! [SV71: $i,SV161: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV161 @ SV71 ) )
= $true )
| ( ( SV161 != SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1873,plain,
! [SV72: $i,SV162: $i] :
( ( ~ ( ( ( c_Int_OBit1 @ SV162 )
!= ( c_Int_OBit1 @ SV72 ) )
| ( SV162 = SV72 ) )
| ~ ( ( SV162 != SV72 )
| ( ( c_Int_OBit1 @ SV162 )
= ( c_Int_OBit1 @ SV72 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1874,plain,
! [SV74: $i,SV163: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV163 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV163 @ SV74 @ ( c_Int_Onumber__class_Onumber__of @ SV163 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(1875,plain,
! [SV75: $i,SV164: $i,SV216: $i] :
( ( ! [SY417: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY417 )
| ( ( c_Groups_Otimes__class_Otimes @ SY417 @ ( c_Groups_Otimes__class_Otimes @ SY417 @ SV216 @ SV164 ) @ SV75 )
= ( c_Groups_Otimes__class_Otimes @ SY417 @ ( c_Groups_Otimes__class_Otimes @ SY417 @ SV216 @ SV75 ) @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(1876,plain,
! [SV76: $i,SV165: $i,SV217: $i] :
( ( ! [SY418: $i,SY419: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY419 )
| ( ( c_Groups_Otimes__class_Otimes @ SY419 @ ( c_Groups_Otimes__class_Otimes @ SY419 @ SY418 @ SV217 ) @ ( c_Groups_Otimes__class_Otimes @ SY419 @ SV165 @ SV76 ) )
= ( c_Groups_Otimes__class_Otimes @ SY419 @ SY418 @ ( c_Groups_Otimes__class_Otimes @ SY419 @ SV217 @ ( c_Groups_Otimes__class_Otimes @ SY419 @ SV165 @ SV76 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1877,plain,
! [SV77: $i] :
( ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1878,plain,
! [SV77: $i] :
( ( ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1879,plain,
! [SV78: $i] :
( ( ~ ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
| ~ ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1880,plain,
! [SV78: $i] :
( ( ~ ( ~ ~ ! [SY322: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY322 ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1881,plain,
! [SV80: $i,SV166: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1882,plain,
! [SV81: $i,SV167: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV167 ) @ ( c_Nat_OSuc @ SV81 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV167 @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1883,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ~ ( class_Int_Onumber @ SV218 )
| ~ ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) ) )
| ~ ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(1884,plain,
! [SV83: $i,SV169: $i] :
( ( ( SV169 != SV83 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV169 @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1885,plain,
! [SV84: $i,SV170: $i,SV219: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
| ( SV170 = SV84 ) )
| ~ ( ( SV170 != SV84 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(1886,plain,
! [SV85: $i,SV171: $i] :
( ( ( ~ ( ( SV171 != SV85 ) ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV171 @ SV85 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1887,plain,
! [SV86: $i,SV172: $i,SV220: $i] :
( ( ! [SY420: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY420 )
| ( ( c_Groups_Otimes__class_Otimes @ SY420 @ SV220 @ ( c_Groups_Otimes__class_Otimes @ SY420 @ SV172 @ SV86 ) )
= ( c_Groups_Otimes__class_Otimes @ SY420 @ SV172 @ ( c_Groups_Otimes__class_Otimes @ SY420 @ SV220 @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(1888,plain,
! [SV88: $i,SV173: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1889,plain,
! [SV90: $i,SV174: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV174 ) @ SV90 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV174 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(1890,plain,
! [SV91: $i,SV175: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
| ~ ( ~ ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1891,plain,
! [SV92: $i,SV176: $i,SV221: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
| ( SV176 = SV92 ) )
| ~ ( ( SV176 != SV92 )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(1892,plain,
! [SV93: $i,SV177: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1893,plain,
! [SV94: $i,SV178: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV178 @ SV94 ) )
= $true )
| ( ( ~ ( ( ( c_Nat_OSuc @ SV178 )
!= SV94 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV178 ) @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1894,plain,
! [SV95: $i,SV179: $i,SV222: $i] :
( ( ! [SY421: $i,SY422: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY422 )
| ( ( c_Groups_Otimes__class_Otimes @ SY422 @ ( c_Groups_Otimes__class_Otimes @ SY422 @ SY421 @ SV222 ) @ ( c_Groups_Otimes__class_Otimes @ SY422 @ SV179 @ SV95 ) )
= ( c_Groups_Otimes__class_Otimes @ SY422 @ SV179 @ ( c_Groups_Otimes__class_Otimes @ SY422 @ ( c_Groups_Otimes__class_Otimes @ SY422 @ SY421 @ SV222 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(1895,plain,
! [SV97: $i,SV180: $i] :
( ( ~ ( ( ( c_Int_OBit0 @ SV180 )
!= ( c_Int_OBit0 @ SV97 ) )
| ( SV180 = SV97 ) )
| ~ ( ( SV180 != SV97 )
| ( ( c_Int_OBit0 @ SV180 )
= ( c_Int_OBit0 @ SV97 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1896,plain,
! [SV98: $i,SV181: $i] :
( ( ~ ( ~ ( ( SV181 != SV98 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
| ( SV181 != SV98 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1897,plain,
! [SV99: $i,SV182: $i,SV223: $i] :
( ( ! [SY423: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY423 @ SV223 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV182 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SY423 @ SV182 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV223 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(1898,plain,
! [SV100: $i,SV183: $i,SV224: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV224 @ SV183 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SV224 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(1899,plain,
! [SV101: $i,SV184: $i] :
( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1900,plain,
! [SV102: $i,SV185: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1901,plain,
! [SV103: $i,SV186: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV186 @ SV103 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV186 @ ( c_Nat_OSuc @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1902,plain,
! [SV104: $i,SV187: $i] :
( ( ( c_Int_OBit1 @ SV187 )
= ( c_Int_OBit0 @ SV104 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1903,plain,
! [SV105: $i,SV188: $i,SV225: $i] :
( ( ! [SY424: $i,SY425: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY425 )
| ( ( c_Groups_Otimes__class_Otimes @ SY425 @ ( c_Groups_Otimes__class_Otimes @ SY425 @ SY424 @ SV225 ) @ ( c_Groups_Otimes__class_Otimes @ SY425 @ SV188 @ SV105 ) )
= ( c_Groups_Otimes__class_Otimes @ SY425 @ ( c_Groups_Otimes__class_Otimes @ SY425 @ SY424 @ SV188 ) @ ( c_Groups_Otimes__class_Otimes @ SY425 @ SV225 @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(1904,plain,
! [SV106: $i,SV189: $i,SV226: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
| ( SV226 = SV106 ) )
| ~ ( ( SV226 != SV106 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(1905,plain,
! [SV107: $i,SV190: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV190 @ SV107 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV107 @ SV190 )
| ( SV190 = SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1906,plain,
! [SV109: $i,SV191: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1907,plain,
! [SV110: $i,SV192: $i] :
( ( ( c_Int_OBit0 @ SV192 )
= ( c_Int_OBit1 @ SV110 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1908,plain,
! [SV112: $i] :
( ( ~ ( ( c_Int_OPls
!= ( c_Int_OBit0 @ SV112 ) )
| ( c_Int_OPls = SV112 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1909,plain,
! [SV112: $i] :
( ( ~ ( ( c_Int_OPls != SV112 )
| ( c_Int_OPls
= ( c_Int_OBit0 @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1910,plain,
! [SV114: $i,SV193: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ SV114 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ ( c_Nat_OSuc @ SV114 ) )
| ( SV114 = SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(1911,plain,
! [SV115: $i,SV194: $i] :
( ( ~ ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
| ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
| ~ ( ~ ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1912,plain,
! [SV116: $i,SV195: $i,SV227: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
| ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1913,plain,
! [SV16: $i,SV126: $i,SV198: $i,SV228: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV228 @ SV198 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV126 @ SV198 ) @ SV16 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV228 @ SV126 ) @ SV198 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(1914,plain,
! [SV39: $i,SV137: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV137 @ SV39 )
= $false )
| ( ( SV39 != SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1915,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
| ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ~ ( ~ ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1916,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1917,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ( ~ ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1918,plain,
! [SV42: $i,SV140: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV140 ) @ SV42 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV140 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1919,plain,
! [SV43: $i,SV141: $i,SV205: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1920,plain,
! [SV45: $i] :
( ( ( c_Int_OMin
!= ( c_Int_OBit1 @ SV45 ) )
| ( c_Int_OMin = SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1921,plain,
! [SV45: $i] :
( ( ( c_Int_OMin != SV45 )
| ( c_Int_OMin
= ( c_Int_OBit1 @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1922,plain,
! [SV47: $i,SV142: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV47 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV142 ) @ ( c_Nat_OSuc @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1923,plain,
! [SV48: $i,SV143: $i,SV206: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV206 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV206 @ SV143 @ SV48 )
= ( c_Groups_Otimes__class_Otimes @ SV206 @ SV48 @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(1924,plain,
! [SV49: $i,SV144: $i,SV207: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
| ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(1925,plain,
! [SV50: $i,SV145: $i] :
( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1849]) ).
