%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW209+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 17.44s 3.19s
% Output : CNFRefutation 17.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 128
% Syntax : Number of formulae : 1166 ( 714 unt; 0 typ; 0 def)
% Number of atoms : 6433 (2534 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 14215 (1693 ~;1624 |; 0 &;10539 @)
% ( 42 <=>; 317 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 116 ( 113 usr; 12 con; 0-5 aty)
% Number of variables : 3416 ( 0 ^;3416 !; 0 ?;3416 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Oswap,type,
c_Fun_Oswap: $i > $i > $i > $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 ).
thf(tp_c_Groups_Ouminus__class_Ouminus,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(tp_c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tp_c_Int_Onat,type,
c_Int_Onat: $i ).
thf(tp_c_Int_Onat__aux,type,
c_Int_Onat__aux: $i > $i > $i ).
thf(tp_c_Int_Oring__1__class_Oof__int,type,
c_Int_Oring__1__class_Oof__int: $i > $i > $i ).
thf(tp_c_Nat_OSuc,type,
c_Nat_OSuc: $i > $i ).
thf(tp_c_Nat_Ocompow,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(tp_c_Nat_Ofunpow,type,
c_Nat_Ofunpow: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat__aux,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(tp_c_Nat__Transfer_Otransfer__morphism,type,
c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).
thf(tp_c_Nat__Transfer_Otsub,type,
c_Nat__Transfer_Otsub: $i > $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 ).
thf(tp_c_Orderings_Oorder__class_Ostrict__mono,type,
c_Orderings_Oorder__class_Ostrict__mono: $i > $i > $i > $o ).
thf(tp_c_Power_Opower_Opower,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(tp_c_RComplete_Onatceiling,type,
c_RComplete_Onatceiling: $i > $i ).
thf(tp_c_RComplete_Onatfloor,type,
c_RComplete_Onatfloor: $i > $i ).
thf(tp_c_RealDef_Oreal,type,
c_RealDef_Oreal: $i > $i ).
thf(tp_c_Record_Oiso__tuple__update__accessor__cong__assist,type,
c_Record_Oiso__tuple__update__accessor__cong__assist: $i > $i > $i > $i > $o ).
thf(tp_c_SEQ_OCauchy,type,
c_SEQ_OCauchy: $i > $i > $o ).
thf(tp_c_SEQ_Oconvergent,type,
c_SEQ_Oconvergent: $i > $i > $o ).
thf(tp_c_SEQ_Odecseq,type,
c_SEQ_Odecseq: $i > $i > $o ).
thf(tp_c_SEQ_Oincseq,type,
c_SEQ_Oincseq: $i > $i > $o ).
thf(tp_c_SEQ_Osubseq,type,
c_SEQ_Osubseq: $i > $o ).
thf(tp_c_SMT_Oz3div,type,
c_SMT_Oz3div: $i > $i > $i ).
thf(tp_c_Transcendental_Oln,type,
c_Transcendental_Oln: $i > $i ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $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_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Ominus,type,
class_Groups_Ominus: $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,type,
class_Groups_Oordered__ab__group__add: $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_Ouminus,type,
class_Groups_Ouminus: $i > $o ).
thf(tp_class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
thf(tp_class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
thf(tp_class_Lattices_Oab__semigroup__idem__mult,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__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_Ometric__space,type,
class_RealVector_Ometric__space: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(tp_class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $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_Oidom,type,
class_Rings_Oidom: $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__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(tp_class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
thf(tp_class_Rings_Oring__1,type,
class_Rings_Oring__1: $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_SEQ_Ocomplete__space,type,
class_SEQ_Ocomplete__space: $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_B_m,type,
sK1_B_m: $i ).
thf(tp_sK2_SY273,type,
sK2_SY273: $i ).
thf(tp_sK3_SY509,type,
sK3_SY509: $i > $i > $i ).
thf(tp_sK4_SY520,type,
sK4_SY520: $i > $i > $i ).
thf(tp_sK5_SY347,type,
sK5_SY347: $i > $i ).
thf(tp_sK6_SY688,type,
sK6_SY688: $i > $i ).
thf(tp_sK7_SY480,type,
sK7_SY480: $i > $i > $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_f____,type,
v_f____: $i ).
thf(tp_v_ga____,type,
v_ga____: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(65,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(66,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(67,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(68,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(69,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(70,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(71,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(72,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(73,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(74,axiom,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(75,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(76,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(77,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(78,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(79,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(80,axiom,
class_Nat_Osemiring__char__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
thf(81,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(82,axiom,
class_Divides_Osemiring__div @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(83,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(84,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(85,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(86,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(87,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(88,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(89,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(90,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(91,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(92,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(93,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(94,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(95,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(96,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(97,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(98,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(99,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(100,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(101,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(102,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(308,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_k ) @ V_j ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(325,axiom,
! [V_l: $i,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 @ V_l )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_l @ V_n ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_l @ V_m ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(326,axiom,
! [V_n: $i,V_k: $i,V_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_j @ V_n ) @ V_k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(492,axiom,
! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ V_n_2 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
thf(858,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(859,axiom,
! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_k @ V_l )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_l )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k @ V_n ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(860,axiom,
! [V_l: $i,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_k @ V_l )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_l ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(861,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 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(862,axiom,
! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_z )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(863,axiom,
! [V_z: $i,V_y: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(864,axiom,
! [V_m: $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_i @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_j ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(865,axiom,
! [V_m: $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_i @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_m ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(866,axiom,
! [V_n_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( 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_n_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(867,axiom,
! [V_i: $i,V_j: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_i ) @ V_i ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(868,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_i ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(884,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(885,axiom,
! [V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_n ) @ V_m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(886,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(889,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(890,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_n ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(892,axiom,
! [V_n_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_n_2 ) )
<=> ( V_m_2 = V_n_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(893,axiom,
! [V_n_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_n_2 @ V_k_2 ) )
<=> ( V_m_2 = V_n_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(1054,axiom,
! [V_n: $i] :
( ( V_n
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(1055,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_n
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1056,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(1057,axiom,
! [V_n_2: $i] :
( ( V_n_2
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(1058,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(1067,axiom,
! [V_y: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ V_x @ V_y )
| ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ V_y @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(1069,axiom,
! [V_xa_2: $i,V_n_2: $i,T_a: $i,V_fa_2: $i] :
( ( hAPP @ V_fa_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_fa_2 ) @ V_xa_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_fa_2 ) @ ( hAPP @ V_fa_2 @ V_xa_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(1072,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1073,axiom,
! [V_k: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_i ) @ V_k )
=> ~ ! [B_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ B_j )
=> ( V_k
!= ( c_Nat_OSuc @ B_j ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessE) ).
thf(1074,axiom,
! [V_k: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_k )
=> ( ( V_k
!= ( c_Nat_OSuc @ V_i ) )
=> ~ ! [B_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ B_j )
=> ( V_k
!= ( c_Nat_OSuc @ B_j ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessE) ).
thf(1083,axiom,
! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ ( c_Nat_OSuc @ V_m_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1084,axiom,
! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_n_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(1085,axiom,
! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m_2 ) @ ( c_Nat_OSuc @ V_n_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(1086,axiom,
! [V_m_2: $i,V_n_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1087,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/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(1088,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/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1089,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1090,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/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(1091,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/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1092,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(1093,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(1103,axiom,
! [V_xa_2: $i,V_fa_2: $i,V_ac_2: $i,V_upd_2: $i,T_b: $i,T_a: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ T_a @ T_b @ V_upd_2 @ V_ac_2 )
=> ( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_ac_2 @ V_xa_2 ) )
= ( hAPP @ V_ac_2 @ V_xa_2 ) )
=> ( ( hAPP @ ( hAPP @ V_upd_2 @ V_fa_2 ) @ V_xa_2 )
= V_xa_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_update__accessor__noopE) ).
thf(1108,axiom,
! [V_n: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(1109,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1110,axiom,
! [V_gb_2: $i,V_b_2: $i,V_a_2: $i,V_fa_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ ( c_Fun_Oswap @ T_a @ T_c @ V_a_2 @ V_b_2 @ V_gb_2 ) )
= ( c_Fun_Oswap @ T_a @ T_b @ V_a_2 @ V_b_2 @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ V_gb_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__swap) ).
thf(1111,axiom,
! [V_gb_2: $i,V_xa_2: $i,V_fa_2: $i,V_ac_2: $i,V_upd_2: $i,T_b: $i,T_a: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ T_a @ T_b @ V_upd_2 @ V_ac_2 )
=> ( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_ac_2 @ V_xa_2 ) )
= ( hAPP @ V_ac_2 @ V_xa_2 ) )
=> ( ( hAPP @ ( hAPP @ V_upd_2 @ ( hAPP @ ( c_Fun_Ocomp @ T_a @ T_a @ T_a @ V_gb_2 ) @ V_fa_2 ) ) @ V_xa_2 )
= ( hAPP @ ( hAPP @ V_upd_2 @ V_gb_2 ) @ V_xa_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_update__accessor__noop__compE) ).
thf(1118,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Rings_Olinordered__idom @ T_a )
=> ( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(1121,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_x != V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(1122,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(1123,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(1124,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_x != V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(1125,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(1126,axiom,
! [V_xa_2: $i,V_ya_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
<=> ( V_xa_2 = V_ya_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(1127,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
| ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(1128,axiom,
! [V_ya_2: $i,V_xa_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 )
| ( V_xa_2 = V_ya_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(1129,axiom,
! [V_ya_2: $i,V_xa_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( V_xa_2 != V_ya_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
| ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(1130,axiom,
! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(1131,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_y != V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(1132,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(1133,axiom,
! [V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(1134,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(1135,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_b )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(1136,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b )
=> ( ( V_b = V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1137,axiom,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a )
=> ( ( V_b = V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(1138,axiom,
! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_z )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(1139,axiom,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_z @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_z @ V_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(1140,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(1141,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( ( V_x != V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(1142,axiom,
! [V_fa_2: $i] :
( ( c_SEQ_Osubseq @ V_fa_2 )
<=> ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ V_fa_2 @ B_m ) @ ( hAPP @ V_fa_2 @ B_n ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__def) ).
thf(1143,axiom,
! [V_P_2: $i,V_n_2: $i,V_m_2: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( V_m_2 = V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(1144,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/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(1145,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/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1146,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1147,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(1148,axiom,
! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 != V_n_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(1149,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(1150,axiom,
! [V_d_2: $i,V_c_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(1151,axiom,
! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(1152,axiom,
! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(1153,axiom,
! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_xa_2: $i,V_gb_2: $i,V_fa_2: $i] :
( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_gb_2 @ V_xa_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_fa_2 ) @ V_gb_2 ) @ V_xa_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(1154,axiom,
! [V_xa_2: $i,V_gb_2: $i,V_fa_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_fa_2 ) @ V_gb_2 ) @ V_xa_2 )
= ( hAPP @ V_fa_2 @ ( hAPP @ V_gb_2 @ V_xa_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
thf(1155,axiom,
! [V_h_2: $i,V_gb_2: $i,T_d: $i,V_fa_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_gb_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_fa_2 ) @ V_gb_2 ) ) @ V_h_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(1156,axiom,
c_SEQ_Osubseq @ v_ga____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I1_J) ).
thf(1157,axiom,
c_SEQ_Osubseq @ v_f____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f_I1_J) ).
thf(1158,axiom,
! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ B_m ) @ ( hAPP @ v_ga____ @ B_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
thf(1159,axiom,
! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ B_m ) @ ( hAPP @ v_f____ @ B_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
thf(1160,axiom,
! [V_gb_2: $i,V_fa_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_fa_2 @ B_x )
= ( hAPP @ V_gb_2 @ B_x ) )
=> ( V_fa_2 = V_gb_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(1161,conjecture,
! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1162,negated_conjecture,
( ( ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B_n ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1161]) ).
thf(1163,plain,
( ( ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B_n ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[1162]) ).
thf(1164,plain,
( ( class_Groups_Oone @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(1165,plain,
( ( class_Groups_Ozero @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(1166,plain,
( ( class_Power_Opower @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(1167,plain,
( ( class_Groups_Ominus @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(1168,plain,
( ( class_Orderings_Oord @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(1169,plain,
( ( class_Rings_Osemiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(1170,plain,
( ( class_Orderings_Oorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(1171,plain,
( ( class_Rings_Omult__zero @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(1172,plain,
( ( class_Rings_Osemiring__0 @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(1173,plain,
( ( class_Rings_Osemiring__1 @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(1174,plain,
( ( class_Groups_Omonoid__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(1175,plain,
( ( class_Groups_Omonoid__mult @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(1176,plain,
( ( class_Orderings_Olinorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(1177,plain,
( ( class_Orderings_Opreorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(1178,plain,
( ( class_Rings_Ozero__neq__one @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(1179,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(1180,plain,
( ( class_Rings_Ocomm__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(1181,plain,
( ( class_Divides_Osemiring__div @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(1182,plain,
( ( class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(1183,plain,
( ( class_Groups_Ocomm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(1184,plain,
( ( class_Rings_Ono__zero__divisors @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(1185,plain,
( ( class_Rings_Oordered__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(1186,plain,
( ( class_Groups_Oab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(1187,plain,
( ( class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(1188,plain,
( ( class_Groups_Oab__semigroup__mult @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(1189,plain,
( ( class_Rings_Olinordered__semidom @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(1190,plain,
( ( class_Rings_Olinordered__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(1191,plain,
( ( class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(1192,plain,
( ( class_Rings_Oordered__comm__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(1193,plain,
( ( class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(1194,plain,
( ( class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(1195,plain,
( ( class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(1196,plain,
( ( class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(1197,plain,
( ( class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(1198,plain,
( ( class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(1199,plain,
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(1200,plain,
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(1201,plain,
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(1202,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_k ) @ V_j ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(1203,plain,
( ( ! [V_l: $i,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 @ V_l )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_l @ V_n ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_l @ V_m ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(1204,plain,
( ( ! [V_n: $i,V_k: $i,V_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_j @ V_n ) @ V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(1205,plain,
( ( ! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ V_n_2 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1206,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[858]) ).
thf(1207,plain,
( ( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_k @ V_l )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_l )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k @ V_n ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[859]) ).
thf(1208,plain,
( ( ! [V_l: $i,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_k @ V_l )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_l ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[860]) ).
thf(1209,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 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[861]) ).
thf(1210,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_z )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[862]) ).
thf(1211,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[863]) ).
thf(1212,plain,
( ( ! [V_m: $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_i @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_j ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[864]) ).
thf(1213,plain,
( ( ! [V_m: $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_i @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[865]) ).
thf(1214,plain,
( ( ! [V_n_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( 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_n_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[866]) ).
thf(1215,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_i ) @ V_i ) )
= $true ),
inference(unfold_def,[status(thm)],[867]) ).
thf(1216,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_i ) )
= $true ),
inference(unfold_def,[status(thm)],[868]) ).