thf(1926,plain,
! [SV145: $i,SV50: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1849]) ).
thf(1927,plain,
! [SV51: $i] :
( ( ( ( c_Int_OBit1 @ SV51 )
!= c_Int_OMin )
| ( SV51 = c_Int_OMin ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1928,plain,
! [SV51: $i] :
( ( ( SV51 != c_Int_OMin )
| ( ( c_Int_OBit1 @ SV51 )
= c_Int_OMin ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1851]) ).
thf(1929,plain,
! [SV208: $i] :
( ( v_na____
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV208 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1930,plain,
! [SV52: $i,SV146: $i] :
( ( ( class_Int_Onumber__ring @ SV146 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV146 @ ( c_Int_Onumber__class_Onumber__of @ SV146 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ SV52 )
= SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1931,plain,
! [SV53: $i,SV147: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ ( c_Nat_OSuc @ SV53 ) )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ SV53 )
| ( SV147
= ( c_Nat_OSuc @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1932,plain,
! [SV54: $i,SV148: $i,SV209: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1933,plain,
! [SV55: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
| ~ ! [SY288: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY288 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1934,plain,
! [SV55: $i] :
( ( ~ ~ ! [SY289: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY289 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1935,plain,
! [SV56: $i,SV149: $i] :
( ( ( ( c_Nat_OSuc @ SV149 )
= ( c_Nat_OSuc @ SV56 ) )
= $false )
| ( ( SV149 = SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1936,plain,
! [SV57: $i,SV150: $i,SV210: $i,SV229: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV229 )
| ( ( c_Groups_Otimes__class_Otimes @ SV229 @ SV210 @ ( c_Groups_Otimes__class_Otimes @ SV229 @ SV150 @ SV57 ) )
= ( c_Groups_Otimes__class_Otimes @ SV229 @ ( c_Groups_Otimes__class_Otimes @ SV229 @ SV210 @ SV150 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(1937,plain,
! [SV58: $i,SV151: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ ( c_Nat_OSuc @ SV58 ) )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ SV58 )
| ( SV151 = SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1938,plain,
! [SV59: $i] :
( ( ( ( c_Int_OBit0 @ SV59 )
!= c_Int_OPls )
| ( SV59 = c_Int_OPls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1939,plain,
! [SV59: $i] :
( ( ( SV59 != c_Int_OPls )
| ( ( c_Int_OBit0 @ SV59 )
= c_Int_OPls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1940,plain,
! [SV60: $i,SV152: $i,SV211: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV211 @ SV152 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV211 @ SV60 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV152 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(1941,plain,
! [SV61: $i,SV153: $i,SV212: $i,SV230: $i] :
( ( ~ ( class_Groups_Oab__semigroup__mult @ SV230 )
| ( ( c_Groups_Otimes__class_Otimes @ SV230 @ ( c_Groups_Otimes__class_Otimes @ SV230 @ SV212 @ SV153 ) @ SV61 )
= ( c_Groups_Otimes__class_Otimes @ SV230 @ SV212 @ ( c_Groups_Otimes__class_Otimes @ SV230 @ SV153 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(1942,plain,
! [SV63: $i,SV154: $i,SV213: $i,SV231: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV231 )
| ( ( c_Groups_Otimes__class_Otimes @ SV231 @ ( c_Groups_Otimes__class_Otimes @ SV231 @ SV213 @ SV154 ) @ SV63 )
= ( c_Groups_Otimes__class_Otimes @ SV231 @ SV213 @ ( c_Groups_Otimes__class_Otimes @ SV231 @ SV154 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(1943,plain,
! [SV65: $i,SV155: $i] :
( ( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1866]) ).
thf(1944,plain,
! [SV65: $i,SV155: $i] :
( ( ~ ( ~ ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1866]) ).
thf(1945,plain,
! [SV66: $i,SV156: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
| ( SV156 = SV66 ) )
| ~ ( ( SV156 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1946,plain,
! [SV67: $i,SV157: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV157 @ SV67 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV157 @ ( c_Nat_OSuc @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1947,plain,
! [SV68: $i,SV158: $i,SV214: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV214 @ SV158 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV158 @ SV68 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV214 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1948,plain,
! [SV69: $i,SV159: $i,SV215: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV159 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV159 @ SV69 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1949,plain,
! [SV70: $i,SV160: $i] :
( ( ~ ( ( ( c_Nat_OSuc @ SV160 )
!= ( c_Nat_OSuc @ SV70 ) )
| ( SV160 = SV70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1950,plain,
! [SV70: $i,SV160: $i] :
( ( ~ ( ( SV160 != SV70 )
| ( ( c_Nat_OSuc @ SV160 )
= ( c_Nat_OSuc @ SV70 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1951,plain,
! [SV71: $i,SV161: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV161 @ SV71 )
= $false )
| ( ( SV161 != SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1952,plain,
! [SV72: $i,SV162: $i] :
( ( ~ ( ( ( c_Int_OBit1 @ SV162 )
!= ( c_Int_OBit1 @ SV72 ) )
| ( SV162 = SV72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1953,plain,
! [SV72: $i,SV162: $i] :
( ( ~ ( ( SV162 != SV72 )
| ( ( c_Int_OBit1 @ SV162 )
= ( c_Int_OBit1 @ SV72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1954,plain,
! [SV74: $i,SV163: $i] :
( ( ( class_Int_Onumber__ring @ SV163 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV163 @ SV74 @ ( c_Int_Onumber__class_Onumber__of @ SV163 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1955,plain,
! [SV75: $i,SV164: $i,SV216: $i,SV232: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV232 )
| ( ( c_Groups_Otimes__class_Otimes @ SV232 @ ( c_Groups_Otimes__class_Otimes @ SV232 @ SV216 @ SV164 ) @ SV75 )
= ( c_Groups_Otimes__class_Otimes @ SV232 @ ( c_Groups_Otimes__class_Otimes @ SV232 @ SV216 @ SV75 ) @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(1956,plain,
! [SV76: $i,SV165: $i,SV217: $i,SV233: $i] :
( ( ! [SY426: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY426 )
| ( ( c_Groups_Otimes__class_Otimes @ SY426 @ ( c_Groups_Otimes__class_Otimes @ SY426 @ SV233 @ SV217 ) @ ( c_Groups_Otimes__class_Otimes @ SY426 @ SV165 @ SV76 ) )
= ( c_Groups_Otimes__class_Otimes @ SY426 @ SV233 @ ( c_Groups_Otimes__class_Otimes @ SY426 @ SV217 @ ( c_Groups_Otimes__class_Otimes @ SY426 @ SV165 @ SV76 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(1957,plain,
! [SV77: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1958,plain,
! [SV77: $i] :
( ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1959,plain,
! [SV78: $i] :
( ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
| ~ ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1879]) ).
thf(1960,plain,
! [SV78: $i] :
( ( ~ ~ ! [SY322: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY322 ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1880]) ).