thf(1217,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)],[884]) ).
thf(1218,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[885]) ).
thf(1219,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)],[886]) ).
thf(1220,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)],[889]) ).
thf(1221,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(1222,plain,
( ( ! [V_n_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_n_2 ) )
<=> ( V_m_2 = V_n_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(1223,plain,
( ( ! [V_n_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_n_2 @ V_k_2 ) )
<=> ( V_m_2 = V_n_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[893]) ).
thf(1224,plain,
( ( ! [V_n: $i] :
( ( V_n
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1054]) ).
thf(1225,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_n
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1055]) ).
thf(1226,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1056]) ).
thf(1227,plain,
( ( ! [V_n_2: $i] :
( ( V_n_2
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1057]) ).
thf(1228,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1058]) ).
thf(1229,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ V_x @ V_y )
| ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ V_y @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1067]) ).
thf(1230,plain,
( ( ! [V_xa_2: $i,V_n_2: $i,T_a: $i,V_fa_2: $i] :
( ( hAPP @ V_fa_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_fa_2 ) @ V_xa_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_fa_2 ) @ ( hAPP @ V_fa_2 @ V_xa_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1069]) ).
thf(1231,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1072]) ).
thf(1232,plain,
( ( ! [V_k: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_i ) @ V_k )
=> ~ ! [B_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ B_j )
=> ( V_k
!= ( c_Nat_OSuc @ B_j ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1073]) ).
thf(1233,plain,
( ( ! [V_k: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_k )
=> ( ( V_k
!= ( c_Nat_OSuc @ V_i ) )
=> ~ ! [B_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ B_j )
=> ( V_k
!= ( c_Nat_OSuc @ B_j ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1074]) ).
thf(1234,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ ( c_Nat_OSuc @ V_m_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1083]) ).
thf(1235,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_n_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1084]) ).
thf(1236,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m_2 ) @ ( c_Nat_OSuc @ V_n_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1085]) ).
thf(1237,plain,
( ( ! [V_m_2: $i,V_n_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1086]) ).
thf(1238,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)],[1087]) ).
thf(1239,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)],[1088]) ).
thf(1240,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)],[1089]) ).
thf(1241,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)],[1090]) ).
thf(1242,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)],[1091]) ).
thf(1243,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)],[1092]) ).
thf(1244,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)],[1093]) ).
thf(1245,plain,
( ( ! [V_xa_2: $i,V_fa_2: $i,V_ac_2: $i,V_upd_2: $i,T_b: $i,T_a: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ T_a @ T_b @ V_upd_2 @ V_ac_2 )
=> ( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_ac_2 @ V_xa_2 ) )
= ( hAPP @ V_ac_2 @ V_xa_2 ) )
=> ( ( hAPP @ ( hAPP @ V_upd_2 @ V_fa_2 ) @ V_xa_2 )
= V_xa_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1103]) ).
thf(1246,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)],[1108]) ).
thf(1247,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)],[1109]) ).
thf(1248,plain,
( ( ! [V_gb_2: $i,V_b_2: $i,V_a_2: $i,V_fa_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ ( c_Fun_Oswap @ T_a @ T_c @ V_a_2 @ V_b_2 @ V_gb_2 ) )
= ( c_Fun_Oswap @ T_a @ T_b @ V_a_2 @ V_b_2 @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ V_gb_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1110]) ).
thf(1249,plain,
( ( ! [V_gb_2: $i,V_xa_2: $i,V_fa_2: $i,V_ac_2: $i,V_upd_2: $i,T_b: $i,T_a: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ T_a @ T_b @ V_upd_2 @ V_ac_2 )
=> ( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_ac_2 @ V_xa_2 ) )
= ( hAPP @ V_ac_2 @ V_xa_2 ) )
=> ( ( hAPP @ ( hAPP @ V_upd_2 @ ( hAPP @ ( c_Fun_Ocomp @ T_a @ T_a @ T_a @ V_gb_2 ) @ V_fa_2 ) ) @ V_xa_2 )
= ( hAPP @ ( hAPP @ V_upd_2 @ V_gb_2 ) @ V_xa_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1111]) ).
thf(1250,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Rings_Olinordered__idom @ T_a )
=> ( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1118]) ).
thf(1251,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_x != V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1121]) ).
thf(1252,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1122]) ).
thf(1253,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1123]) ).
thf(1254,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_x != V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1124]) ).
thf(1255,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1125]) ).
thf(1256,plain,
( ( ! [V_xa_2: $i,V_ya_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
<=> ( V_xa_2 = V_ya_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1126]) ).
thf(1257,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
| ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1127]) ).
thf(1258,plain,
( ( ! [V_ya_2: $i,V_xa_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 )
| ( V_xa_2 = V_ya_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1128]) ).
thf(1259,plain,
( ( ! [V_ya_2: $i,V_xa_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( V_xa_2 != V_ya_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
| ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1129]) ).
thf(1260,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1130]) ).
thf(1261,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_y != V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1131]) ).
thf(1262,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1132]) ).
thf(1263,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1133]) ).
thf(1264,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1134]) ).
thf(1265,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_b )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1135]) ).
thf(1266,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b )
=> ( ( V_b = V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1136]) ).
thf(1267,plain,
( ( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a )
=> ( ( V_b = V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1137]) ).
thf(1268,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_z )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1138]) ).
thf(1269,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_z @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_z @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1139]) ).
thf(1270,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1140]) ).
thf(1271,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( ( V_x != V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1141]) ).
thf(1272,plain,
( ( ! [V_fa_2: $i] :
( ( c_SEQ_Osubseq @ V_fa_2 )
<=> ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ V_fa_2 @ B_m ) @ ( hAPP @ V_fa_2 @ B_n ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1142]) ).
thf(1273,plain,
( ( ! [V_P_2: $i,V_n_2: $i,V_m_2: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( V_m_2 = V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1143]) ).
thf(1274,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)],[1144]) ).
thf(1275,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)],[1145]) ).
thf(1276,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[1146]) ).
thf(1277,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)],[1147]) ).
thf(1278,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 != V_n_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1148]) ).
thf(1279,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[1149]) ).
thf(1280,plain,
( ( ! [V_d_2: $i,V_c_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1150]) ).
thf(1281,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1151]) ).
thf(1282,plain,
( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1152]) ).
thf(1283,plain,
( ( ! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_xa_2: $i,V_gb_2: $i,V_fa_2: $i] :
( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_gb_2 @ V_xa_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_fa_2 ) @ V_gb_2 ) @ V_xa_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1153]) ).
thf(1284,plain,
( ( ! [V_xa_2: $i,V_gb_2: $i,V_fa_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_fa_2 ) @ V_gb_2 ) @ V_xa_2 )
= ( hAPP @ V_fa_2 @ ( hAPP @ V_gb_2 @ V_xa_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1154]) ).
thf(1285,plain,
( ( ! [V_h_2: $i,V_gb_2: $i,T_d: $i,V_fa_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_gb_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_fa_2 ) @ V_gb_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1155]) ).
thf(1286,plain,
( ( c_SEQ_Osubseq @ v_ga____ )
= $true ),
inference(unfold_def,[status(thm)],[1156]) ).
thf(1287,plain,
( ( c_SEQ_Osubseq @ v_f____ )
= $true ),
inference(unfold_def,[status(thm)],[1157]) ).
thf(1288,plain,
( ( ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ B_m ) @ ( hAPP @ v_ga____ @ B_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1158]) ).
thf(1289,plain,
( ( ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ B_m ) @ ( hAPP @ v_f____ @ B_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1159]) ).
thf(1290,plain,
( ( ! [V_gb_2: $i,V_fa_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_fa_2 @ B_x )
= ( hAPP @ V_gb_2 @ B_x ) )
=> ( V_fa_2 = V_gb_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1160]) ).
thf(1291,plain,
( ( ! [SY273: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ sK1_B_m @ SY273 )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK1_B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ SY273 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1163]) ).
thf(1292,plain,
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ sK1_B_m @ sK2_SY273 )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK1_B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK2_SY273 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1291]) ).
thf(1293,plain,
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ sK1_B_m @ sK2_SY273 )
= $true ),
inference(standard_cnf,[status(thm)],[1292]) ).
thf(1294,plain,
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK1_B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK2_SY273 ) )
= $false ),
inference(standard_cnf,[status(thm)],[1292]) ).
thf(1295,plain,
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK1_B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK2_SY273 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[1294]) ).
thf(1296,plain,
( ( ! [V_gb_2: $i,V_fa_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_fa_2 @ B_x )
= ( hAPP @ V_gb_2 @ B_x ) )
=> ( V_fa_2 = V_gb_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(1297,plain,
( ( ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ B_m ) @ ( hAPP @ v_f____ @ B_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(1298,plain,
( ( ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ B_m ) @ ( hAPP @ v_ga____ @ B_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(1299,plain,
( ( c_SEQ_Osubseq @ v_f____ )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(1300,plain,
( ( c_SEQ_Osubseq @ v_ga____ )
= $true ),
inference(copy,[status(thm)],[1286]) ).
thf(1301,plain,
( ( ! [V_h_2: $i,V_gb_2: $i,T_d: $i,V_fa_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_gb_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_fa_2 ) @ V_gb_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1285]) ).
thf(1302,plain,
( ( ! [V_xa_2: $i,V_gb_2: $i,V_fa_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_fa_2 ) @ V_gb_2 ) @ V_xa_2 )
= ( hAPP @ V_fa_2 @ ( hAPP @ V_gb_2 @ V_xa_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1284]) ).
thf(1303,plain,
( ( ! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_xa_2: $i,V_gb_2: $i,V_fa_2: $i] :
( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_gb_2 @ V_xa_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_fa_2 ) @ V_gb_2 ) @ V_xa_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1283]) ).
thf(1304,plain,
( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1282]) ).
thf(1305,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1281]) ).
thf(1306,plain,
( ( ! [V_d_2: $i,V_c_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1280]) ).
thf(1307,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[1279]) ).
thf(1308,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 != V_n_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1278]) ).
thf(1309,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)],[1277]) ).
thf(1310,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(1311,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)],[1275]) ).
thf(1312,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)],[1274]) ).
thf(1313,plain,
( ( ! [V_P_2: $i,V_n_2: $i,V_m_2: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( V_m_2 = V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1273]) ).
thf(1314,plain,
( ( ! [V_fa_2: $i] :
( ( c_SEQ_Osubseq @ V_fa_2 )
<=> ! [B_m: $i,B_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B_m @ B_n )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ V_fa_2 @ B_m ) @ ( hAPP @ V_fa_2 @ B_n ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(1315,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( ( V_x != V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1271]) ).
thf(1316,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(1317,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_z @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_z @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(1318,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_z )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(1319,plain,
( ( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a )
=> ( ( V_b = V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(1320,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b )
=> ( ( V_b = V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(1321,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_b )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_c @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(1322,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_c )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(1323,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(1324,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_a @ V_b )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_b @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(1325,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_y != V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(1326,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(1327,plain,
( ( ! [V_ya_2: $i,V_xa_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( V_xa_2 != V_ya_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
| ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(1328,plain,
( ( ! [V_ya_2: $i,V_xa_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 )
| ( V_xa_2 = V_ya_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(1329,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
| ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(1330,plain,
( ( ! [V_xa_2: $i,V_ya_2: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_ya_2 @ V_xa_2 )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_xa_2 @ V_ya_2 )
<=> ( V_xa_2 = V_ya_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(1331,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(1332,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_x != V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(1333,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(1334,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1252]) ).
thf(1335,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( V_x != V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1336,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Rings_Olinordered__idom @ T_a )
=> ( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ T_a @ V_y @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1250]) ).
thf(1337,plain,
( ( ! [V_gb_2: $i,V_xa_2: $i,V_fa_2: $i,V_ac_2: $i,V_upd_2: $i,T_b: $i,T_a: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ T_a @ T_b @ V_upd_2 @ V_ac_2 )
=> ( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_ac_2 @ V_xa_2 ) )
= ( hAPP @ V_ac_2 @ V_xa_2 ) )
=> ( ( hAPP @ ( hAPP @ V_upd_2 @ ( hAPP @ ( c_Fun_Ocomp @ T_a @ T_a @ T_a @ V_gb_2 ) @ V_fa_2 ) ) @ V_xa_2 )
= ( hAPP @ ( hAPP @ V_upd_2 @ V_gb_2 ) @ V_xa_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(1338,plain,
( ( ! [V_gb_2: $i,V_b_2: $i,V_a_2: $i,V_fa_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ ( c_Fun_Oswap @ T_a @ T_c @ V_a_2 @ V_b_2 @ V_gb_2 ) )
= ( c_Fun_Oswap @ T_a @ T_b @ V_a_2 @ V_b_2 @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_fa_2 ) @ V_gb_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1339,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)],[1247]) ).
thf(1340,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(1341,plain,
( ( ! [V_xa_2: $i,V_fa_2: $i,V_ac_2: $i,V_upd_2: $i,T_b: $i,T_a: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ T_a @ T_b @ V_upd_2 @ V_ac_2 )
=> ( ( ( hAPP @ V_fa_2 @ ( hAPP @ V_ac_2 @ V_xa_2 ) )
= ( hAPP @ V_ac_2 @ V_xa_2 ) )
=> ( ( hAPP @ ( hAPP @ V_upd_2 @ V_fa_2 ) @ V_xa_2 )
= V_xa_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1245]) ).
thf(1342,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)],[1244]) ).
thf(1343,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)],[1243]) ).
thf(1344,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)],[1242]) ).
thf(1345,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)],[1241]) ).
thf(1346,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)],[1240]) ).
thf(1347,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)],[1239]) ).
thf(1348,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)],[1238]) ).
thf(1349,plain,
( ( ! [V_m_2: $i,V_n_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ ( c_Nat_OSuc @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(1350,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_m_2 ) @ ( c_Nat_OSuc @ V_n_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1351,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ ( c_Nat_OSuc @ V_n_2 ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(1352,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ ( c_Nat_OSuc @ V_m_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(1353,plain,
( ( ! [V_k: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_k )
=> ( ( V_k
!= ( c_Nat_OSuc @ V_i ) )
=> ~ ! [B_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ B_j )
=> ( V_k
!= ( c_Nat_OSuc @ B_j ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(1354,plain,
( ( ! [V_k: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_i ) @ V_k )
=> ~ ! [B_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ B_j )
=> ( V_k
!= ( c_Nat_OSuc @ B_j ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1355,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(1356,plain,
( ( ! [V_xa_2: $i,V_n_2: $i,T_a: $i,V_fa_2: $i] :
( ( hAPP @ V_fa_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_fa_2 ) @ V_xa_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_fa_2 ) @ ( hAPP @ V_fa_2 @ V_xa_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1230]) ).
thf(1357,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ V_x @ V_y )
| ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ V_y @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(1358,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1228]) ).
thf(1359,plain,
( ( ! [V_n_2: $i] :
( ( V_n_2
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(1360,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(copy,[status(thm)],[1226]) ).