thf(1961,plain,
! [SV80: $i,SV166: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1962,plain,
! [SV80: $i,SV166: $i] :
( ( ~ ( ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1963,plain,
! [SV81: $i,SV167: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV167 ) @ ( c_Nat_OSuc @ SV81 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV167 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1964,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ( ~ ( class_Int_Onumber @ SV218 ) )
= $true )
| ( ( ~ ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) ) )
| ~ ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(1965,plain,
! [SV83: $i,SV169: $i] :
( ( ( SV169 = SV83 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV169 @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1966,plain,
! [SV84: $i,SV170: $i,SV219: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
| ( SV170 = SV84 ) )
| ~ ( ( SV170 != SV84 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1967,plain,
! [SV85: $i,SV171: $i] :
( ( ( SV171 != SV85 )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV171 @ SV85 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(1968,plain,
! [SV86: $i,SV172: $i,SV220: $i,SV234: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV234 )
| ( ( c_Groups_Otimes__class_Otimes @ SV234 @ SV220 @ ( c_Groups_Otimes__class_Otimes @ SV234 @ SV172 @ SV86 ) )
= ( c_Groups_Otimes__class_Otimes @ SV234 @ SV172 @ ( c_Groups_Otimes__class_Otimes @ SV234 @ SV220 @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(1969,plain,
! [SV88: $i,SV173: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1970,plain,
! [SV88: $i,SV173: $i] :
( ( ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1971,plain,
! [SV90: $i,SV174: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV174 ) @ SV90 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV174 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1972,plain,
! [SV91: $i,SV175: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1973,plain,
! [SV91: $i,SV175: $i] :
( ( ~ ( ~ ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1974,plain,
! [SV92: $i,SV176: $i,SV221: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
| ( SV176 = SV92 ) )
| ~ ( ( SV176 != SV92 )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(1975,plain,
! [SV93: $i,SV177: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1976,plain,
! [SV93: $i,SV177: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1977,plain,
! [SV94: $i,SV178: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV178 @ SV94 )
= $false )
| ( ( ~ ( ( ( c_Nat_OSuc @ SV178 )
!= SV94 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV178 ) @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1978,plain,
! [SV95: $i,SV179: $i,SV222: $i,SV235: $i] :
( ( ! [SY427: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY427 )
| ( ( c_Groups_Otimes__class_Otimes @ SY427 @ ( c_Groups_Otimes__class_Otimes @ SY427 @ SV235 @ SV222 ) @ ( c_Groups_Otimes__class_Otimes @ SY427 @ SV179 @ SV95 ) )
= ( c_Groups_Otimes__class_Otimes @ SY427 @ SV179 @ ( c_Groups_Otimes__class_Otimes @ SY427 @ ( c_Groups_Otimes__class_Otimes @ SY427 @ SV235 @ SV222 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(1979,plain,
! [SV97: $i,SV180: $i] :
( ( ~ ( ( ( c_Int_OBit0 @ SV180 )
!= ( c_Int_OBit0 @ SV97 ) )
| ( SV180 = SV97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(1980,plain,
! [SV97: $i,SV180: $i] :
( ( ~ ( ( SV180 != SV97 )
| ( ( c_Int_OBit0 @ SV180 )
= ( c_Int_OBit0 @ SV97 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(1981,plain,
! [SV98: $i,SV181: $i] :
( ( ~ ( ~ ( ( SV181 != SV98 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1982,plain,
! [SV98: $i,SV181: $i] :
( ( ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
| ( SV181 != SV98 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1983,plain,
! [SV99: $i,SV182: $i,SV223: $i,SV236: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV236 @ SV223 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV182 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV236 @ SV182 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV223 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(1984,plain,
! [SV100: $i,SV183: $i,SV224: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV224 @ SV183 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SV224 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(1985,plain,
! [SV101: $i,SV184: $i] :
( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1986,plain,
! [SV184: $i,SV101: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1987,plain,
! [SV102: $i,SV185: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(1988,plain,
! [SV102: $i,SV185: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(1989,plain,
! [SV103: $i,SV186: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV186 @ SV103 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV186 @ ( c_Nat_OSuc @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1990,plain,
! [SV105: $i,SV188: $i,SV225: $i,SV237: $i] :
( ( ! [SY428: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ SY428 )
| ( ( c_Groups_Otimes__class_Otimes @ SY428 @ ( c_Groups_Otimes__class_Otimes @ SY428 @ SV237 @ SV225 ) @ ( c_Groups_Otimes__class_Otimes @ SY428 @ SV188 @ SV105 ) )
= ( c_Groups_Otimes__class_Otimes @ SY428 @ ( c_Groups_Otimes__class_Otimes @ SY428 @ SV237 @ SV188 ) @ ( c_Groups_Otimes__class_Otimes @ SY428 @ SV225 @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(1991,plain,
! [SV106: $i,SV189: $i,SV226: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
| ( SV226 = SV106 ) )
| ~ ( ( SV226 != SV106 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1992,plain,
! [SV107: $i,SV190: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV190 @ SV107 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV107 @ SV190 )
| ( SV190 = SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1993,plain,
! [SV109: $i,SV191: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(1994,plain,
! [SV109: $i,SV191: $i] :
( ( ~ ( ~ ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(1995,plain,
! [SV112: $i] :
( ( ( c_Int_OPls
!= ( c_Int_OBit0 @ SV112 ) )
| ( c_Int_OPls = SV112 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(1996,plain,
! [SV112: $i] :
( ( ( c_Int_OPls != SV112 )
| ( c_Int_OPls
= ( c_Int_OBit0 @ SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(1997,plain,
! [SV114: $i,SV193: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ SV114 ) )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ ( c_Nat_OSuc @ SV114 ) )
| ( SV114 = SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1998,plain,
! [SV115: $i,SV194: $i] :
( ( ~ ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
| ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1911]) ).
thf(1999,plain,
! [SV115: $i,SV194: $i] :
( ( ~ ( ~ ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1911]) ).
thf(2000,plain,
! [SV116: $i,SV195: $i,SV227: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
| ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ~ ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2001,plain,
! [SV137: $i,SV39: $i] :
( ( ( SV39 = SV137 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV137 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2002,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
| ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2003,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ~ ( ~ ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2004,plain,
! [SV41: $i,SV139: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(2005,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(2006,plain,
! [SV43: $i,SV141: $i,SV205: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(2007,plain,
! [SV205: $i,SV43: $i,SV141: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(2008,plain,
! [SV45: $i] :
( ( ( c_Int_OMin
!= ( c_Int_OBit1 @ SV45 ) )
= $true )
| ( ( c_Int_OMin = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(2009,plain,
! [SV45: $i] :
( ( ( c_Int_OMin != SV45 )
= $true )
| ( ( c_Int_OMin
= ( c_Int_OBit1 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(2010,plain,
! [SV48: $i,SV143: $i,SV206: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV206 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV206 @ SV143 @ SV48 )
= ( c_Groups_Otimes__class_Otimes @ SV206 @ SV48 @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2011,plain,
! [SV49: $i,SV144: $i,SV207: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
| ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2012,plain,
! [SV207: $i,SV49: $i,SV144: $i] :
( ( ~ ( ~ ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2013,plain,
! [SV50: $i,SV145: $i] :
( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(2014,plain,
! [SV145: $i,SV50: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2015,plain,
! [SV51: $i] :
( ( ( ( c_Int_OBit1 @ SV51 )
!= c_Int_OMin )
= $true )
| ( ( SV51 = c_Int_OMin )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2016,plain,
! [SV51: $i] :
( ( ( SV51 != c_Int_OMin )
= $true )
| ( ( ( c_Int_OBit1 @ SV51 )
= c_Int_OMin )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2017,plain,
! [SV53: $i,SV147: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ SV53 ) )
= $true )
| ( ( SV147
= ( c_Nat_OSuc @ SV53 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ ( c_Nat_OSuc @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2018,plain,
! [SV54: $i,SV148: $i,SV209: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(2019,plain,
! [SV209: $i,SV54: $i,SV148: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(2020,plain,
! [SV55: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 ) )
= $true )
| ( ( ~ ! [SY288: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2021,plain,
! [SV55: $i] :
( ( ( ~ ~ ! [SY289: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY289 ) ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2022,plain,
! [SV57: $i,SV150: $i,SV210: $i,SV229: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV229 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV229 @ SV210 @ ( c_Groups_Otimes__class_Otimes @ SV229 @ SV150 @ SV57 ) )
= ( c_Groups_Otimes__class_Otimes @ SV229 @ ( c_Groups_Otimes__class_Otimes @ SV229 @ SV210 @ SV150 ) @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2023,plain,
! [SV58: $i,SV151: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ SV58 ) )
= $true )
| ( ( SV151 = SV58 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ ( c_Nat_OSuc @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2024,plain,
! [SV59: $i] :
( ( ( ( c_Int_OBit0 @ SV59 )
!= c_Int_OPls )
= $true )
| ( ( SV59 = c_Int_OPls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2025,plain,
! [SV59: $i] :
( ( ( SV59 != c_Int_OPls )
= $true )
| ( ( ( c_Int_OBit0 @ SV59 )
= c_Int_OPls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2026,plain,
! [SV60: $i,SV152: $i,SV211: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV211 @ SV152 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV211 @ SV60 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV152 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2027,plain,
! [SV61: $i,SV153: $i,SV212: $i,SV230: $i] :
( ( ( ~ ( class_Groups_Oab__semigroup__mult @ SV230 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV230 @ ( c_Groups_Otimes__class_Otimes @ SV230 @ SV212 @ SV153 ) @ SV61 )
= ( c_Groups_Otimes__class_Otimes @ SV230 @ SV212 @ ( c_Groups_Otimes__class_Otimes @ SV230 @ SV153 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2028,plain,
! [SV63: $i,SV154: $i,SV213: $i,SV231: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV231 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV231 @ ( c_Groups_Otimes__class_Otimes @ SV231 @ SV213 @ SV154 ) @ SV63 )
= ( c_Groups_Otimes__class_Otimes @ SV231 @ SV213 @ ( c_Groups_Otimes__class_Otimes @ SV231 @ SV154 @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2029,plain,
! [SV65: $i,SV155: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(2030,plain,
! [SV65: $i,SV155: $i] :
( ( ~ ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2031,plain,
! [SV66: $i,SV156: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true )
| ( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
| ( SV156 = SV66 ) )
| ~ ( ( SV156 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2032,plain,
! [SV68: $i,SV158: $i,SV214: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV214 @ SV158 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV158 @ SV68 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV214 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2033,plain,
! [SV69: $i,SV159: $i,SV215: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV159 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV159 @ SV69 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2034,plain,
! [SV70: $i,SV160: $i] :
( ( ( ( c_Nat_OSuc @ SV160 )
!= ( c_Nat_OSuc @ SV70 ) )
| ( SV160 = SV70 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2035,plain,
! [SV70: $i,SV160: $i] :
( ( ( SV160 != SV70 )
| ( ( c_Nat_OSuc @ SV160 )
= ( c_Nat_OSuc @ SV70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1950]) ).
thf(2036,plain,
! [SV71: $i,SV161: $i] :
( ( ( SV161 = SV71 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV161 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2037,plain,
! [SV72: $i,SV162: $i] :
( ( ( ( c_Int_OBit1 @ SV162 )
!= ( c_Int_OBit1 @ SV72 ) )
| ( SV162 = SV72 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2038,plain,
! [SV72: $i,SV162: $i] :
( ( ( SV162 != SV72 )
| ( ( c_Int_OBit1 @ SV162 )
= ( c_Int_OBit1 @ SV72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(2039,plain,
! [SV75: $i,SV164: $i,SV216: $i,SV232: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV232 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV232 @ ( c_Groups_Otimes__class_Otimes @ SV232 @ SV216 @ SV164 ) @ SV75 )
= ( c_Groups_Otimes__class_Otimes @ SV232 @ ( c_Groups_Otimes__class_Otimes @ SV232 @ SV216 @ SV75 ) @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2040,plain,
! [SV76: $i,SV165: $i,SV217: $i,SV233: $i,SV238: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV238 )
| ( ( c_Groups_Otimes__class_Otimes @ SV238 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV233 @ SV217 ) @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV165 @ SV76 ) )
= ( c_Groups_Otimes__class_Otimes @ SV238 @ SV233 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV217 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV165 @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2041,plain,
! [SV77: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2042,plain,
! [SV77: $i] :
( ( ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2043,plain,
! [SV78: $i] :
( ( ( ~ ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $true )
| ( ( ~ ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2044,plain,
! [SV78: $i] :
( ( ( ~ ~ ! [SY322: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY322 ) ) ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2045,plain,
! [SV80: $i,SV166: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2046,plain,
! [SV80: $i,SV166: $i] :
( ( ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2047,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ( class_Int_Onumber @ SV218 )
= $false )
| ( ( ~ ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) ) )
| ~ ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2048,plain,
! [SV84: $i,SV170: $i,SV219: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
| ( SV170 = SV84 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2049,plain,
! [SV219: $i,SV84: $i,SV170: $i] :
( ( ~ ( ( SV170 != SV84 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2050,plain,
! [SV85: $i,SV171: $i] :
( ( ( SV171 = SV85 )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV171 @ SV85 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2051,plain,
! [SV86: $i,SV172: $i,SV220: $i,SV234: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV234 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV234 @ SV220 @ ( c_Groups_Otimes__class_Otimes @ SV234 @ SV172 @ SV86 ) )
= ( c_Groups_Otimes__class_Otimes @ SV234 @ SV172 @ ( c_Groups_Otimes__class_Otimes @ SV234 @ SV220 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2052,plain,
! [SV88: $i,SV173: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2053,plain,
! [SV88: $i,SV173: $i] :
( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2054,plain,
! [SV91: $i,SV175: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(2055,plain,
! [SV91: $i,SV175: $i] :
( ( ~ ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2056,plain,
! [SV92: $i,SV176: $i,SV221: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
| ( SV176 = SV92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1974]) ).
thf(2057,plain,
! [SV221: $i,SV92: $i,SV176: $i] :
( ( ~ ( ( SV176 != SV92 )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1974]) ).
thf(2058,plain,
! [SV93: $i,SV177: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2059,plain,
! [SV93: $i,SV177: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2060,plain,
! [SV94: $i,SV178: $i] :
( ( ( ~ ( ( ( c_Nat_OSuc @ SV178 )
!= SV94 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV178 ) @ SV94 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV178 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(2061,plain,
! [SV95: $i,SV179: $i,SV222: $i,SV235: $i,SV239: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV239 )
| ( ( c_Groups_Otimes__class_Otimes @ SV239 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV235 @ SV222 ) @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV179 @ SV95 ) )
= ( c_Groups_Otimes__class_Otimes @ SV239 @ SV179 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV235 @ SV222 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2062,plain,
! [SV97: $i,SV180: $i] :
( ( ( ( c_Int_OBit0 @ SV180 )
!= ( c_Int_OBit0 @ SV97 ) )
| ( SV180 = SV97 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1979]) ).
thf(2063,plain,
! [SV97: $i,SV180: $i] :
( ( ( SV180 != SV97 )
| ( ( c_Int_OBit0 @ SV180 )
= ( c_Int_OBit0 @ SV97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1980]) ).
thf(2064,plain,
! [SV98: $i,SV181: $i] :
( ( ~ ( ( SV181 != SV98 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2065,plain,
! [SV98: $i,SV181: $i] :
( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
| ( SV181 != SV98 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2066,plain,
! [SV99: $i,SV182: $i,SV223: $i,SV236: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV236 @ SV223 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV182 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV236 @ SV182 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV223 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2067,plain,
! [SV100: $i,SV183: $i,SV224: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV224 @ SV183 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SV224 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV100 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2068,plain,
! [SV101: $i,SV184: $i] :
( ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2069,plain,
! [SV184: $i,SV101: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2070,plain,
! [SV102: $i,SV185: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2071,plain,
! [SV102: $i,SV185: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2072,plain,
! [SV105: $i,SV188: $i,SV225: $i,SV237: $i,SV240: $i] :
( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV240 )
| ( ( c_Groups_Otimes__class_Otimes @ SV240 @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV237 @ SV225 ) @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV188 @ SV105 ) )
= ( c_Groups_Otimes__class_Otimes @ SV240 @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV237 @ SV188 ) @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV225 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2073,plain,
! [SV106: $i,SV189: $i,SV226: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
| ( SV226 = SV106 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2074,plain,
! [SV189: $i,SV106: $i,SV226: $i] :
( ( ~ ( ( SV226 != SV106 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2075,plain,
! [SV190: $i,SV107: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV107 @ SV190 ) )
= $true )
| ( ( SV190 = SV107 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV190 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2076,plain,
! [SV109: $i,SV191: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2077,plain,
! [SV109: $i,SV191: $i] :
( ( ~ ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1994]) ).