thf(1361,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n )
=> ( V_n
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(1362,plain,
( ( ! [V_n: $i] :
( ( V_n
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1224]) ).
thf(1363,plain,
( ( ! [V_n_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_n_2 @ V_k_2 ) )
<=> ( V_m_2 = V_n_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(1364,plain,
( ( ! [V_n_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_n_2 ) )
<=> ( V_m_2 = V_n_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(1365,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(1366,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)],[1220]) ).
thf(1367,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)],[1219]) ).
thf(1368,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1218]) ).
thf(1369,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)],[1217]) ).
thf(1370,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_i ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(1371,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_i ) @ V_i ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(1372,plain,
( ( ! [V_n_2: $i,V_m_2: $i,V_k_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( 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_n_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1373,plain,
( ( ! [V_m: $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_i @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1374,plain,
( ( ! [V_m: $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_i @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_j ) ) ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1375,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(1376,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_z )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_y @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(1377,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 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1378,plain,
( ( ! [V_l: $i,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_k @ V_l )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_k ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_j @ V_l ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1379,plain,
( ( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_k @ V_l )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_l )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_k @ V_n ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1380,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_i @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1381,plain,
( ( ! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ V_n_2 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1382,plain,
( ( ! [V_n: $i,V_k: $i,V_j: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_j @ V_n ) @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1383,plain,
( ( ! [V_l: $i,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 @ V_l )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_l @ V_n ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_l @ V_m ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1384,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_k ) @ V_j ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1385,plain,
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(1386,plain,
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(1387,plain,
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(1388,plain,
( ( class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(1389,plain,
( ( class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1390,plain,
( ( class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1391,plain,
( ( class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1392,plain,
( ( class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1393,plain,
( ( class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1394,plain,
( ( class_Rings_Oordered__comm__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1395,plain,
( ( class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(1396,plain,
( ( class_Rings_Olinordered__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1397,plain,
( ( class_Rings_Olinordered__semidom @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1398,plain,
( ( class_Groups_Oab__semigroup__mult @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1399,plain,
( ( class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1400,plain,
( ( class_Groups_Oab__semigroup__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(1401,plain,
( ( class_Rings_Oordered__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1185]) ).
thf(1402,plain,
( ( class_Rings_Ono__zero__divisors @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1184]) ).
thf(1403,plain,
( ( class_Groups_Ocomm__monoid__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1183]) ).
thf(1404,plain,
( ( class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1182]) ).
thf(1405,plain,
( ( class_Divides_Osemiring__div @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(1406,plain,
( ( class_Rings_Ocomm__semiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(1407,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1179]) ).
thf(1408,plain,
( ( class_Rings_Ozero__neq__one @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1409,plain,
( ( class_Orderings_Opreorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1177]) ).
thf(1410,plain,
( ( class_Orderings_Olinorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(1411,plain,
( ( class_Groups_Omonoid__mult @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(1412,plain,
( ( class_Groups_Omonoid__add @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1413,plain,
( ( class_Rings_Osemiring__1 @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(1414,plain,
( ( class_Rings_Osemiring__0 @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(1415,plain,
( ( class_Rings_Omult__zero @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1416,plain,
( ( class_Orderings_Oorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(1417,plain,
( ( class_Rings_Osemiring @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(1418,plain,
( ( class_Orderings_Oord @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(1419,plain,
( ( class_Groups_Ominus @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(1420,plain,
( ( class_Power_Opower @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1166]) ).
thf(1421,plain,
( ( class_Groups_Ozero @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1165]) ).
thf(1422,plain,
( ( class_Groups_Oone @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1423,plain,
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ sK1_B_m @ sK2_SY273 )
= $true ),
inference(copy,[status(thm)],[1293]) ).
thf(1424,plain,
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK1_B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK2_SY273 ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1425,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ~ ( ( SX0
!= ( c_Nat_OSuc @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( SX0
!= ( c_Nat_OSuc @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1353]) ).
thf(1426,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1329]) ).
thf(1427,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Opreorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1324]) ).
thf(1428,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ( SX2 != SX1 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX0 @ SX1 )
| ( c_Orderings_Oord__class_Oless @ SX3 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1321]) ).
thf(1429,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ~ ( ( SX1 != SX0 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1331]) ).
thf(1430,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SX6 @ SX5 @ SX4 @ SX3 ) @ SX2 )
!= SX1 )
| ( ( hAPP @ SX3 @ ( hAPP @ SX2 @ SX0 ) )
= ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1304]) ).
thf(1431,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX3 @ SX2 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX1 @ SX2 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX3 @ SX0 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1379]) ).
thf(1432,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Opreorder @ SX3 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX2 @ SX1 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1318]) ).
thf(1433,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)],[1351]) ).
thf(1434,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)],[1345]) ).
thf(1435,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 @ SX2 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1373]) ).
thf(1436,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 @ SX2 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SX0 @ SX1 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1383]) ).
thf(1437,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 @ SX2 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1374]) ).
thf(1438,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ( SX2 != SX1 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1322]) ).
thf(1439,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX3 @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX3 @ SX1 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1378]) ).
thf(1440,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( c_SEQ_Osubseq @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ SX2 ) ) ) )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ SX2 ) ) )
| ( c_SEQ_Osubseq @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1314]) ).
thf(1441,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Opreorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1316]) ).
thf(1442,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SX5 @ SX4 @ SX3 @ SX2 )
| ( ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) )
!= ( hAPP @ SX2 @ SX0 ) )
| ( ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1341]) ).
thf(1443,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)],[1352]) ).
thf(1444,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1362]) ).
thf(1445,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)],[1347]) ).
thf(1446,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)],[1364]) ).
thf(1447,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1296]) ).
thf(1448,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SX1 )
!= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SX1 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1381]) ).
thf(1449,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Opreorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1333]) ).
thf(1450,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX1 ) @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1380]) ).
thf(1451,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ( ( SX2 != SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1313]) ).
thf(1452,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1312]) ).
thf(1453,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Opreorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1334]) ).
thf(1454,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1330]) ).
thf(1455,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)],[1349]) ).
thf(1456,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)],[1309]) ).
thf(1457,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1323]) ).
thf(1458,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)],[1344]) ).
thf(1459,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX2 @ SX1 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX0 @ SX2 )
| ( c_Orderings_Oord__class_Oless @ SX3 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1317]) ).
thf(1460,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ( SX0
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SX0 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SX0 )
| ( SX0
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1359]) ).
thf(1461,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)],[1348]) ).
thf(1462,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ~ ( ~ ( ~ ( ( SX1 != SX0 ) )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) )
| ( SX1 != SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1327]) ).
thf(1463,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)],[1346]) ).
thf(1464,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Rings_Olinordered__idom @ SX2 )
| ~ ( ( SX1 != SX0 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1336]) ).
thf(1465,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SX1 ) @ SX0 )
| ~ ! [SX2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( SX0
!= ( c_Nat_OSuc @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1354]) ).
thf(1466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ SX0 ) @ ( hAPP @ v_ga____ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1298]) ).
thf(1467,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 )
| ( SX1 = SX0 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 )
| ( SX1 = SX0 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1328]) ).
thf(1468,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX1 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ 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_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX1 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1372]) ).
thf(1469,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)],[1308]) ).
thf(1470,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX0
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1361]) ).
thf(1471,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Opreorder @ SX1 )
| ~ ( c_Orderings_Oord__class_Oless @ SX1 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1326]) ).
thf(1472,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 @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SX2 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1382]) ).
thf(1473,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX2 @ SX1 )
| ( SX2 != SX0 )
| ( c_Orderings_Oord__class_Oless @ SX3 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1319]) ).
thf(1474,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ SX0 ) @ ( hAPP @ v_f____ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1297]) ).
thf(1475,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ~ ( ( SX1 != SX0 ) )
| ( c_Orderings_Oord__class_Oless @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1315]) ).
thf(1476,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1325]) ).
thf(1477,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)],[1342]) ).
thf(1478,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i,SX9: $i,SX10: $i] :
( ( ( hAPP @ SX10 @ ( hAPP @ SX9 @ SX8 ) )
!= ( hAPP @ SX7 @ ( hAPP @ SX6 @ SX5 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SX4 @ SX3 @ SX2 @ SX10 ) @ SX9 ) @ SX8 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SX1 @ SX3 @ SX0 @ SX7 ) @ SX6 ) @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1303]) ).
thf(1479,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SX8 @ SX7 @ SX6 @ SX5 ) @ SX4 )
!= ( hAPP @ ( c_Fun_Ocomp @ SX3 @ SX7 @ SX6 @ SX2 ) @ SX1 ) )
| ( ( hAPP @ SX5 @ ( hAPP @ SX4 @ SX0 ) )
= ( hAPP @ SX2 @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1305]) ).
thf(1480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SX7 @ SX6 @ SX5 @ SX4 ) @ SX3 )
!= ( hAPP @ ( c_Fun_Ocomp @ SX2 @ SX6 @ SX5 @ SX1 ) @ SX0 ) )
| ! [SX8: $i] :
( ( hAPP @ SX4 @ ( hAPP @ SX3 @ SX8 ) )
= ( hAPP @ SX1 @ ( hAPP @ SX0 @ SX8 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1306]) ).
thf(1481,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1335]) ).
thf(1482,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ~ ( c_Orderings_Oord__class_Oless @ SX3 @ SX2 @ SX1 )
| ( SX1 != SX0 )
| ( c_Orderings_Oord__class_Oless @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1320]) ).
thf(1483,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)],[1343]) ).
thf(1484,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 @ SX2 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1376]) ).
thf(1485,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 @ SX2 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1375]) ).
thf(1486,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)],[1363]) ).
thf(1487,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SX6 @ SX5 @ SX4 @ SX3 )
| ( ( hAPP @ SX2 @ ( hAPP @ SX3 @ SX1 ) )
!= ( hAPP @ SX3 @ SX1 ) )
| ( ( hAPP @ ( hAPP @ SX4 @ ( hAPP @ ( c_Fun_Ocomp @ SX6 @ SX6 @ SX6 @ SX0 ) @ SX2 ) ) @ SX1 )
= ( hAPP @ ( hAPP @ SX4 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1337]) ).
thf(1488,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( c_Orderings_Oord__class_Oless @ SX2 @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1332]) ).
thf(1489,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1311]) ).
thf(1490,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)],[1339]) ).
thf(1491,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)],[1350]) ).
thf(1492,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 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX2 @ SX0 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1377]) ).
thf(1493,plain,
! [SV1: $i] :
( ( ! [SY274: $i,SY275: $i,SY276: $i,SY277: $i,SY278: $i,SY279: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY279 @ SY278 @ SY277 @ SY276 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY275 @ SY279 @ SY277 @ SY274 ) @ SV1 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY275 @ SY278 @ SY277 @ ( hAPP @ ( c_Fun_Ocomp @ SY279 @ SY278 @ SY275 @ SY276 ) @ SY274 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1494,plain,
! [SV2: $i] :
( ( ! [SY280: $i,SY281: $i,SY282: $i,SY283: $i,SY284: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY284 @ SY283 @ SY282 @ SY281 ) @ SY280 ) @ SV2 )
= ( hAPP @ SY281 @ ( hAPP @ SY280 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1495,plain,
! [SV3: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1496,plain,
! [SV4: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1497,plain,
! [SV5: $i] :
( ( ! [SY285: $i,SY286: $i,SY287: $i,SY288: $i,SY289: $i,SY290: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY290 @ SY289 @ SY288 @ SY287 ) @ ( c_Fun_Oswap @ SY288 @ SY290 @ SY286 @ SY285 @ SV5 ) )
= ( c_Fun_Oswap @ SY288 @ SY289 @ SY286 @ SY285 @ ( hAPP @ ( c_Fun_Ocomp @ SY290 @ SY289 @ SY288 @ SY287 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1498,plain,
! [SV6: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV6 @ ( c_Nat_OSuc @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1499,plain,
! [SV7: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV7 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1500,plain,
! [SV8: $i] :
( ( ! [SY291: $i,SY292: $i,SY293: $i] :
( ( hAPP @ SY293 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY292 @ SY292 ) @ SY291 ) @ SY293 ) @ SV8 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY292 @ SY292 ) @ SY291 ) @ SY293 ) @ ( hAPP @ SY293 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1501,plain,
! [SV9: $i] :
( ( ! [SY294: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SY294 @ SV9 )
| ( SY294 = SV9 )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SV9 @ SY294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1502,plain,