thf(2078,plain,
! [SV112: $i] :
( ( ( c_Int_OPls
!= ( c_Int_OBit0 @ SV112 ) )
= $true )
| ( ( c_Int_OPls = SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2079,plain,
! [SV112: $i] :
( ( ( c_Int_OPls != SV112 )
= $true )
| ( ( c_Int_OPls
= ( c_Int_OBit0 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2080,plain,
! [SV114: $i,SV193: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ SV114 )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ ( c_Nat_OSuc @ SV114 ) )
| ( SV114 = SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2081,plain,
! [SV115: $i,SV194: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
| ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2082,plain,
! [SV115: $i,SV194: $i] :
( ( ~ ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2083,plain,
! [SV116: $i,SV195: $i,SV227: $i] :
( ( ~ ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
| ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2084,plain,
! [SV195: $i,SV116: $i,SV227: $i] :
( ( ~ ( ~ ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2085,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
| ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2086,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ~ ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2087,plain,
! [SV41: $i,SV139: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2088,plain,
! [SV41: $i,SV139: $i] :
( ( ( ~ ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2089,plain,
! [SV43: $i,SV141: $i,SV205: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2090,plain,
! [SV205: $i,SV43: $i,SV141: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2091,plain,
! [SV45: $i] :
( ( ( c_Int_OMin
= ( c_Int_OBit1 @ SV45 ) )
= $false )
| ( ( c_Int_OMin = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2092,plain,
! [SV45: $i] :
( ( ( c_Int_OMin = SV45 )
= $false )
| ( ( c_Int_OMin
= ( c_Int_OBit1 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2093,plain,
! [SV49: $i,SV144: $i,SV207: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
| ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2094,plain,
! [SV207: $i,SV49: $i,SV144: $i] :
( ( ~ ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2012]) ).
thf(2095,plain,
! [SV50: $i,SV145: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2096,plain,
! [SV145: $i,SV50: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2097,plain,
! [SV51: $i] :
( ( ( ( c_Int_OBit1 @ SV51 )
= c_Int_OMin )
= $false )
| ( ( SV51 = c_Int_OMin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2098,plain,
! [SV51: $i] :
( ( ( SV51 = c_Int_OMin )
= $false )
| ( ( ( c_Int_OBit1 @ SV51 )
= c_Int_OMin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2099,plain,
! [SV53: $i,SV147: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ SV53 ) )
= $false )
| ( ( SV147
= ( c_Nat_OSuc @ SV53 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ ( c_Nat_OSuc @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2100,plain,
! [SV54: $i,SV148: $i,SV209: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2101,plain,
! [SV209: $i,SV54: $i,SV148: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2019]) ).
thf(2102,plain,
! [SV55: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $false )
| ( ( ~ ! [SY288: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY288 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2103,plain,
! [SV55: $i] :
( ( ( ~ ! [SY289: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY289 ) ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2104,plain,
! [SV57: $i,SV150: $i,SV210: $i,SV229: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV229 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV229 @ SV210 @ ( c_Groups_Otimes__class_Otimes @ SV229 @ SV150 @ SV57 ) )
= ( c_Groups_Otimes__class_Otimes @ SV229 @ ( c_Groups_Otimes__class_Otimes @ SV229 @ SV210 @ SV150 ) @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2105,plain,
! [SV58: $i,SV151: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ SV58 ) )
= $false )
| ( ( SV151 = SV58 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ ( c_Nat_OSuc @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2106,plain,
! [SV59: $i] :
( ( ( ( c_Int_OBit0 @ SV59 )
= c_Int_OPls )
= $false )
| ( ( SV59 = c_Int_OPls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2107,plain,
! [SV59: $i] :
( ( ( SV59 = c_Int_OPls )
= $false )
| ( ( ( c_Int_OBit0 @ SV59 )
= c_Int_OPls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2108,plain,
! [SV61: $i,SV153: $i,SV212: $i,SV230: $i] :
( ( ( class_Groups_Oab__semigroup__mult @ SV230 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV230 @ ( c_Groups_Otimes__class_Otimes @ SV230 @ SV212 @ SV153 ) @ SV61 )
= ( c_Groups_Otimes__class_Otimes @ SV230 @ SV212 @ ( c_Groups_Otimes__class_Otimes @ SV230 @ SV153 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2109,plain,
! [SV63: $i,SV154: $i,SV213: $i,SV231: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV231 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV231 @ ( c_Groups_Otimes__class_Otimes @ SV231 @ SV213 @ SV154 ) @ SV63 )
= ( c_Groups_Otimes__class_Otimes @ SV231 @ SV213 @ ( c_Groups_Otimes__class_Otimes @ SV231 @ SV154 @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2110,plain,
! [SV65: $i,SV155: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) ) )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2111,plain,
! [SV65: $i,SV155: $i] :
( ( ( ~ ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2112,plain,
! [SV66: $i,SV156: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
| ( SV156 = SV66 ) )
| ~ ( ( SV156 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2113,plain,
! [SV214: $i,SV68: $i,SV158: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV158 @ SV68 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV214 ) @ SV68 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV214 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2114,plain,
! [SV215: $i,SV69: $i,SV159: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV159 @ SV69 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV69 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2115,plain,
! [SV70: $i,SV160: $i] :
( ( ( ( c_Nat_OSuc @ SV160 )
!= ( c_Nat_OSuc @ SV70 ) )
= $true )
| ( ( SV160 = SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2116,plain,
! [SV70: $i,SV160: $i] :
( ( ( SV160 != SV70 )
= $true )
| ( ( ( c_Nat_OSuc @ SV160 )
= ( c_Nat_OSuc @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2117,plain,
! [SV72: $i,SV162: $i] :
( ( ( ( c_Int_OBit1 @ SV162 )
!= ( c_Int_OBit1 @ SV72 ) )
= $true )
| ( ( SV162 = SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2118,plain,
! [SV72: $i,SV162: $i] :
( ( ( SV162 != SV72 )
= $true )
| ( ( ( c_Int_OBit1 @ SV162 )
= ( c_Int_OBit1 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2119,plain,
! [SV75: $i,SV164: $i,SV216: $i,SV232: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV232 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV232 @ ( c_Groups_Otimes__class_Otimes @ SV232 @ SV216 @ SV164 ) @ SV75 )
= ( c_Groups_Otimes__class_Otimes @ SV232 @ ( c_Groups_Otimes__class_Otimes @ SV232 @ SV216 @ SV75 ) @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2120,plain,
! [SV76: $i,SV165: $i,SV217: $i,SV233: $i,SV238: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV238 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV238 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV233 @ SV217 ) @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV165 @ SV76 ) )
= ( c_Groups_Otimes__class_Otimes @ SV238 @ SV233 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV217 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV165 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2121,plain,
! [SV77: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2122,plain,
! [SV77: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2123,plain,
! [SV78: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $false )
| ( ( ~ ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2124,plain,
! [SV78: $i] :
( ( ( ~ ! [SY322: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY322 ) ) ) )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2125,plain,
! [SV80: $i,SV166: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2126,plain,
! [SV80: $i,SV166: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2127,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) ) )
| ~ ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 ) ) )
= $false )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2128,plain,
! [SV84: $i,SV170: $i,SV219: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
| ( SV170 = SV84 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2129,plain,
! [SV219: $i,SV84: $i,SV170: $i] :
( ( ( SV170 != SV84 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2130,plain,
! [SV85: $i,SV171: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV171 @ SV85 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SV171 )
= $true )
| ( ( SV171 = SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2131,plain,
! [SV86: $i,SV172: $i,SV220: $i,SV234: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV234 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV234 @ SV220 @ ( c_Groups_Otimes__class_Otimes @ SV234 @ SV172 @ SV86 ) )
= ( c_Groups_Otimes__class_Otimes @ SV234 @ SV172 @ ( c_Groups_Otimes__class_Otimes @ SV234 @ SV220 @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2132,plain,
! [SV88: $i,SV173: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2133,plain,
! [SV88: $i,SV173: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2134,plain,
! [SV91: $i,SV175: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true )
| ( ( ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2135,plain,
! [SV91: $i,SV175: $i] :
( ( ( ~ ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2136,plain,
! [SV92: $i,SV176: $i,SV221: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
| ( SV176 = SV92 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2137,plain,
! [SV221: $i,SV92: $i,SV176: $i] :
( ( ( SV176 != SV92 )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2138,plain,
! [SV93: $i,SV177: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2139,plain,
! [SV93: $i,SV177: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2140,plain,
! [SV94: $i,SV178: $i] :
( ( ( ( c_Nat_OSuc @ SV178 )
!= SV94 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV178 ) @ SV94 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV178 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2141,plain,
! [SV95: $i,SV179: $i,SV222: $i,SV235: $i,SV239: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV239 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV239 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV235 @ SV222 ) @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV179 @ SV95 ) )
= ( c_Groups_Otimes__class_Otimes @ SV239 @ SV179 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV235 @ SV222 ) @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2142,plain,
! [SV97: $i,SV180: $i] :
( ( ( ( c_Int_OBit0 @ SV180 )
!= ( c_Int_OBit0 @ SV97 ) )
= $true )
| ( ( SV180 = SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2143,plain,
! [SV97: $i,SV180: $i] :
( ( ( SV180 != SV97 )
= $true )
| ( ( ( c_Int_OBit0 @ SV180 )
= ( c_Int_OBit0 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2144,plain,
! [SV98: $i,SV181: $i] :
( ( ( ~ ( ( SV181 != SV98 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2145,plain,
! [SV98: $i,SV181: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) ) )
= $true )
| ( ( SV181 != SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2146,plain,
! [SV99: $i,SV182: $i,SV223: $i,SV236: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV236 @ SV223 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV182 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV236 @ SV182 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV223 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2147,plain,
! [SV101: $i,SV184: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2068]) ).
thf(2148,plain,
! [SV184: $i,SV101: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2069]) ).
thf(2149,plain,
! [SV102: $i,SV185: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2150,plain,
! [SV102: $i,SV185: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2151,plain,
! [SV105: $i,SV188: $i,SV225: $i,SV237: $i,SV240: $i] :
( ( ( ~ ( class_Rings_Ocomm__semiring__1 @ SV240 ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV240 @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV237 @ SV225 ) @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV188 @ SV105 ) )
= ( c_Groups_Otimes__class_Otimes @ SV240 @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV237 @ SV188 ) @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV225 @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2072]) ).
thf(2152,plain,
! [SV106: $i,SV189: $i,SV226: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
| ( SV226 = SV106 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2153,plain,
! [SV189: $i,SV106: $i,SV226: $i] :
( ( ( SV226 != SV106 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2154,plain,
! [SV190: $i,SV107: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV107 @ SV190 )
= $false )
| ( ( SV190 = SV107 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV190 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2155,plain,
! [SV109: $i,SV191: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2156,plain,
! [SV109: $i,SV191: $i] :
( ( ( ~ ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2157,plain,
! [SV112: $i] :
( ( ( c_Int_OPls
= ( c_Int_OBit0 @ SV112 ) )
= $false )
| ( ( c_Int_OPls = SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2158,plain,
! [SV112: $i] :
( ( ( c_Int_OPls = SV112 )
= $false )
| ( ( c_Int_OPls
= ( c_Int_OBit0 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2159,plain,
! [SV114: $i,SV193: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ ( c_Nat_OSuc @ SV114 ) ) )
= $true )
| ( ( SV114 = SV193 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2160,plain,
! [SV115: $i,SV194: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $true )
| ( ( ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2161,plain,
! [SV115: $i,SV194: $i] :
( ( ( ~ ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2162,plain,
! [SV116: $i,SV195: $i,SV227: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
| ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2163,plain,
! [SV195: $i,SV116: $i,SV227: $i] :
( ( ~ ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2164,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
= $true )
| ( ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2165,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ( ~ ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2166,plain,
! [SV41: $i,SV139: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2167,plain,
! [SV41: $i,SV139: $i] :
( ( ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2168,plain,
! [SV43: $i,SV141: $i,SV205: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2169,plain,
! [SV205: $i,SV43: $i,SV141: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2170,plain,
! [SV49: $i,SV144: $i,SV207: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
= $true )
| ( ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2171,plain,
! [SV207: $i,SV49: $i,SV144: $i] :
( ( ( ~ ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2172,plain,
! [SV50: $i,SV145: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2173,plain,
! [SV145: $i,SV50: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2174,plain,
! [SV53: $i,SV147: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ SV53 )
= $true )
| ( ( SV147
= ( c_Nat_OSuc @ SV53 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV147 @ ( c_Nat_OSuc @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2099]) ).
thf(2175,plain,
! [SV54: $i,SV148: $i,SV209: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2176,plain,
! [SV209: $i,SV54: $i,SV148: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2177,plain,
! [SV55: $i] :
( ( ( ! [SY288: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY288 ) ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2178,plain,
! [SV55: $i] :
( ( ( ! [SY289: $i] :
( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY289 ) ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2103]) ).
thf(2179,plain,
! [SV58: $i,SV151: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ SV58 )
= $true )
| ( ( SV151 = SV58 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV151 @ ( c_Nat_OSuc @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2180,plain,
! [SV65: $i,SV155: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
= $false )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2181,plain,
! [SV65: $i,SV155: $i] :
( ( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
| ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2182,plain,
! [SV66: $i,SV156: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
| ( SV156 = SV66 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2183,plain,
! [SV66: $i,SV156: $i] :
( ( ( ~ ( ( SV156 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2184,plain,
! [SV214: $i,SV68: $i,SV158: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV158 @ SV68 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV214 ) @ SV68 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV214 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2185,plain,
! [SV215: $i,SV69: $i,SV159: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV159 @ SV69 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV69 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV215 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2186,plain,
! [SV70: $i,SV160: $i] :
( ( ( ( c_Nat_OSuc @ SV160 )
= ( c_Nat_OSuc @ SV70 ) )
= $false )
| ( ( SV160 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2187,plain,
! [SV70: $i,SV160: $i] :
( ( ( SV160 = SV70 )
= $false )
| ( ( ( c_Nat_OSuc @ SV160 )
= ( c_Nat_OSuc @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2188,plain,
! [SV72: $i,SV162: $i] :
( ( ( ( c_Int_OBit1 @ SV162 )
= ( c_Int_OBit1 @ SV72 ) )
= $false )
| ( ( SV162 = SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2189,plain,
! [SV72: $i,SV162: $i] :
( ( ( SV162 = SV72 )
= $false )
| ( ( ( c_Int_OBit1 @ SV162 )
= ( c_Int_OBit1 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2190,plain,
! [SV76: $i,SV165: $i,SV217: $i,SV233: $i,SV238: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV238 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV238 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV233 @ SV217 ) @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV165 @ SV76 ) )
= ( c_Groups_Otimes__class_Otimes @ SV238 @ SV233 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV217 @ ( c_Groups_Otimes__class_Otimes @ SV238 @ SV165 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2191,plain,
! [SV77: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2192,plain,
! [SV77: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV77 )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2193,plain,
! [SV78: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
= $true )
| ( ( ~ ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2123]) ).