! [SV10: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV10 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1503,plain,
! [SV11: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV11 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1504,plain,
! [SV12: $i] :
( ( ! [SY295: $i,SY296: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SY296 ) @ SY295 ) ) @ SV12 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SY296 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SY295 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1505,plain,
! [SV13: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY298 @ SY297 ) @ SV13 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY298 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY297 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1506,plain,
! [SV14: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY300 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY299 @ SV14 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY299 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY300 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1507,plain,
! [SV15: $i] :
( ( ! [SY301: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SY301 ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SV15 ) @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1508,plain,
! [SV16: $i] :
( ( ! [SY302: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY302 @ SV16 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV16 @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1509,plain,
! [SV17: $i] :
( ( ! [SY303: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY303 @ SV17 ) @ SY303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1510,plain,
! [SV18: $i] :
( ( ! [SY304: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY304 @ SV18 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1511,plain,
! [SV19: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY306 @ SY305 ) @ SV19 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY306 @ SV19 ) @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1512,plain,
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK1_B_m ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ sK2_SY273 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1513,plain,
! [SV20: $i] :
( ( ! [SY307: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY307 @ SV20 )
| ~ ( ( SV20
!= ( c_Nat_OSuc @ SY307 ) ) )
| ~ ! [SY308: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY307 @ SY308 )
| ( SV20
!= ( c_Nat_OSuc @ SY308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1514,plain,
! [SV21: $i] :
( ( ! [SY309: $i,SY310: $i] :
( ~ ( class_Orderings_Olinorder @ SY310 )
| ( c_Orderings_Oord__class_Oless @ SY310 @ SY309 @ SV21 )
| ( SY309 = SV21 )
| ( c_Orderings_Oord__class_Oless @ SY310 @ SV21 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1515,plain,
! [SV22: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( class_Orderings_Opreorder @ SY312 )
| ~ ( c_Orderings_Oord__class_Oless @ SY312 @ SY311 @ SV22 )
| ~ ( c_Orderings_Oord__class_Oless @ SY312 @ SV22 @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1516,plain,
! [SV23: $i] :
( ( ! [SY313: $i,SY314: $i,SY315: $i] :
( ~ ( class_Orderings_Oorder @ SY315 )
| ( SY314 != SY313 )
| ~ ( c_Orderings_Oord__class_Oless @ SY315 @ SV23 @ SY313 )
| ( c_Orderings_Oord__class_Oless @ SY315 @ SV23 @ SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1517,plain,
! [SV24: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ( class_Orderings_Olinorder @ SY317 )
| ~ ( ( SY316 != SV24 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY317 @ SY316 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SY317 @ SV24 @ SY316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1518,plain,
! [SV25: $i] :
( ( ! [SY318: $i,SY319: $i,SY320: $i,SY321: $i,SY322: $i,SY323: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY323 @ SY322 @ SY321 @ SY320 ) @ SY319 )
!= SY318 )
| ( ( hAPP @ SY320 @ ( hAPP @ SY319 @ SV25 ) )
= ( hAPP @ SY318 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1519,plain,
! [SV26: $i] :
( ( ! [SY324: $i,SY325: $i,SY326: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY326 @ SY325 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY324 @ SY325 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY326 @ SV26 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY324 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1520,plain,
! [SV27: $i] :
( ( ! [SY327: $i,SY328: $i,SY329: $i] :
( ~ ( class_Orderings_Opreorder @ SY329 )
| ~ ( c_Orderings_Oord__class_Oless @ SY329 @ SY328 @ SY327 )
| ~ ( c_Orderings_Oord__class_Oless @ SY329 @ SY327 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SY329 @ SY328 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1521,plain,
! [SV28: $i] :
( ( ! [SY330: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY330 @ ( c_Nat_OSuc @ SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY330 @ SV28 )
| ( SY330 = SV28 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY330 @ SV28 )
| ( SY330 = SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY330 @ ( c_Nat_OSuc @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1522,plain,
! [SV29: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY332 @ SY331 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY331 @ SV29 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY332 ) @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1523,plain,
! [SV30: $i] :
( ( ! [SY333: $i,SY334: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY334 @ SY333 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY334 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY333 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1524,plain,
! [SV31: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY336 @ SY335 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY336 @ SV31 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SY335 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1525,plain,
! [SV32: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY338 @ SY337 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY338 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV32 @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1526,plain,
! [SV33: $i] :
( ( ! [SY339: $i,SY340: $i,SY341: $i] :
( ~ ( class_Orderings_Oord @ SY341 )
| ( SY340 != SY339 )
| ~ ( c_Orderings_Oord__class_Oless @ SY341 @ SY339 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SY341 @ SY340 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1527,plain,
! [SV34: $i] :
( ( ! [SY342: $i,SY343: $i,SY344: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY344 @ SY343 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY342 @ SV34 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY344 @ SY342 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY343 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1528,plain,
! [SV35: $i] :
( ( ~ ( ~ ( ~ ( c_SEQ_Osubseq @ SV35 )
| ! [SY345: $i,SY346: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY345 @ SY346 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY345 ) @ ( hAPP @ SV35 @ SY346 ) ) ) )
| ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY347 @ SY348 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY347 ) @ ( hAPP @ SV35 @ SY348 ) ) )
| ( c_SEQ_Osubseq @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1529,plain,
! [SV36: $i] :
( ( ! [SY349: $i,SY350: $i] :
( ~ ( class_Orderings_Opreorder @ SY350 )
| ~ ( c_Orderings_Oord__class_Oless @ SY350 @ SY349 @ SV36 )
| ~ ( c_Orderings_Oord__class_Oless @ SY350 @ SV36 @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1530,plain,
! [SV37: $i] :
( ( ! [SY351: $i,SY352: $i,SY353: $i,SY354: $i,SY355: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY355 @ SY354 @ SY353 @ SY352 )
| ( ( hAPP @ SY351 @ ( hAPP @ SY352 @ SV37 ) )
!= ( hAPP @ SY352 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SY353 @ SY351 ) @ SV37 )
= SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1531,plain,
! [SV38: $i] :
( ( ! [SY356: $i] :
~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY356 @ SV38 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SY356 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SY356 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY356 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1532,plain,
! [SV39: $i] :
( ( ~ ( ( SV39
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1533,plain,
! [SV40: $i] :
( ( ! [SY357: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY357 @ SV40 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY357 @ ( c_Nat_OSuc @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1534,plain,
! [SV41: $i] :
( ( ! [SY358: $i,SY359: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY359 @ SY358 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY359 @ SV41 ) )
| ( SY358 = SV41 ) )
| ~ ( ( SY358 != SV41 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY359 @ SY358 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY359 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1535,plain,
! [SV42: $i] :
( ( ! [SY360: $i] :
( ~ ! [SY361: $i] :
( ( hAPP @ SY360 @ SY361 )
= ( hAPP @ SV42 @ SY361 ) )
| ( SY360 = SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1536,plain,
! [SV43: $i] :
( ( ! [SY362: $i] :
~ ( ~ ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SY362 )
!= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
| ( SY362 = SV43 ) )
| ~ ( ( SY362 != SV43 )
| ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SY362 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1537,plain,
! [SV44: $i] :
( ( ! [SY363: $i,SY364: $i] :
( ~ ( class_Orderings_Opreorder @ SY364 )
| ~ ( c_Orderings_Oord__class_Oless @ SY364 @ SY363 @ SV44 )
| ~ ( c_Orderings_Oord__class_Oless @ SY364 @ SV44 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1538,plain,
! [SV45: $i] :
( ( ! [SY365: $i,SY366: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY366 @ SY365 ) @ SV45 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY366 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1539,plain,
! [SV46: $i] :
( ( ! [SY367: $i,SY368: $i] :
( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY368 @ SY367 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SY367 ) @ SY368 ) ) )
| ~ ( ( SY368 != SY367 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SY367 ) @ SY368 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY367 @ SY368 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SY367 ) @ SY368 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SY367 ) @ SY368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1540,plain,
! [SV47: $i] :
( ( ! [SY369: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY369 @ SV47 )
| ( SY369 != SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1541,plain,
! [SV48: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ~ ( class_Orderings_Opreorder @ SY371 )
| ~ ( c_Orderings_Oord__class_Oless @ SY371 @ SY370 @ SV48 )
| ~ ( c_Orderings_Oord__class_Oless @ SY371 @ SV48 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1542,plain,
! [SV49: $i] :
( ( ! [SY372: $i,SY373: $i] :
( ~ ( class_Orderings_Olinorder @ SY373 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY373 @ SY372 @ SV49 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SY373 @ SV49 @ SY372 )
| ( SV49 = SY372 ) )
| ~ ( ( SV49 != SY372 )
| ~ ( c_Orderings_Oord__class_Oless @ SY373 @ SV49 @ SY372 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1543,plain,
! [SV50: $i] :
( ( ! [SY374: $i] :
( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY374 @ SV50 )
| ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY374 @ ( c_Nat_OSuc @ SV50 ) )
| ( SY374 = SV50 ) )
| ~ ( ( SY374 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY374 @ ( c_Nat_OSuc @ SV50 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1544,plain,
! [SV51: $i] :
( ( ! [SY375: $i] :
( ~ ( ( SY375 != SV51 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY375 @ SV51 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SY375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1545,plain,
! [SV52: $i] :
( ( ! [SY376: $i,SY377: $i] :
( ~ ( class_Orderings_Oorder @ SY377 )
| ~ ( c_Orderings_Oord__class_Oless @ SY377 @ SY376 @ SV52 )
| ~ ( c_Orderings_Oord__class_Oless @ SY377 @ SV52 @ SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1546,plain,
! [SV53: $i] :
( ( ! [SY378: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY378 @ ( c_Nat_OSuc @ SV53 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY378 @ SV53 )
| ( SY378 = SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1547,plain,
! [SV54: $i] :
( ( ! [SY379: $i,SY380: $i,SY381: $i] :
( ~ ( class_Orderings_Oorder @ SY381 )
| ~ ( c_Orderings_Oord__class_Oless @ SY381 @ SY380 @ SY379 )
| ~ ( c_Orderings_Oord__class_Oless @ SY381 @ SV54 @ SY380 )
| ( c_Orderings_Oord__class_Oless @ SY381 @ SV54 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1548,plain,
! [SV55: $i] :
( ( ~ ( ~ ( ~ ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
| ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1549,plain,
! [SV56: $i] :
( ( ! [SY382: $i] :
( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY382 @ SV56 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY382 @ ( c_Nat_OSuc @ SV56 ) )
| ( SV56 = SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1550,plain,
! [SV57: $i] :
( ( ! [SY383: $i,SY384: $i] :
( ~ ( class_Orderings_Olinorder @ SY384 )
| ~ ( ~ ( ~ ( ( SY383 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SY384 @ SY383 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SY384 @ SV57 @ SY383 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SY384 @ SY383 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SY384 @ SV57 @ SY383 ) )
| ( SY383 != SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1551,plain,
! [SV58: $i] :
( ( ! [SY385: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY385 @ SV58 )
| ~ ( ( ( c_Nat_OSuc @ SY385 )
!= SV58 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY385 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1552,plain,
! [SV59: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ( class_Rings_Olinordered__idom @ SY387 )
| ~ ( ( SY386 != SV59 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY387 @ SY386 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SY387 @ SV59 @ SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1553,plain,
! [SV60: $i] :
( ( ! [SY388: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY388 ) @ SV60 )
| ~ ! [SY389: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY388 @ SY389 )
| ( SV60
!= ( c_Nat_OSuc @ SY389 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1554,plain,
! [SV61: $i] :
( ( ! [SY390: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV61 @ SY390 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ SV61 ) @ ( hAPP @ v_ga____ @ SY390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1555,plain,
! [SV62: $i] :
( ( ! [SY391: $i,SY392: $i] :
( ~ ( class_Orderings_Olinorder @ SY392 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SY392 @ SY391 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SY392 @ SV62 @ SY391 )
| ( SY391 = SV62 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SY392 @ SV62 @ SY391 )
| ( SY391 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SY392 @ SY391 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1556,plain,
! [SV63: $i] :
( ( ! [SY393: $i,SY394: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY394 @ SY393 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY394 @ SV63 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY393 @ SV63 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY393 @ SV63 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY394 @ SY393 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY394 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1557,plain,
! [SV64: $i] :
( ( ! [SY395: $i] :
~ ( ~ ( ~ ( ( SY395 != SV64 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY395 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SY395 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY395 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SY395 ) )
| ( SY395 != SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1558,plain,
! [SV65: $i] :
( ( ! [SY396: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY396 @ SV65 )
| ( SV65
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1559,plain,
! [SV66: $i] :
( ( ! [SY397: $i] :
( ~ ( class_Orderings_Opreorder @ SY397 )
| ~ ( c_Orderings_Oord__class_Oless @ SY397 @ SV66 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1560,plain,
! [SV67: $i] :
( ( ! [SY398: $i,SY399: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY399 @ SY398 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY399 @ SV67 ) @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1561,plain,
! [SV68: $i] :
( ( ! [SY400: $i,SY401: $i,SY402: $i] :
( ~ ( class_Orderings_Oorder @ SY402 )
| ~ ( c_Orderings_Oord__class_Oless @ SY402 @ SY401 @ SY400 )
| ( SY401 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SY402 @ SV68 @ SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1562,plain,
! [SV69: $i] :
( ( ! [SY403: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV69 @ SY403 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ SV69 ) @ ( hAPP @ v_f____ @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1563,plain,
! [SV70: $i] :
( ( ! [SY404: $i,SY405: $i] :
( ~ ( class_Orderings_Olinorder @ SY405 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY405 @ SY404 @ SV70 )
| ~ ( ( SY404 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SY405 @ SV70 @ SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1564,plain,
! [SV71: $i] :
( ( ! [SY406: $i,SY407: $i] :
( ~ ( class_Orderings_Oorder @ SY407 )
| ~ ( c_Orderings_Oord__class_Oless @ SY407 @ SY406 @ SV71 )
| ( SV71 != SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1565,plain,
! [SV72: $i] :
( ( ! [SY408: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY408 ) @ ( c_Nat_OSuc @ SV72 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY408 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1566,plain,
! [SV73: $i] :
( ( ! [SY409: $i,SY410: $i,SY411: $i,SY412: $i,SY413: $i,SY414: $i,SY415: $i,SY416: $i,SY417: $i,SY418: $i] :
( ( ( hAPP @ SY418 @ ( hAPP @ SY417 @ SY416 ) )
!= ( hAPP @ SY415 @ ( hAPP @ SY414 @ SY413 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY412 @ SY411 @ SY410 @ SY418 ) @ SY417 ) @ SY416 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY409 @ SY411 @ SV73 @ SY415 ) @ SY414 ) @ SY413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1567,plain,
! [SV74: $i] :
( ( ! [SY419: $i,SY420: $i,SY421: $i,SY422: $i,SY423: $i,SY424: $i,SY425: $i,SY426: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY426 @ SY425 @ SY424 @ SY423 ) @ SY422 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY421 @ SY425 @ SY424 @ SY420 ) @ SY419 ) )
| ( ( hAPP @ SY423 @ ( hAPP @ SY422 @ SV74 ) )
= ( hAPP @ SY420 @ ( hAPP @ SY419 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1568,plain,
! [SV75: $i] :
( ( ! [SY427: $i,SY428: $i,SY429: $i,SY430: $i,SY431: $i,SY432: $i,SY433: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY433 @ SY432 @ SY431 @ SY430 ) @ SY429 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY428 @ SY432 @ SY431 @ SY427 ) @ SV75 ) )
| ! [SY434: $i] :
( ( hAPP @ SY430 @ ( hAPP @ SY429 @ SY434 ) )
= ( hAPP @ SY427 @ ( hAPP @ SV75 @ SY434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1569,plain,