thf(2194,plain,
! [SV78: $i] :
( ( ( ! [SY322: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY322 ) ) ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2195,plain,
! [SV80: $i,SV166: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2196,plain,
! [SV80: $i,SV166: $i] :
( ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
| ( SV166
= ( c_Nat_OSuc @ SV80 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2197,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ( ~ ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) ) ) )
= $false )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2198,plain,
! [SV168: $i,SV218: $i,SV82: $i] :
( ( ( ~ ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 ) ) )
= $false )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2199,plain,
! [SV84: $i,SV170: $i,SV219: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
= $true )
| ( ( SV170 = SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2200,plain,
! [SV219: $i,SV84: $i,SV170: $i] :
( ( ( SV170 != SV84 )
= $true )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2201,plain,
! [SV85: $i,SV171: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV171 @ SV85 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SV171 )
= $true )
| ( ( SV171 = SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2202,plain,
! [SV88: $i,SV173: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2203,plain,
! [SV88: $i,SV173: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
| ( SV173 = SV88 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2204,plain,
! [SV91: $i,SV175: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2205,plain,
! [SV91: $i,SV175: $i] :
( ( ( ~ ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2206,plain,
! [SV92: $i,SV176: $i,SV221: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
= $true )
| ( ( SV176 = SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2207,plain,
! [SV221: $i,SV92: $i,SV176: $i] :
( ( ( SV176 != SV92 )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2208,plain,
! [SV93: $i,SV177: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2209,plain,
! [SV93: $i,SV177: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV177 @ SV93 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV177 ) @ ( c_Nat_OSuc @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2210,plain,
! [SV94: $i,SV178: $i] :
( ( ( ( c_Nat_OSuc @ SV178 )
= SV94 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV178 ) @ SV94 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV178 @ SV94 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2211,plain,
! [SV95: $i,SV179: $i,SV222: $i,SV235: $i,SV239: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV239 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV239 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV235 @ SV222 ) @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV179 @ SV95 ) )
= ( c_Groups_Otimes__class_Otimes @ SV239 @ SV179 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ ( c_Groups_Otimes__class_Otimes @ SV239 @ SV235 @ SV222 ) @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2212,plain,
! [SV97: $i,SV180: $i] :
( ( ( ( c_Int_OBit0 @ SV180 )
= ( c_Int_OBit0 @ SV97 ) )
= $false )
| ( ( SV180 = SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2213,plain,
! [SV97: $i,SV180: $i] :
( ( ( SV180 = SV97 )
= $false )
| ( ( ( c_Int_OBit0 @ SV180 )
= ( c_Int_OBit0 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2214,plain,
! [SV98: $i,SV181: $i] :
( ( ( SV181 != SV98 )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2215,plain,
! [SV98: $i,SV181: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
= $false )
| ( ( SV181 != SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2216,plain,
! [SV223: $i,SV236: $i,SV99: $i,SV182: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV182 @ SV99 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV236 @ SV182 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV223 @ SV99 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV236 @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2217,plain,
! [SV101: $i,SV184: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2218,plain,
! [SV184: $i,SV101: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2219,plain,
! [SV102: $i,SV185: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2220,plain,
! [SV102: $i,SV185: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV185 @ SV102 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV185 ) @ ( c_Nat_OSuc @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2221,plain,
! [SV105: $i,SV188: $i,SV225: $i,SV237: $i,SV240: $i] :
( ( ( class_Rings_Ocomm__semiring__1 @ SV240 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ SV240 @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV237 @ SV225 ) @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV188 @ SV105 ) )
= ( c_Groups_Otimes__class_Otimes @ SV240 @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV237 @ SV188 ) @ ( c_Groups_Otimes__class_Otimes @ SV240 @ SV225 @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2222,plain,
! [SV106: $i,SV189: $i,SV226: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
= $true )
| ( ( SV226 = SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2223,plain,
! [SV189: $i,SV106: $i,SV226: $i] :
( ( ( SV226 != SV106 )
= $true )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2224,plain,
! [SV109: $i,SV191: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2225,plain,
! [SV109: $i,SV191: $i] :
( ( ( ~ ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2226,plain,
! [SV114: $i,SV193: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ ( c_Nat_OSuc @ SV114 ) )
= $false )
| ( ( SV114 = SV193 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV193 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2227,plain,
! [SV115: $i,SV194: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $false )
| ( ( ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2228,plain,
! [SV115: $i,SV194: $i] :
( ( ( ~ ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
= $false )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2229,plain,
! [SV116: $i,SV195: $i,SV227: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
= $true )
| ( ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2230,plain,
! [SV195: $i,SV116: $i,SV227: $i] :
( ( ( ~ ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2231,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
= $false )
| ( ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2232,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( SV138 = SV40 ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2233,plain,
! [SV41: $i,SV139: $i] :
( ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2234,plain,
! [SV41: $i,SV139: $i] :
( ( ( SV139
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2167]) ).
thf(2235,plain,
! [SV139: $i,SV41: $i] :
( ( ( SV41
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV139 @ SV41 )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2167]) ).
thf(2236,plain,
! [SV43: $i,SV141: $i,SV205: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2237,plain,
! [SV205: $i,SV43: $i,SV141: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV141 @ SV43 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV141 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV205 ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2238,plain,
! [SV49: $i,SV144: $i,SV207: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
= $false )
| ( ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2239,plain,
! [SV207: $i,SV49: $i,SV144: $i] :
( ( ( ( SV144 = SV49 )
| ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2240,plain,
! [SV50: $i,SV145: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2172]) ).
thf(2241,plain,
! [SV50: $i,SV145: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV145 @ SV50 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV50 @ ( c_Nat_OSuc @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2242,plain,
! [SV54: $i,SV148: $i,SV209: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2243,plain,
! [SV209: $i,SV54: $i,SV148: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV148 @ SV54 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV148 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV209 ) @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2244,plain,
! [SV55: $i] :
( ( ( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( sK1_SY288 @ SV55 ) ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2177]) ).
thf(2245,plain,
! [SV241: $i,SV55: $i] :
( ( ( SV55
!= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV241 ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2246,plain,
! [SV65: $i,SV155: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2247,plain,
! [SV65: $i,SV155: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV155 )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2248,plain,
! [SV155: $i,SV65: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV65 )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV155 @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2249,plain,
! [SV66: $i,SV156: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
| ( SV156 = SV66 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2182]) ).
thf(2250,plain,
! [SV66: $i,SV156: $i] :
( ( ( ( SV156 != SV66 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2251,plain,
! [SV78: $i] :
( ( ( ! [SY321: $i] :
( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SY321 ) ) ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2252,plain,
! [SV242: $i,SV78: $i] :
( ( ( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV242 ) ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2253,plain,
! [SV80: $i,SV166: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
= $true )
| ( ( SV166
= ( c_Nat_OSuc @ SV80 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2195]) ).
thf(2254,plain,
! [SV80: $i,SV166: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ SV80 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2255,plain,
! [SV80: $i,SV166: $i] :
( ( ( SV166
= ( c_Nat_OSuc @ SV80 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV166 @ ( c_Nat_OSuc @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2256,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
!= SV82 )
| ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) ) )
= $true )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2257,plain,
! [SV168: $i,SV218: $i,SV82: $i] :
( ( ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
| ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 ) )
= $true )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2258,plain,
! [SV84: $i,SV170: $i,SV219: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
= $false )
| ( ( SV170 = SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2259,plain,
! [SV219: $i,SV84: $i,SV170: $i] :
( ( ( SV170 = SV84 )
= $false )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV170 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV219 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2260,plain,
! [SV85: $i,SV171: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV171 @ SV85 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV85 @ SV171 )
= $true )
| ( ( SV171 = SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2261,plain,
! [SV88: $i,SV173: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
= $true )
| ( ( SV173 = SV88 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2262,plain,
! [SV88: $i,SV173: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ SV88 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2203]) ).
thf(2263,plain,
! [SV88: $i,SV173: $i] :
( ( ( SV173 = SV88 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV173 @ ( c_Nat_OSuc @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2203]) ).
thf(2264,plain,
! [SV91: $i,SV175: $i] :
( ( ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2265,plain,
! [SV91: $i,SV175: $i] :
( ( ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2266,plain,
! [SV92: $i,SV176: $i,SV221: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
= $false )
| ( ( SV176 = SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2267,plain,
! [SV221: $i,SV92: $i,SV176: $i] :
( ( ( SV176 = SV92 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV176 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV221 ) @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2268,plain,
! [SV98: $i,SV181: $i] :
( ( ( SV181 = SV98 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2214]) ).
thf(2269,plain,
! [SV98: $i,SV181: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
= $false )
| ( ( SV181 != SV98 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2270,plain,
! [SV181: $i,SV98: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 )
= $false )
| ( ( SV181 != SV98 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2271,plain,
! [SV223: $i,SV236: $i,SV99: $i,SV182: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV182 @ SV99 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV236 @ SV182 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV223 @ SV99 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV236 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2272,plain,
! [SV101: $i,SV184: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2273,plain,
! [SV101: $i,SV184: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV184 @ SV101 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV101 ) @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2274,plain,
! [SV106: $i,SV189: $i,SV226: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
= $false )
| ( ( SV226 = SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2275,plain,
! [SV189: $i,SV106: $i,SV226: $i] :
( ( ( SV226 = SV106 )
= $false )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV226 @ SV189 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV106 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2276,plain,
! [SV109: $i,SV191: $i] :
( ( ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2277,plain,
! [SV109: $i,SV191: $i] :
( ( ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2278,plain,
! [SV115: $i,SV194: $i] :
( ( ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2279,plain,
! [SV115: $i,SV194: $i] :
( ( ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= $true )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2280,plain,
! [SV116: $i,SV195: $i,SV227: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
= $false )
| ( ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2281,plain,
! [SV195: $i,SV116: $i,SV227: $i] :
( ( ( ( SV227 = SV116 )
| ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2282,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( SV138 = SV40 )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2283,plain,
! [SV40: $i,SV138: $i,SV204: $i] :
( ( ( SV204
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2284,plain,
! [SV204: $i,SV40: $i,SV138: $i] :
( ( ( SV138 = SV40 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV138 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV204 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2285,plain,
! [SV207: $i,SV49: $i,SV144: $i] :
( ( ( SV144 = SV49 )
= $true )
| ( ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2286,plain,
! [SV207: $i,SV49: $i,SV144: $i] :
( ( ( SV144 = SV49 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2287,plain,
! [SV49: $i,SV144: $i,SV207: $i] :
( ( ( SV207
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV144 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV207 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2288,plain,
! [SV55: $i] :
( ( ( SV55
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( sK1_SY288 @ SV55 ) ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2289,plain,
! [SV241: $i,SV55: $i] :
( ( ( SV55
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV241 ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2290,plain,
! [SV66: $i,SV156: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) ) )
= $true )
| ( ( SV156 = SV66 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2291,plain,
! [SV66: $i,SV156: $i] :
( ( ( SV156 != SV66 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2292,plain,
! [SV78: $i] :
( ( ( SV78
!= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( sK2_SY321 @ SV78 ) ) ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2251]) ).
thf(2293,plain,
! [SV242: $i,SV78: $i] :
( ( ( SV78
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV242 ) ) )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2294,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
!= SV82 )
= $true )
| ( ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
= $true )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2295,plain,
! [SV168: $i,SV218: $i,SV82: $i] :
( ( ( SV82
!= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
= $true )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 )
= $true )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2296,plain,
! [SV91: $i,SV175: $i] :
( ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2297,plain,
! [SV175: $i,SV91: $i] :
( ( ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2298,plain,
! [SV91: $i,SV175: $i] :
( ( ( SV175
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true )
| ( ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2299,plain,
! [SV98: $i,SV181: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 )
= $true )
| ( ( SV181 = SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2300,plain,
! [SV98: $i,SV181: $i] :
( ( ( SV181 = SV98 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2301,plain,
! [SV98: $i,SV181: $i] :
( ( ( SV181 = SV98 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV98 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2302,plain,
! [SV109: $i,SV191: $i] :
( ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2303,plain,
! [SV191: $i,SV109: $i] :
( ( ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2304,plain,
! [SV109: $i,SV191: $i] :
( ( ( SV191
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2305,plain,
! [SV115: $i,SV194: $i] :
( ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2278]) ).
thf(2306,plain,
! [SV194: $i,SV115: $i] :
( ( ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2278]) ).
thf(2307,plain,
! [SV115: $i,SV194: $i] :
( ( ( SV194
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2308,plain,
! [SV195: $i,SV116: $i,SV227: $i] :
( ( ( SV227 = SV116 )
= $true )
| ( ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2309,plain,
! [SV195: $i,SV116: $i,SV227: $i] :
( ( ( SV227 = SV116 )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2310,plain,
! [SV116: $i,SV227: $i,SV195: $i] :
( ( ( SV195
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV227 @ SV195 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV116 @ SV195 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2311,plain,
! [SV66: $i,SV156: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
= $false )
| ( ( SV156 = SV66 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2312,plain,
! [SV66: $i,SV156: $i] :
( ( ( SV156 = SV66 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ ( c_Nat_OSuc @ SV66 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2313,plain,
! [SV78: $i] :
( ( ( SV78
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( sK2_SY321 @ SV78 ) ) ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2314,plain,
! [SV242: $i,SV78: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ tc_Nat_Onat @ SV78 )
= $false )
| ( ( SV78
= ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ SV242 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2315,plain,
! [SV82: $i,SV168: $i,SV218: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 )
= $false )
| ( ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
= $true )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2316,plain,
! [SV168: $i,SV218: $i,SV82: $i] :
( ( ( SV82
= ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 ) )
= $false )
| ( ( ( c_Int_Onumber__class_Onumber__of @ SV218 @ SV168 )
= SV82 )
= $true )
| ( ( class_Int_Onumber @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2317,plain,
! [SV91: $i,SV175: $i] :
( ( ( SV175
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2296]) ).
thf(2318,plain,
! [SV175: $i,SV91: $i] :
( ( ( SV91
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2319,plain,
! [SV91: $i,SV175: $i] :
( ( ( SV175
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( SV91
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2320,plain,
! [SV109: $i,SV191: $i] :
( ( ( SV191
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2302]) ).
thf(2321,plain,
! [SV191: $i,SV109: $i] :
( ( ( SV109
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2303]) ).
thf(2322,plain,
! [SV109: $i,SV191: $i] :
( ( ( SV191
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( SV109
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2323,plain,
! [SV115: $i,SV194: $i] :
( ( ( SV194
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2305]) ).
thf(2324,plain,
! [SV194: $i,SV115: $i] :
( ( ( SV115
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2306]) ).
thf(2325,plain,
! [SV115: $i,SV194: $i] :
( ( ( SV194
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( SV115
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2326,plain,
! [SV175: $i,SV91: $i] :
( ( ( SV91
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( SV175
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV175 @ SV91 )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2327,plain,
! [SV191: $i,SV109: $i] :
( ( ( SV109
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( SV191
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV191 @ SV109 )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2328,plain,
! [SV194: $i,SV115: $i] :
( ( ( SV115
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( SV194
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= $false )
| ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ SV194 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2329,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1362,2328,2327,2326,2324,2323,2321,2320,2318,2317,2316,2315,2314,2313,2312,2311,2310,2309,2308,2301,2300,2299,2289,2288,2287,2286,2285,2284,2283,2282,2275,2274,2273,2272,2271,2267,2266,2263,2262,2261,2260,2259,2258,2255,2254,2253,2248,2247,2246,2243,2242,2241,2240,2237,2236,2235,2234,2233,2226,2221,2220,2219,2213,2212,2211,2210,2209,2208,2192,2191,2190,2189,2188,2187,2186,2185,2184,2179,2174,2158,2157,2154,2131,2119,2109,2108,2107,2106,2104,2098,2097,2092,2091,2067,2036,2026,2010,2001,1989,1971,1965,1963,1954,1946,1935,1930,1929,1922,1918,1913,1907,1902,1838,1837,1836,1835,1834,1833,1831,1830,1826,1824,1821,1809,1802,1800,1792,1786,1777,1775,1758,1756,1749,1748,1744,1743,1742,1741,1737,1736,1735,1734,1732,1731,1730,1728,1676,1673,1646,1645,1644,1636,1634,1633,1632,1631,1630,1627,1626,1618,1617,1611,1610,1608,1607,1523,1522,1521,1520,1519,1518,1517,1516,1515,1514,1513,1512,1511,1510,1509,1508,1507,1506,1505,1504,1503,1502,1501,1500,1499,1498,1497,1496,1495,1494,1493,1492,1491,1490,1489,1488,1487,1486,1485,1417,1397,1396,1386,1385,1383,1382]) ).
thf(2330,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 16:56:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.62/3.84 .......
% 21.62/3.84
% 21.62/3.84 No.of.Axioms: 167
% 21.62/3.84
% 21.62/3.84 Length.of.Defs: 0
% 21.62/3.84
% 21.62/3.84 Contains.Choice.Funs: false
% 21.62/3.84 ...............................................
% 21.62/3.84
% 21.62/3.84 ********************************
% 21.62/3.84 * All subproblems solved! *
% 21.62/3.84 ********************************
% 21.62/3.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:167,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2329,loop_count:0,foatp_calls:1,translation:fof_full)
% 21.62/3.84
% 21.62/3.84 %**** Beginning of derivation protocol ****
% 21.62/3.84 % SZS output start CNFRefutation
% See solution above
% 21.62/3.86
% 21.62/3.86 %**** End of derivation protocol ****
% 21.62/3.86 %**** no. of clauses in derivation: 1312 ****
% 21.62/3.86 %**** clause counter: 2329 ****
% 21.62/3.86
% 21.62/3.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:167,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2329,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------