! [SV76: $i] :
( ( ! [SY435: $i,SY436: $i] :
( ~ ( class_Orderings_Oorder @ SY436 )
| ~ ( c_Orderings_Oord__class_Oless @ SY436 @ SY435 @ SV76 )
| ( SY435 != SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1570,plain,
! [SV77: $i] :
( ( ! [SY437: $i,SY438: $i,SY439: $i] :
( ~ ( class_Orderings_Oord @ SY439 )
| ~ ( c_Orderings_Oord__class_Oless @ SY439 @ SY438 @ SY437 )
| ( SY437 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SY439 @ SY438 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1571,plain,
! [SV78: $i] :
( ( ! [SY440: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY440 ) @ SV78 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY440 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1572,plain,
! [SV79: $i] :
( ( ! [SY441: $i,SY442: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY442 @ SY441 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY442 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV79 @ SY441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1573,plain,
! [SV80: $i] :
( ( ! [SY443: $i,SY444: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY444 @ SY443 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY444 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY443 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1574,plain,
! [SV81: $i] :
( ( ! [SY445: $i,SY446: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY446 @ SY445 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SY445 ) )
| ( SY446 = SV81 ) )
| ~ ( ( SY446 != SV81 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY446 @ SY445 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SY445 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1575,plain,
! [SV82: $i] :
( ( ! [SY447: $i,SY448: $i,SY449: $i,SY450: $i,SY451: $i,SY452: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY452 @ SY451 @ SY450 @ SY449 )
| ( ( hAPP @ SY448 @ ( hAPP @ SY449 @ SY447 ) )
!= ( hAPP @ SY449 @ SY447 ) )
| ( ( hAPP @ ( hAPP @ SY450 @ ( hAPP @ ( c_Fun_Ocomp @ SY452 @ SY452 @ SY452 @ SV82 ) @ SY448 ) ) @ SY447 )
= ( hAPP @ ( hAPP @ SY450 @ SV82 ) @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1576,plain,
! [SV83: $i] :
( ( ! [SY453: $i,SY454: $i] :
( ~ ( class_Orderings_Oorder @ SY454 )
| ~ ( c_Orderings_Oord__class_Oless @ SY454 @ SY453 @ SV83 )
| ( SY453 != SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1577,plain,
! [SV84: $i] :
( ( ! [SY455: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY455 @ SV84 )
| ( SV84 != SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1578,plain,
! [SV85: $i] :
( ( ! [SY456: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY456 @ SV85 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY456 ) @ ( c_Nat_OSuc @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1579,plain,
! [SV86: $i] :
( ( ! [SY457: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY457 ) @ ( c_Nat_OSuc @ SV86 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY457 @ SV86 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY457 @ SV86 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY457 ) @ ( c_Nat_OSuc @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1580,plain,
! [SV87: $i] :
( ( ! [SY458: $i,SY459: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY459 @ SY458 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY459 @ SV87 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY458 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1581,plain,
! [SV1: $i,SV88: $i] :
( ( ! [SY460: $i,SY461: $i,SY462: $i,SY463: $i,SY464: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY464 @ SY463 @ SY462 @ SY461 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY460 @ SY464 @ SY462 @ SV88 ) @ SV1 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY460 @ SY463 @ SY462 @ ( hAPP @ ( c_Fun_Ocomp @ SY464 @ SY463 @ SY460 @ SY461 ) @ SV88 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1582,plain,
! [SV2: $i,SV89: $i] :
( ( ! [SY465: $i,SY466: $i,SY467: $i,SY468: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY468 @ SY467 @ SY466 @ SY465 ) @ SV89 ) @ SV2 )
= ( hAPP @ SY465 @ ( hAPP @ SV89 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1583,plain,
! [SV3: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV3 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1584,plain,
! [SV4: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV4 @ SV4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1585,plain,
! [SV5: $i,SV90: $i] :
( ( ! [SY469: $i,SY470: $i,SY471: $i,SY472: $i,SY473: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY473 @ SY472 @ SY471 @ SY470 ) @ ( c_Fun_Oswap @ SY471 @ SY473 @ SY469 @ SV90 @ SV5 ) )
= ( c_Fun_Oswap @ SY471 @ SY472 @ SY469 @ SV90 @ ( hAPP @ ( c_Fun_Ocomp @ SY473 @ SY472 @ SY471 @ SY470 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1586,plain,
! [SV7: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV7 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1587,plain,
! [SV8: $i,SV91: $i] :
( ( ! [SY474: $i,SY475: $i] :
( ( hAPP @ SY475 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY474 @ SY474 ) @ SV91 ) @ SY475 ) @ SV8 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY474 @ SY474 ) @ SV91 ) @ SY475 ) @ ( hAPP @ SY475 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1588,plain,
! [SV9: $i,SV92: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SV92 @ SV9 )
| ( SV92 = SV9 )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SV9 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1589,plain,
! [SV10: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV10 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1590,plain,
! [SV11: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV11 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1591,plain,
! [SV12: $i,SV93: $i] :
( ( ! [SY476: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SY476 ) @ SV93 ) ) @ SV12 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SY476 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SV93 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1592,plain,
! [SV13: $i,SV94: $i] :
( ( ! [SY477: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY477 @ SV94 ) @ SV13 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY477 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV94 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1593,plain,
! [SV14: $i,SV95: $i] :
( ( ! [SY478: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY478 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV95 @ SV14 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV95 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY478 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1594,plain,
! [SV15: $i,SV96: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SV96 ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SV15 ) @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1595,plain,
! [SV16: $i,SV97: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV97 @ SV16 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV16 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1596,plain,
! [SV17: $i,SV98: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV98 @ SV17 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1597,plain,
! [SV18: $i,SV99: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV99 @ SV18 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1598,plain,
! [SV19: $i,SV100: $i] :
( ( ! [SY479: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY479 @ SV100 ) @ SV19 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY479 @ SV19 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1599,plain,
! [SV20: $i,SV101: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
| ~ ( ( SV20
!= ( c_Nat_OSuc @ SV101 ) ) )
| ~ ! [SY480: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SY480 )
| ( SV20
!= ( c_Nat_OSuc @ SY480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1600,plain,
! [SV21: $i,SV102: $i] :
( ( ! [SY481: $i] :
( ~ ( class_Orderings_Olinorder @ SY481 )
| ( c_Orderings_Oord__class_Oless @ SY481 @ SV102 @ SV21 )
| ( SV102 = SV21 )
| ( c_Orderings_Oord__class_Oless @ SY481 @ SV21 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1601,plain,
! [SV22: $i,SV103: $i] :
( ( ! [SY482: $i] :
( ~ ( class_Orderings_Opreorder @ SY482 )
| ~ ( c_Orderings_Oord__class_Oless @ SY482 @ SV103 @ SV22 )
| ~ ( c_Orderings_Oord__class_Oless @ SY482 @ SV22 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1602,plain,
! [SV23: $i,SV104: $i] :
( ( ! [SY483: $i,SY484: $i] :
( ~ ( class_Orderings_Oorder @ SY484 )
| ( SY483 != SV104 )
| ~ ( c_Orderings_Oord__class_Oless @ SY484 @ SV23 @ SV104 )
| ( c_Orderings_Oord__class_Oless @ SY484 @ SV23 @ SY483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1603,plain,
! [SV24: $i,SV105: $i] :
( ( ! [SY485: $i] :
( ~ ( class_Orderings_Olinorder @ SY485 )
| ~ ( ( SV105 != SV24 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY485 @ SV105 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SY485 @ SV24 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1604,plain,
! [SV25: $i,SV106: $i] :
( ( ! [SY486: $i,SY487: $i,SY488: $i,SY489: $i,SY490: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY490 @ SY489 @ SY488 @ SY487 ) @ SY486 )
!= SV106 )
| ( ( hAPP @ SY487 @ ( hAPP @ SY486 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1605,plain,
! [SV26: $i,SV107: $i] :
( ( ! [SY491: $i,SY492: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY492 @ SY491 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV107 @ SY491 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY492 @ SV26 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV107 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1606,plain,
! [SV27: $i,SV108: $i] :
( ( ! [SY493: $i,SY494: $i] :
( ~ ( class_Orderings_Opreorder @ SY494 )
| ~ ( c_Orderings_Oord__class_Oless @ SY494 @ SY493 @ SV108 )
| ~ ( c_Orderings_Oord__class_Oless @ SY494 @ SV108 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SY494 @ SY493 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1607,plain,
! [SV28: $i,SV109: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1608,plain,
! [SV29: $i,SV110: $i] :
( ( ! [SY495: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY495 @ SV110 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV110 @ SV29 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SY495 ) @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1609,plain,
! [SV30: $i,SV111: $i] :
( ( ! [SY496: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY496 @ SV111 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY496 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV111 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1610,plain,
! [SV31: $i,SV112: $i] :
( ( ! [SY497: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY497 @ SV112 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY497 @ SV31 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV112 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SY497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1611,plain,
! [SV32: $i,SV113: $i] :
( ( ! [SY498: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY498 @ SV113 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY498 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV32 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1612,plain,
! [SV33: $i,SV114: $i] :
( ( ! [SY499: $i,SY500: $i] :
( ~ ( class_Orderings_Oord @ SY500 )
| ( SY499 != SV114 )
| ~ ( c_Orderings_Oord__class_Oless @ SY500 @ SV114 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SY500 @ SY499 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1613,plain,
! [SV34: $i,SV115: $i] :
( ( ! [SY501: $i,SY502: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY502 @ SY501 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV115 @ SV34 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY502 @ SV115 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY501 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1614,plain,
! [SV35: $i] :
( ( ~ ( ~ ( c_SEQ_Osubseq @ SV35 )
| ! [SY345: $i,SY346: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY345 @ SY346 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY345 ) @ ( hAPP @ SV35 @ SY346 ) ) ) )
| ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY347 @ SY348 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY347 ) @ ( hAPP @ SV35 @ SY348 ) ) )
| ( c_SEQ_Osubseq @ SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1615,plain,
! [SV36: $i,SV116: $i] :
( ( ! [SY503: $i] :
( ~ ( class_Orderings_Opreorder @ SY503 )
| ~ ( c_Orderings_Oord__class_Oless @ SY503 @ SV116 @ SV36 )
| ~ ( c_Orderings_Oord__class_Oless @ SY503 @ SV36 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1616,plain,
! [SV37: $i,SV117: $i] :
( ( ! [SY504: $i,SY505: $i,SY506: $i,SY507: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY507 @ SY506 @ SY505 @ SY504 )
| ( ( hAPP @ SV117 @ ( hAPP @ SY504 @ SV37 ) )
!= ( hAPP @ SY504 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SY505 @ SV117 ) @ SV37 )
= SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1617,plain,
! [SV38: $i,SV118: $i] :
( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1618,plain,
! [SV39: $i] :
( ( ( ~ ( ( SV39
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1619,plain,
! [SV40: $i,SV119: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV119 @ SV40 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV119 @ ( c_Nat_OSuc @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1620,plain,
! [SV41: $i,SV120: $i] :
( ( ! [SY508: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY508 @ SV120 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY508 @ SV41 ) )
| ( SV120 = SV41 ) )
| ~ ( ( SV120 != SV41 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY508 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY508 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1621,plain,
! [SV42: $i,SV121: $i] :
( ( ~ ! [SY509: $i] :
( ( hAPP @ SV121 @ SY509 )
= ( hAPP @ SV42 @ SY509 ) )
| ( SV121 = SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1622,plain,
! [SV43: $i,SV122: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
!= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
| ( SV122 = SV43 ) )
| ~ ( ( SV122 != SV43 )
| ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1623,plain,
! [SV44: $i,SV123: $i] :
( ( ! [SY510: $i] :
( ~ ( class_Orderings_Opreorder @ SY510 )
| ~ ( c_Orderings_Oord__class_Oless @ SY510 @ SV123 @ SV44 )
| ~ ( c_Orderings_Oord__class_Oless @ SY510 @ SV44 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1624,plain,
! [SV45: $i,SV124: $i] :
( ( ! [SY511: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY511 @ SV124 ) @ SV45 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY511 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1625,plain,
! [SV46: $i,SV125: $i] :
( ( ! [SY512: $i] :
( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY512 @ SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SY512 ) ) )
| ~ ( ( SY512 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SY512 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SY512 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SY512 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SY512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1626,plain,
! [SV47: $i,SV126: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV126 @ SV47 )
| ( SV126 != SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1627,plain,
! [SV48: $i,SV127: $i] :
( ( ! [SY513: $i] :
( ~ ( class_Orderings_Opreorder @ SY513 )
| ~ ( c_Orderings_Oord__class_Oless @ SY513 @ SV127 @ SV48 )
| ~ ( c_Orderings_Oord__class_Oless @ SY513 @ SV48 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1628,plain,
! [SV49: $i,SV128: $i] :
( ( ! [SY514: $i] :
( ~ ( class_Orderings_Olinorder @ SY514 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY514 @ SV128 @ SV49 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SY514 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SY514 @ SV49 @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1629,plain,
! [SV50: $i,SV129: $i] :
( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
| ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
| ( SV129 = SV50 ) )
| ~ ( ( SV129 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1630,plain,
! [SV51: $i,SV130: $i] :
( ( ~ ( ( SV130 != SV51 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV130 @ SV51 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1631,plain,
! [SV52: $i,SV131: $i] :
( ( ! [SY515: $i] :
( ~ ( class_Orderings_Oorder @ SY515 )
| ~ ( c_Orderings_Oord__class_Oless @ SY515 @ SV131 @ SV52 )
| ~ ( c_Orderings_Oord__class_Oless @ SY515 @ SV52 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1632,plain,
! [SV53: $i,SV132: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ ( c_Nat_OSuc @ SV53 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ SV53 )
| ( SV132 = SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1633,plain,
! [SV54: $i,SV133: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ~ ( class_Orderings_Oorder @ SY517 )
| ~ ( c_Orderings_Oord__class_Oless @ SY517 @ SY516 @ SV133 )
| ~ ( c_Orderings_Oord__class_Oless @ SY517 @ SV54 @ SY516 )
| ( c_Orderings_Oord__class_Oless @ SY517 @ SV54 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1634,plain,
! [SV55: $i] :
( ( ~ ( ~ ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
| ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1635,plain,
! [SV56: $i,SV134: $i] :
( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ SV56 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ ( c_Nat_OSuc @ SV56 ) )
| ( SV56 = SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1636,plain,
! [SV57: $i,SV135: $i] :
( ( ! [SY518: $i] :
( ~ ( class_Orderings_Olinorder @ SY518 )
| ~ ( ~ ( ~ ( ( SV135 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SY518 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SY518 @ SV57 @ SV135 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SY518 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SY518 @ SV57 @ SV135 ) )
| ( SV135 != SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1637,plain,
! [SV58: $i,SV136: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV136 @ SV58 )
| ~ ( ( ( c_Nat_OSuc @ SV136 )
!= SV58 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV136 ) @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1638,plain,
! [SV59: $i,SV137: $i] :
( ( ! [SY519: $i] :
( ~ ( class_Rings_Olinordered__idom @ SY519 )
| ~ ( ( SV137 != SV59 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY519 @ SV137 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SY519 @ SV59 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1639,plain,
! [SV60: $i,SV138: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
| ~ ! [SY520: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV138 @ SY520 )
| ( SV60
!= ( c_Nat_OSuc @ SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1640,plain,
! [SV139: $i,SV61: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV61 @ SV139 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ SV61 ) @ ( hAPP @ v_ga____ @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1641,plain,
! [SV62: $i,SV140: $i] :
( ( ! [SY521: $i] :
( ~ ( class_Orderings_Olinorder @ SY521 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SY521 @ SV140 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SY521 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SY521 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SY521 @ SV140 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1642,plain,
! [SV63: $i,SV141: $i] :
( ( ! [SY522: $i] :
~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY522 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY522 @ SV63 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY522 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY522 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1643,plain,
! [SV64: $i,SV142: $i] :
( ( ~ ( ~ ( ~ ( ( SV142 != SV64 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
| ( SV142 != SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1644,plain,
! [SV65: $i,SV143: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV143 @ SV65 )
| ( SV65
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1645,plain,
! [SV66: $i,SV144: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV144 )
| ~ ( c_Orderings_Oord__class_Oless @ SV144 @ SV66 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1646,plain,
! [SV67: $i,SV145: $i] :
( ( ! [SY523: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY523 @ SV145 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY523 @ SV67 ) @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1647,plain,
! [SV68: $i,SV146: $i] :
( ( ! [SY524: $i,SY525: $i] :
( ~ ( class_Orderings_Oorder @ SY525 )
| ~ ( c_Orderings_Oord__class_Oless @ SY525 @ SY524 @ SV146 )
| ( SY524 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SY525 @ SV68 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1648,plain,
! [SV147: $i,SV69: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV69 @ SV147 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ SV69 ) @ ( hAPP @ v_f____ @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1649,plain,
! [SV70: $i,SV148: $i] :
( ( ! [SY526: $i] :
( ~ ( class_Orderings_Olinorder @ SY526 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SY526 @ SV148 @ SV70 )
| ~ ( ( SV148 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SY526 @ SV70 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1650,plain,
! [SV71: $i,SV149: $i] :
( ( ! [SY527: $i] :
( ~ ( class_Orderings_Oorder @ SY527 )
| ~ ( c_Orderings_Oord__class_Oless @ SY527 @ SV149 @ SV71 )
| ( SV71 != SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1651,plain,
! [SV72: $i,SV150: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV150 ) @ ( c_Nat_OSuc @ SV72 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV150 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1652,plain,
! [SV73: $i,SV151: $i] :
( ( ! [SY528: $i,SY529: $i,SY530: $i,SY531: $i,SY532: $i,SY533: $i,SY534: $i,SY535: $i,SY536: $i] :
( ( ( hAPP @ SY536 @ ( hAPP @ SY535 @ SY534 ) )
!= ( hAPP @ SY533 @ ( hAPP @ SY532 @ SY531 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY530 @ SY529 @ SY528 @ SY536 ) @ SY535 ) @ SY534 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SY529 @ SV73 @ SY533 ) @ SY532 ) @ SY531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1653,plain,
! [SV74: $i,SV152: $i] :
( ( ! [SY537: $i,SY538: $i,SY539: $i,SY540: $i,SY541: $i,SY542: $i,SY543: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY543 @ SY542 @ SY541 @ SY540 ) @ SY539 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY538 @ SY542 @ SY541 @ SY537 ) @ SV152 ) )
| ( ( hAPP @ SY540 @ ( hAPP @ SY539 @ SV74 ) )
= ( hAPP @ SY537 @ ( hAPP @ SV152 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1654,plain,
! [SV75: $i,SV153: $i] :
( ( ! [SY544: $i,SY545: $i,SY546: $i,SY547: $i,SY548: $i,SY549: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY549 @ SY548 @ SY547 @ SY546 ) @ SY545 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY544 @ SY548 @ SY547 @ SV153 ) @ SV75 ) )
| ! [SY550: $i] :
( ( hAPP @ SY546 @ ( hAPP @ SY545 @ SY550 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1655,plain,
! [SV76: $i,SV154: $i] :
( ( ! [SY551: $i] :
( ~ ( class_Orderings_Oorder @ SY551 )
| ~ ( c_Orderings_Oord__class_Oless @ SY551 @ SV154 @ SV76 )
| ( SV154 != SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1656,plain,
! [SV77: $i,SV155: $i] :
( ( ! [SY552: $i,SY553: $i] :
( ~ ( class_Orderings_Oord @ SY553 )
| ~ ( c_Orderings_Oord__class_Oless @ SY553 @ SY552 @ SV155 )
| ( SV155 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SY553 @ SY552 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1657,plain,
! [SV78: $i,SV156: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV156 ) @ SV78 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1658,plain,
! [SV79: $i,SV157: $i] :
( ( ! [SY554: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY554 @ SV157 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY554 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV79 @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1659,plain,
! [SV80: $i,SV158: $i] :
( ( ! [SY555: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY555 @ SV158 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY555 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV158 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1660,plain,
! [SV81: $i,SV159: $i] :
( ( ! [SY556: $i] :
~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY556 @ SV159 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
| ( SY556 = SV81 ) )
| ~ ( ( SY556 != SV81 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY556 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1661,plain,
! [SV82: $i,SV160: $i] :
( ( ! [SY557: $i,SY558: $i,SY559: $i,SY560: $i,SY561: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY561 @ SY560 @ SY559 @ SY558 )
| ( ( hAPP @ SY557 @ ( hAPP @ SY558 @ SV160 ) )
!= ( hAPP @ SY558 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SY559 @ ( hAPP @ ( c_Fun_Ocomp @ SY561 @ SY561 @ SY561 @ SV82 ) @ SY557 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SY559 @ SV82 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1662,plain,
! [SV83: $i,SV161: $i] :
( ( ! [SY562: $i] :
( ~ ( class_Orderings_Oorder @ SY562 )
| ~ ( c_Orderings_Oord__class_Oless @ SY562 @ SV161 @ SV83 )
| ( SV161 != SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1663,plain,
! [SV84: $i,SV162: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV162 @ SV84 )
| ( SV84 != SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1664,plain,
! [SV85: $i,SV163: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV163 @ SV85 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV163 ) @ ( c_Nat_OSuc @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1665,plain,
! [SV86: $i,SV164: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1666,plain,
! [SV87: $i,SV165: $i] :
( ( ! [SY563: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY563 @ SV165 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY563 @ SV87 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV165 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1667,plain,
! [SV1: $i,SV88: $i,SV166: $i] :
( ( ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY567 @ SY566 @ SY565 @ SY564 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SY567 @ SY565 @ SV88 ) @ SV1 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SY566 @ SY565 @ ( hAPP @ ( c_Fun_Ocomp @ SY567 @ SY566 @ SV166 @ SY564 ) @ SV88 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1668,plain,
! [SV2: $i,SV89: $i,SV167: $i] :
( ( ! [SY568: $i,SY569: $i,SY570: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY570 @ SY569 @ SY568 @ SV167 ) @ SV89 ) @ SV2 )
= ( hAPP @ SV167 @ ( hAPP @ SV89 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1669,plain,
! [SV5: $i,SV90: $i,SV168: $i] :
( ( ! [SY571: $i,SY572: $i,SY573: $i,SY574: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY574 @ SY573 @ SY572 @ SY571 ) @ ( c_Fun_Oswap @ SY572 @ SY574 @ SV168 @ SV90 @ SV5 ) )
= ( c_Fun_Oswap @ SY572 @ SY573 @ SV168 @ SV90 @ ( hAPP @ ( c_Fun_Ocomp @ SY574 @ SY573 @ SY572 @ SY571 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1670,plain,
! [SV8: $i,SV91: $i,SV169: $i] :
( ( ! [SY575: $i] :
( ( hAPP @ SY575 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV169 @ SV169 ) @ SV91 ) @ SY575 ) @ SV8 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV169 @ SV169 ) @ SV91 ) @ SY575 ) @ ( hAPP @ SY575 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1671,plain,
! [SV9: $i,SV92: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SV92 @ SV9 )
| ( SV92 = SV9 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SV9 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1672,plain,
! [SV12: $i,SV93: $i,SV170: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SV170 ) @ SV93 ) ) @ SV12 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SV170 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ SV93 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1673,plain,
! [SV13: $i,SV94: $i,SV171: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV171 @ SV94 ) @ SV13 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV171 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV94 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1674,plain,
! [SV14: $i,SV95: $i,SV172: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV172 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV95 @ SV14 ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV95 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV172 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1675,plain,
! [SV17: $i,SV98: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV98 @ SV17 ) @ SV98 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1676,plain,
! [SV18: $i,SV99: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV99 @ SV18 ) @ SV18 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1677,plain,
! [SV19: $i,SV100: $i,SV173: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV173 @ SV100 ) @ SV19 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV173 @ SV19 ) @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1678,plain,
! [SV20: $i,SV101: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 ) )
= $true )
| ( ( ~ ( ( SV20
!= ( c_Nat_OSuc @ SV101 ) ) )
| ~ ! [SY480: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SY480 )
| ( SV20
!= ( c_Nat_OSuc @ SY480 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1679,plain,
! [SV21: $i,SV102: $i,SV174: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV174 )
| ( c_Orderings_Oord__class_Oless @ SV174 @ SV102 @ SV21 )
| ( SV102 = SV21 )
| ( c_Orderings_Oord__class_Oless @ SV174 @ SV21 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1680,plain,
! [SV22: $i,SV103: $i,SV175: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV175 )
| ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV103 @ SV22 )
| ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV22 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1681,plain,
! [SV23: $i,SV104: $i,SV176: $i] :
( ( ! [SY576: $i] :
( ~ ( class_Orderings_Oorder @ SY576 )
| ( SV176 != SV104 )
| ~ ( c_Orderings_Oord__class_Oless @ SY576 @ SV23 @ SV104 )
| ( c_Orderings_Oord__class_Oless @ SY576 @ SV23 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1682,plain,
! [SV24: $i,SV105: $i,SV177: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV177 )
| ~ ( ( SV105 != SV24 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1683,plain,
! [SV25: $i,SV106: $i,SV178: $i] :
( ( ! [SY577: $i,SY578: $i,SY579: $i,SY580: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY580 @ SY579 @ SY578 @ SY577 ) @ SV178 )
!= SV106 )
| ( ( hAPP @ SY577 @ ( hAPP @ SV178 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1684,plain,
! [SV26: $i,SV107: $i,SV179: $i] :
( ( ! [SY581: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY581 @ SV179 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV107 @ SV179 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY581 @ SV26 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV107 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1685,plain,
! [SV27: $i,SV108: $i,SV180: $i] :
( ( ! [SY582: $i] :
( ~ ( class_Orderings_Opreorder @ SY582 )
| ~ ( c_Orderings_Oord__class_Oless @ SY582 @ SV180 @ SV108 )
| ~ ( c_Orderings_Oord__class_Oless @ SY582 @ SV108 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SY582 @ SV180 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1686,plain,
! [SV28: $i,SV109: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1687,plain,
! [SV29: $i,SV110: $i,SV181: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV110 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV110 @ SV29 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV181 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1688,plain,
! [SV30: $i,SV111: $i,SV182: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV182 @ SV111 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV182 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV111 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1689,plain,
! [SV31: $i,SV112: $i,SV183: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV112 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV31 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV112 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1690,plain,
! [SV32: $i,SV113: $i,SV184: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV184 @ SV113 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV184 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV32 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1691,plain,
! [SV33: $i,SV114: $i,SV185: $i] :
( ( ! [SY583: $i] :
( ~ ( class_Orderings_Oord @ SY583 )
| ( SV185 != SV114 )
| ~ ( c_Orderings_Oord__class_Oless @ SY583 @ SV114 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SY583 @ SV185 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1692,plain,
! [SV34: $i,SV115: $i,SV186: $i] :
( ( ! [SY584: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY584 @ SV186 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV115 @ SV34 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SY584 @ SV115 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV186 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1693,plain,
! [SV35: $i] :
( ( ~ ( ~ ( c_SEQ_Osubseq @ SV35 )
| ! [SY345: $i,SY346: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY345 @ SY346 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY345 ) @ ( hAPP @ SV35 @ SY346 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1694,plain,
! [SV35: $i] :
( ( ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY347 @ SY348 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY347 ) @ ( hAPP @ SV35 @ SY348 ) ) )
| ( c_SEQ_Osubseq @ SV35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1695,plain,
! [SV36: $i,SV116: $i,SV187: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV187 )
| ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV116 @ SV36 )
| ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV36 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1696,plain,
! [SV37: $i,SV117: $i,SV188: $i] :
( ( ! [SY585: $i,SY586: $i,SY587: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY587 @ SY586 @ SY585 @ SV188 )
| ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
!= ( hAPP @ SV188 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SY585 @ SV117 ) @ SV37 )
= SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1697,plain,
! [SV38: $i,SV118: $i] :
( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1698,plain,
! [SV39: $i] :
( ( ( SV39
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1699,plain,
! [SV40: $i,SV119: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV119 @ SV40 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV119 @ ( c_Nat_OSuc @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1700,plain,
! [SV41: $i,SV120: $i,SV189: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
| ( SV120 = SV41 ) )
| ~ ( ( SV120 != SV41 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1701,plain,
! [SV42: $i,SV121: $i] :
( ( ( ~ ! [SY509: $i] :
( ( hAPP @ SV121 @ SY509 )
= ( hAPP @ SV42 @ SY509 ) ) )
= $true )
| ( ( SV121 = SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1702,plain,
! [SV43: $i,SV122: $i] :
( ( ~ ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
!= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
| ( SV122 = SV43 ) )
| ~ ( ( SV122 != SV43 )
| ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1703,plain,
! [SV44: $i,SV123: $i,SV190: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV190 )
| ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV123 @ SV44 )
| ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV44 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1704,plain,
! [SV45: $i,SV124: $i,SV191: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV191 @ SV124 ) @ SV45 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV191 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1705,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1706,plain,
! [SV47: $i,SV126: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV126 @ SV47 ) )
= $true )
| ( ( SV126 != SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1707,plain,
! [SV48: $i,SV127: $i,SV193: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV193 )
| ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV127 @ SV48 )
| ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV48 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1708,plain,
! [SV49: $i,SV128: $i,SV194: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV194 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1709,plain,
! [SV50: $i,SV129: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
| ( SV129 = SV50 ) )
| ~ ( ( SV129 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1710,plain,
! [SV51: $i,SV130: $i] :
( ( ( ~ ( ( SV130 != SV51 ) ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV130 @ SV51 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1711,plain,
! [SV52: $i,SV131: $i,SV195: $i] :
( ( ~ ( class_Orderings_Oorder @ SV195 )
| ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV131 @ SV52 )
| ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV52 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1712,plain,
! [SV53: $i,SV132: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ ( c_Nat_OSuc @ SV53 ) ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ SV53 )
| ( SV132 = SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1713,plain,
! [SV54: $i,SV133: $i,SV196: $i] :
( ( ! [SY588: $i] :
( ~ ( class_Orderings_Oorder @ SY588 )
| ~ ( c_Orderings_Oord__class_Oless @ SY588 @ SV196 @ SV133 )
| ~ ( c_Orderings_Oord__class_Oless @ SY588 @ SV54 @ SV196 )
| ( c_Orderings_Oord__class_Oless @ SY588 @ SV54 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1714,plain,
! [SV55: $i] :
( ( ~ ( ~ ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1715,plain,
! [SV55: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
| ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1716,plain,
! [SV56: $i,SV134: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ SV56 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ ( c_Nat_OSuc @ SV56 ) )
| ( SV56 = SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1717,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV197 )
| ~ ( ~ ( ~ ( ( SV135 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ( SV135 != SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1718,plain,
! [SV58: $i,SV136: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV136 @ SV58 ) )
= $true )
| ( ( ~ ( ( ( c_Nat_OSuc @ SV136 )
!= SV58 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV136 ) @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1719,plain,
! [SV59: $i,SV137: $i,SV198: $i] :
( ( ~ ( class_Rings_Olinordered__idom @ SV198 )
| ~ ( ( SV137 != SV59 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1720,plain,
! [SV60: $i,SV138: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 ) )
= $true )
| ( ( ~ ! [SY520: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV138 @ SY520 )
| ( SV60
!= ( c_Nat_OSuc @ SY520 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1721,plain,
! [SV139: $i,SV61: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV61 @ SV139 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ SV61 ) @ ( hAPP @ v_ga____ @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1722,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV199 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1723,plain,
! [SV63: $i,SV141: $i,SV200: $i] :
( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1724,plain,
! [SV64: $i,SV142: $i] :
( ( ~ ( ~ ( ( SV142 != SV64 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
| ( SV142 != SV64 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1725,plain,
! [SV65: $i,SV143: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV143 @ SV65 ) )
= $true )
| ( ( SV65
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1726,plain,
! [SV66: $i,SV144: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV144 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV144 @ SV66 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1727,plain,
! [SV67: $i,SV145: $i,SV201: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV201 @ SV145 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV201 @ SV67 ) @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1728,plain,
! [SV68: $i,SV146: $i,SV202: $i] :
( ( ! [SY589: $i] :
( ~ ( class_Orderings_Oorder @ SY589 )
| ~ ( c_Orderings_Oord__class_Oless @ SY589 @ SV202 @ SV146 )
| ( SV202 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SY589 @ SV68 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1729,plain,
! [SV147: $i,SV69: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV69 @ SV147 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ SV69 ) @ ( hAPP @ v_f____ @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1730,plain,
! [SV70: $i,SV148: $i,SV203: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV203 )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 )
| ~ ( ( SV148 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1731,plain,
! [SV71: $i,SV149: $i,SV204: $i] :
( ( ~ ( class_Orderings_Oorder @ SV204 )
| ~ ( c_Orderings_Oord__class_Oless @ SV204 @ SV149 @ SV71 )
| ( SV71 != SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1732,plain,
! [SV72: $i,SV150: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV150 ) @ ( c_Nat_OSuc @ SV72 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV150 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1733,plain,
! [SV73: $i,SV151: $i,SV205: $i] :
( ( ! [SY590: $i,SY591: $i,SY592: $i,SY593: $i,SY594: $i,SY595: $i,SY596: $i,SY597: $i] :
( ( ( hAPP @ SY597 @ ( hAPP @ SY596 @ SY595 ) )
!= ( hAPP @ SY594 @ ( hAPP @ SY593 @ SY592 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY591 @ SY590 @ SV205 @ SY597 ) @ SY596 ) @ SY595 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SY590 @ SV73 @ SY594 ) @ SY593 ) @ SY592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1734,plain,
! [SV74: $i,SV152: $i,SV206: $i] :
( ( ! [SY598: $i,SY599: $i,SY600: $i,SY601: $i,SY602: $i,SY603: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY603 @ SY602 @ SY601 @ SY600 ) @ SY599 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY598 @ SY602 @ SY601 @ SV206 ) @ SV152 ) )
| ( ( hAPP @ SY600 @ ( hAPP @ SY599 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1735,plain,
! [SV75: $i,SV153: $i,SV207: $i] :
( ( ! [SY604: $i,SY605: $i,SY606: $i,SY607: $i,SY608: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY608 @ SY607 @ SY606 @ SY605 ) @ SY604 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SY607 @ SY606 @ SV153 ) @ SV75 ) )
| ! [SY550: $i] :
( ( hAPP @ SY605 @ ( hAPP @ SY604 @ SY550 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1736,plain,
! [SV76: $i,SV154: $i,SV208: $i] :
( ( ~ ( class_Orderings_Oorder @ SV208 )
| ~ ( c_Orderings_Oord__class_Oless @ SV208 @ SV154 @ SV76 )
| ( SV154 != SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1737,plain,
! [SV77: $i,SV155: $i,SV209: $i] :
( ( ! [SY610: $i] :
( ~ ( class_Orderings_Oord @ SY610 )
| ~ ( c_Orderings_Oord__class_Oless @ SY610 @ SV209 @ SV155 )
| ( SV155 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SY610 @ SV209 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1738,plain,
! [SV78: $i,SV156: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV156 ) @ SV78 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1739,plain,
! [SV79: $i,SV157: $i,SV210: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV210 @ SV157 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV210 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV79 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1740,plain,
! [SV80: $i,SV158: $i,SV211: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV211 @ SV158 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV211 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV158 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1741,plain,
! [SV81: $i,SV159: $i,SV212: $i] :
( ( ~ ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
| ( SV212 = SV81 ) )
| ~ ( ( SV212 != SV81 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1742,plain,
! [SV82: $i,SV160: $i,SV213: $i] :
( ( ! [SY611: $i,SY612: $i,SY613: $i,SY614: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY614 @ SY613 @ SY612 @ SY611 )
| ( ( hAPP @ SV213 @ ( hAPP @ SY611 @ SV160 ) )
!= ( hAPP @ SY611 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SY612 @ ( hAPP @ ( c_Fun_Ocomp @ SY614 @ SY614 @ SY614 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SY612 @ SV82 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1743,plain,
! [SV83: $i,SV161: $i,SV214: $i] :
( ( ~ ( class_Orderings_Oorder @ SV214 )
| ~ ( c_Orderings_Oord__class_Oless @ SV214 @ SV161 @ SV83 )
| ( SV161 != SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1744,plain,
! [SV84: $i,SV162: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV162 @ SV84 ) )
= $true )
| ( ( SV84 != SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1745,plain,
! [SV85: $i,SV163: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV163 @ SV85 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV163 ) @ ( c_Nat_OSuc @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1746,plain,
! [SV86: $i,SV164: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1747,plain,
! [SV87: $i,SV165: $i,SV215: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV215 @ SV165 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV215 @ SV87 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV165 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1748,plain,
! [SV1: $i,SV88: $i,SV166: $i,SV216: $i] :
( ( ! [SY615: $i,SY616: $i,SY617: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY617 @ SY616 @ SY615 @ SV216 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SY617 @ SY615 @ SV88 ) @ SV1 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SY616 @ SY615 @ ( hAPP @ ( c_Fun_Ocomp @ SY617 @ SY616 @ SV166 @ SV216 ) @ SV88 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1749,plain,
! [SV2: $i,SV89: $i,SV167: $i,SV217: $i] :
( ( ! [SY618: $i,SY619: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY619 @ SY618 @ SV217 @ SV167 ) @ SV89 ) @ SV2 )
= ( hAPP @ SV167 @ ( hAPP @ SV89 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1750,plain,
! [SV5: $i,SV90: $i,SV168: $i,SV218: $i] :
( ( ! [SY620: $i,SY621: $i,SY622: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY622 @ SY621 @ SY620 @ SV218 ) @ ( c_Fun_Oswap @ SY620 @ SY622 @ SV168 @ SV90 @ SV5 ) )
= ( c_Fun_Oswap @ SY620 @ SY621 @ SV168 @ SV90 @ ( hAPP @ ( c_Fun_Ocomp @ SY622 @ SY621 @ SY620 @ SV218 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1751,plain,
! [SV8: $i,SV91: $i,SV169: $i,SV219: $i] :
( ( ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV169 @ SV169 ) @ SV91 ) @ SV219 ) @ SV8 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV169 @ SV169 ) @ SV91 ) @ SV219 ) @ ( hAPP @ SV219 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1752,plain,
! [SV9: $i,SV92: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SV92 @ SV9 )
= $true )
| ( ( SV92 = SV9 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ SV9 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1753,plain,
! [SV20: $i,SV101: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false )
| ( ( ~ ( ( SV20
!= ( c_Nat_OSuc @ SV101 ) ) )
| ~ ! [SY480: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SY480 )
| ( SV20
!= ( c_Nat_OSuc @ SY480 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1754,plain,
! [SV21: $i,SV102: $i,SV174: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV174 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ SV174 @ SV102 @ SV21 )
| ( SV102 = SV21 )
| ( c_Orderings_Oord__class_Oless @ SV174 @ SV21 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1755,plain,
! [SV22: $i,SV103: $i,SV175: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV175 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV103 @ SV22 )
| ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV22 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1756,plain,
! [SV23: $i,SV104: $i,SV176: $i,SV220: $i] :
( ( ~ ( class_Orderings_Oorder @ SV220 )
| ( SV176 != SV104 )
| ~ ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV104 )
| ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1757,plain,
! [SV24: $i,SV105: $i,SV177: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV177 ) )
= $true )
| ( ( ~ ( ( SV105 != SV24 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1758,plain,
! [SV25: $i,SV106: $i,SV178: $i,SV221: $i] :
( ( ! [SY623: $i,SY624: $i,SY625: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY625 @ SY624 @ SY623 @ SV221 ) @ SV178 )
!= SV106 )
| ( ( hAPP @ SV221 @ ( hAPP @ SV178 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1759,plain,
! [SV26: $i,SV107: $i,SV179: $i,SV222: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV222 @ SV179 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV107 @ SV179 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV222 @ SV26 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV107 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1760,plain,
! [SV27: $i,SV108: $i,SV180: $i,SV223: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV223 )
| ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV108 )
| ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV108 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1761,plain,
! [SV28: $i,SV109: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1762,plain,
! [SV28: $i,SV109: $i] :
( ( ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1763,plain,
! [SV29: $i,SV110: $i,SV181: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV110 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV110 @ SV29 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV181 ) @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1764,plain,
! [SV30: $i,SV111: $i,SV182: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV182 @ SV111 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV182 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV111 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1765,plain,
! [SV31: $i,SV112: $i,SV183: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV112 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV31 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV112 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1766,plain,
! [SV32: $i,SV113: $i,SV184: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV184 @ SV113 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV184 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV32 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1767,plain,
! [SV33: $i,SV114: $i,SV185: $i,SV224: $i] :
( ( ~ ( class_Orderings_Oord @ SV224 )
| ( SV185 != SV114 )
| ~ ( c_Orderings_Oord__class_Oless @ SV224 @ SV114 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SV224 @ SV185 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1768,plain,
! [SV34: $i,SV115: $i,SV186: $i,SV225: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV225 @ SV186 )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV115 @ SV34 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV225 @ SV115 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV186 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1769,plain,
! [SV35: $i] :
( ( ~ ( c_SEQ_Osubseq @ SV35 )
| ! [SY345: $i,SY346: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY345 @ SY346 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY345 ) @ ( hAPP @ SV35 @ SY346 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1770,plain,
! [SV35: $i] :
( ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY347 @ SY348 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY347 ) @ ( hAPP @ SV35 @ SY348 ) ) )
| ( c_SEQ_Osubseq @ SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1771,plain,
! [SV36: $i,SV116: $i,SV187: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV187 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV116 @ SV36 )
| ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV36 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1772,plain,
! [SV37: $i,SV117: $i,SV188: $i,SV226: $i] :
( ( ! [SY626: $i,SY627: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY627 @ SY626 @ SV226 @ SV188 )
| ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
!= ( hAPP @ SV188 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SV226 @ SV117 ) @ SV37 )
= SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1773,plain,
! [SV38: $i,SV118: $i] :
( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1774,plain,
! [SV118: $i,SV38: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1775,plain,
! [SV39: $i] :
( ( ( SV39
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1776,plain,
! [SV40: $i,SV119: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV119 @ SV40 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV119 @ ( c_Nat_OSuc @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1777,plain,
! [SV41: $i,SV120: $i,SV189: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
| ( SV120 = SV41 ) )
| ~ ( ( SV120 != SV41 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1778,plain,
! [SV42: $i,SV121: $i] :
( ( ( ! [SY509: $i] :
( ( hAPP @ SV121 @ SY509 )
= ( hAPP @ SV42 @ SY509 ) ) )
= $false )
| ( ( SV121 = SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1779,plain,
! [SV43: $i,SV122: $i] :
( ( ~ ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
!= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
| ( SV122 = SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1780,plain,
! [SV43: $i,SV122: $i] :
( ( ~ ( ( SV122 != SV43 )
| ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1781,plain,
! [SV44: $i,SV123: $i,SV190: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV190 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV123 @ SV44 )
| ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV44 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1782,plain,
! [SV45: $i,SV124: $i,SV191: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV191 @ SV124 ) @ SV45 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV191 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1783,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) ) )
= $true )
| ( ( ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1784,plain,
! [SV47: $i,SV126: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV126 @ SV47 )
= $false )
| ( ( SV126 != SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1785,plain,
! [SV48: $i,SV127: $i,SV193: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV193 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV127 @ SV48 )
| ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV48 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1786,plain,
! [SV49: $i,SV128: $i,SV194: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV194 ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1787,plain,
! [SV50: $i,SV129: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
| ( SV129 = SV50 ) )
| ~ ( ( SV129 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1788,plain,
! [SV51: $i,SV130: $i] :
( ( ( SV130 != SV51 )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV130 @ SV51 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1789,plain,
! [SV52: $i,SV131: $i,SV195: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV195 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV131 @ SV52 )
| ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV52 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1790,plain,
! [SV53: $i,SV132: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ ( c_Nat_OSuc @ SV53 ) )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ SV53 )
| ( SV132 = SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1791,plain,
! [SV54: $i,SV133: $i,SV196: $i,SV227: $i] :
( ( ~ ( class_Orderings_Oorder @ SV227 )
| ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV196 @ SV133 )
| ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV196 )
| ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1792,plain,
! [SV55: $i] :
( ( ~ ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1793,plain,
! [SV55: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
| ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1794,plain,
! [SV56: $i,SV134: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ SV56 ) )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ ( c_Nat_OSuc @ SV56 ) )
| ( SV56 = SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1795,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( SV135 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ( SV135 != SV57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1796,plain,
! [SV58: $i,SV136: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV136 @ SV58 )
= $false )
| ( ( ~ ( ( ( c_Nat_OSuc @ SV136 )
!= SV58 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV136 ) @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1797,plain,
! [SV59: $i,SV137: $i,SV198: $i] :
( ( ( ~ ( class_Rings_Olinordered__idom @ SV198 ) )
= $true )
| ( ( ~ ( ( SV137 != SV59 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1798,plain,
! [SV60: $i,SV138: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
= $false )
| ( ( ~ ! [SY520: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV138 @ SY520 )
| ( SV60
!= ( c_Nat_OSuc @ SY520 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1799,plain,
! [SV139: $i,SV61: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV61 @ SV139 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ SV61 ) @ ( hAPP @ v_ga____ @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1800,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV199 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1801,plain,
! [SV63: $i,SV141: $i,SV200: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1802,plain,
! [SV64: $i,SV142: $i] :
( ( ~ ( ~ ( ( SV142 != SV64 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1803,plain,
! [SV64: $i,SV142: $i] :
( ( ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
| ( SV142 != SV64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1804,plain,
! [SV65: $i,SV143: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV143 @ SV65 )
= $false )
| ( ( SV65
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1805,plain,
! [SV66: $i,SV144: $i] :
( ( ( class_Orderings_Opreorder @ SV144 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV144 @ SV66 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1806,plain,
! [SV67: $i,SV145: $i,SV201: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV201 @ SV145 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV201 @ SV67 ) @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1807,plain,
! [SV68: $i,SV146: $i,SV202: $i,SV228: $i] :
( ( ~ ( class_Orderings_Oorder @ SV228 )
| ~ ( c_Orderings_Oord__class_Oless @ SV228 @ SV202 @ SV146 )
| ( SV202 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SV228 @ SV68 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(1808,plain,
! [SV147: $i,SV69: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV69 @ SV147 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ SV69 ) @ ( hAPP @ v_f____ @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1809,plain,
! [SV70: $i,SV148: $i,SV203: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV203 ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 )
| ~ ( ( SV148 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(1810,plain,
! [SV71: $i,SV149: $i,SV204: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV204 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV204 @ SV149 @ SV71 )
| ( SV71 != SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1811,plain,
! [SV72: $i,SV150: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV150 ) @ ( c_Nat_OSuc @ SV72 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV150 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1812,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i] :
( ( ! [SY628: $i,SY629: $i,SY630: $i,SY631: $i,SY632: $i,SY633: $i,SY634: $i] :
( ( ( hAPP @ SY634 @ ( hAPP @ SY633 @ SY632 ) )
!= ( hAPP @ SY631 @ ( hAPP @ SY630 @ SY629 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY628 @ SV229 @ SV205 @ SY634 ) @ SY633 ) @ SY632 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SY631 ) @ SY630 ) @ SY629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(1813,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i] :
( ( ! [SY635: $i,SY636: $i,SY637: $i,SY638: $i,SY639: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY639 @ SY638 @ SY637 @ SY636 ) @ SY635 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SY638 @ SY637 @ SV206 ) @ SV152 ) )
| ( ( hAPP @ SY636 @ ( hAPP @ SY635 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1814,plain,
! [SV75: $i,SV153: $i,SV207: $i,SV231: $i] :
( ( ! [SY640: $i,SY641: $i,SY642: $i,SY643: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY643 @ SY642 @ SY641 @ SY640 ) @ SV231 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SY642 @ SY641 @ SV153 ) @ SV75 ) )
| ! [SY644: $i] :
( ( hAPP @ SY640 @ ( hAPP @ SV231 @ SY644 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(1815,plain,
! [SV76: $i,SV154: $i,SV208: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV208 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV208 @ SV154 @ SV76 )
| ( SV154 != SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1816,plain,
! [SV77: $i,SV155: $i,SV209: $i,SV232: $i] :
( ( ~ ( class_Orderings_Oord @ SV232 )
| ~ ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV155 )
| ( SV155 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1817,plain,
! [SV78: $i,SV156: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV156 ) @ SV78 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV156 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1818,plain,
! [SV79: $i,SV157: $i,SV210: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV210 @ SV157 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV210 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV79 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1819,plain,
! [SV80: $i,SV158: $i,SV211: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV211 @ SV158 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV211 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV158 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1820,plain,
! [SV81: $i,SV159: $i,SV212: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
| ( SV212 = SV81 ) )
| ~ ( ( SV212 != SV81 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1821,plain,
! [SV82: $i,SV160: $i,SV213: $i,SV233: $i] :
( ( ! [SY645: $i,SY646: $i,SY647: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY647 @ SY646 @ SY645 @ SV233 )
| ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
!= ( hAPP @ SV233 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SY645 @ ( hAPP @ ( c_Fun_Ocomp @ SY647 @ SY647 @ SY647 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SY645 @ SV82 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1822,plain,
! [SV83: $i,SV161: $i,SV214: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV214 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV214 @ SV161 @ SV83 )
| ( SV161 != SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(1823,plain,
! [SV84: $i,SV162: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV162 @ SV84 )
= $false )
| ( ( SV84 != SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1824,plain,
! [SV85: $i,SV163: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV163 @ SV85 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV163 ) @ ( c_Nat_OSuc @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1825,plain,
! [SV86: $i,SV164: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1826,plain,
! [SV86: $i,SV164: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1827,plain,
! [SV87: $i,SV165: $i,SV215: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV215 @ SV165 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV215 @ SV87 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV165 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1828,plain,
! [SV1: $i,SV88: $i,SV166: $i,SV216: $i,SV234: $i] :
( ( ! [SY648: $i,SY649: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY649 @ SY648 @ SV234 @ SV216 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SY649 @ SV234 @ SV88 ) @ SV1 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SY648 @ SV234 @ ( hAPP @ ( c_Fun_Ocomp @ SY649 @ SY648 @ SV166 @ SV216 ) @ SV88 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(1829,plain,
! [SV2: $i,SV89: $i,SV167: $i,SV217: $i,SV235: $i] :
( ( ! [SY650: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY650 @ SV235 @ SV217 @ SV167 ) @ SV89 ) @ SV2 )
= ( hAPP @ SV167 @ ( hAPP @ SV89 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(1830,plain,
! [SV5: $i,SV90: $i,SV168: $i,SV218: $i,SV236: $i] :
( ( ! [SY651: $i,SY652: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY652 @ SY651 @ SV236 @ SV218 ) @ ( c_Fun_Oswap @ SV236 @ SY652 @ SV168 @ SV90 @ SV5 ) )
= ( c_Fun_Oswap @ SV236 @ SY651 @ SV168 @ SV90 @ ( hAPP @ ( c_Fun_Ocomp @ SY652 @ SY651 @ SV236 @ SV218 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1831,plain,
! [SV101: $i,SV20: $i] :
( ( ( ~ ( ( SV20
!= ( c_Nat_OSuc @ SV101 ) ) ) )
= $true )
| ( ( ~ ! [SY480: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SY480 )
| ( SV20
!= ( c_Nat_OSuc @ SY480 ) ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1832,plain,
! [SV21: $i,SV102: $i,SV174: $i] :
( ( ( class_Orderings_Olinorder @ SV174 )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ SV174 @ SV102 @ SV21 )
| ( SV102 = SV21 )
| ( c_Orderings_Oord__class_Oless @ SV174 @ SV21 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1833,plain,
! [SV22: $i,SV103: $i,SV175: $i] :
( ( ( class_Orderings_Opreorder @ SV175 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV103 @ SV22 )
| ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV22 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1834,plain,
! [SV23: $i,SV104: $i,SV176: $i,SV220: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV220 ) )
= $true )
| ( ( ( SV176 != SV104 )
| ~ ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV104 )
| ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1835,plain,
! [SV24: $i,SV105: $i,SV177: $i] :
( ( ( class_Orderings_Olinorder @ SV177 )
= $false )
| ( ( ~ ( ( SV105 != SV24 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1836,plain,
! [SV25: $i,SV106: $i,SV178: $i,SV221: $i,SV237: $i] :
( ( ! [SY653: $i,SY654: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY654 @ SY653 @ SV237 @ SV221 ) @ SV178 )
!= SV106 )
| ( ( hAPP @ SV221 @ ( hAPP @ SV178 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(1837,plain,
! [SV26: $i,SV107: $i,SV179: $i,SV222: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV222 @ SV179 ) )
= $true )
| ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV107 @ SV179 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV222 @ SV26 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV107 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1838,plain,
! [SV27: $i,SV108: $i,SV180: $i,SV223: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV223 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV108 )
| ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV108 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1839,plain,
! [SV28: $i,SV109: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1840,plain,
! [SV28: $i,SV109: $i] :
( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1841,plain,
! [SV29: $i,SV110: $i,SV181: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV110 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV110 @ SV29 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV181 ) @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1842,plain,
! [SV30: $i,SV111: $i,SV182: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV182 @ SV111 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV182 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV111 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1843,plain,
! [SV31: $i,SV112: $i,SV183: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV112 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV31 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV112 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1844,plain,
! [SV32: $i,SV113: $i,SV184: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV184 @ SV113 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV184 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV32 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1845,plain,
! [SV33: $i,SV114: $i,SV185: $i,SV224: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV224 ) )
= $true )
| ( ( ( SV185 != SV114 )
| ~ ( c_Orderings_Oord__class_Oless @ SV224 @ SV114 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SV224 @ SV185 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(1846,plain,
! [SV34: $i,SV115: $i,SV186: $i,SV225: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV225 @ SV186 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV115 @ SV34 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV225 @ SV115 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV186 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1847,plain,
! [SV35: $i] :
( ( ( ~ ( c_SEQ_Osubseq @ SV35 ) )
= $true )
| ( ( ! [SY345: $i,SY346: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY345 @ SY346 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY345 ) @ ( hAPP @ SV35 @ SY346 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1848,plain,
! [SV35: $i] :
( ( ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY347 @ SY348 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY347 ) @ ( hAPP @ SV35 @ SY348 ) ) ) )
= $true )
| ( ( c_SEQ_Osubseq @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1849,plain,
! [SV36: $i,SV116: $i,SV187: $i] :
( ( ( class_Orderings_Opreorder @ SV187 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV116 @ SV36 )
| ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV36 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1850,plain,
! [SV37: $i,SV117: $i,SV188: $i,SV226: $i,SV238: $i] :
( ( ! [SY655: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY655 @ SV238 @ SV226 @ SV188 )
| ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
!= ( hAPP @ SV188 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SV226 @ SV117 ) @ SV37 )
= SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1851,plain,
! [SV38: $i,SV118: $i] :
( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1852,plain,
! [SV118: $i,SV38: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1853,plain,
! [SV41: $i,SV120: $i,SV189: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
| ( SV120 = SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1777]) ).
thf(1854,plain,
! [SV189: $i,SV41: $i,SV120: $i] :
( ( ~ ( ( SV120 != SV41 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1777]) ).
thf(1855,plain,
! [SV42: $i,SV121: $i] :
( ( ( ( hAPP @ SV121 @ ( sK3_SY509 @ SV42 @ SV121 ) )
= ( hAPP @ SV42 @ ( sK3_SY509 @ SV42 @ SV121 ) ) )
= $false )
| ( ( SV121 = SV42 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1778]) ).
thf(1856,plain,
! [SV43: $i,SV122: $i] :
( ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
!= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
| ( SV122 = SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1857,plain,
! [SV43: $i,SV122: $i] :
( ( ( SV122 != SV43 )
| ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1858,plain,
! [SV44: $i,SV123: $i,SV190: $i] :
( ( ( class_Orderings_Opreorder @ SV190 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV123 @ SV44 )
| ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV44 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1859,plain,
! [SV45: $i,SV124: $i,SV191: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV191 @ SV124 ) @ SV45 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV191 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1860,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $false )
| ( ( ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1861,plain,
! [SV47: $i,SV126: $i] :
( ( ( SV126 = SV47 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV126 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1862,plain,
! [SV48: $i,SV127: $i,SV193: $i] :
( ( ( class_Orderings_Opreorder @ SV193 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV127 @ SV48 )
| ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV48 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1863,plain,
! [SV49: $i,SV128: $i,SV194: $i] :
( ( ( class_Orderings_Olinorder @ SV194 )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
| ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1864,plain,
! [SV50: $i,SV129: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true )
| ( ( ~ ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
| ( SV129 = SV50 ) )
| ~ ( ( SV129 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1865,plain,
! [SV51: $i,SV130: $i] :
( ( ( SV130 = SV51 )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV130 @ SV51 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1866,plain,
! [SV52: $i,SV131: $i,SV195: $i] :
( ( ( class_Orderings_Oorder @ SV195 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV131 @ SV52 )
| ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV52 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1867,plain,
! [SV53: $i,SV132: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ SV53 ) )
= $true )
| ( ( SV132 = SV53 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ ( c_Nat_OSuc @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1868,plain,
! [SV54: $i,SV133: $i,SV196: $i,SV227: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV227 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV196 @ SV133 )
| ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV196 )
| ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1869,plain,
! [SV55: $i] :
( ( ( ~ ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(1870,plain,
! [SV55: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 ) )
= $true )
| ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1871,plain,
! [SV56: $i,SV134: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ SV56 )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ ( c_Nat_OSuc @ SV56 ) )
| ( SV56 = SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1872,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( class_Orderings_Olinorder @ SV197 )
= $false )
| ( ( ~ ( ~ ( ~ ( ( SV135 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ( SV135 != SV57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1873,plain,
! [SV58: $i,SV136: $i] :
( ( ( ~ ( ( ( c_Nat_OSuc @ SV136 )
!= SV58 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV136 ) @ SV58 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV136 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1874,plain,
! [SV59: $i,SV137: $i,SV198: $i] :
( ( ( class_Rings_Olinordered__idom @ SV198 )
= $false )
| ( ( ~ ( ( SV137 != SV59 ) )
| ~ ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1875,plain,
! [SV60: $i,SV138: $i] :
( ( ( ! [SY520: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV138 @ SY520 )
| ( SV60
!= ( c_Nat_OSuc @ SY520 ) ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1876,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( class_Orderings_Olinorder @ SV199 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1877,plain,
! [SV63: $i,SV141: $i,SV200: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1801]) ).
thf(1878,plain,
! [SV200: $i,SV63: $i,SV141: $i] :
( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1801]) ).
thf(1879,plain,
! [SV64: $i,SV142: $i] :
( ( ~ ( ( SV142 != SV64 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1880,plain,
! [SV64: $i,SV142: $i] :
( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
| ( SV142 != SV64 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1881,plain,
! [SV143: $i,SV65: $i] :
( ( ( SV65
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV143 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1882,plain,
! [SV66: $i,SV144: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV144 @ SV66 @ SV66 )
= $false )
| ( ( class_Orderings_Opreorder @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1883,plain,
! [SV67: $i,SV145: $i,SV201: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV201 @ SV145 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV201 @ SV67 ) @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1884,plain,
! [SV68: $i,SV146: $i,SV202: $i,SV228: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV228 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV228 @ SV202 @ SV146 )
| ( SV202 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SV228 @ SV68 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1885,plain,
! [SV70: $i,SV148: $i,SV203: $i] :
( ( ( class_Orderings_Olinorder @ SV203 )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 )
| ~ ( ( SV148 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1886,plain,
! [SV71: $i,SV149: $i,SV204: $i] :
( ( ( class_Orderings_Oorder @ SV204 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV204 @ SV149 @ SV71 )
| ( SV71 != SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1887,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i] :
( ( ! [SY656: $i,SY657: $i,SY658: $i,SY659: $i,SY660: $i,SY661: $i] :
( ( ( hAPP @ SY661 @ ( hAPP @ SY660 @ SY659 ) )
!= ( hAPP @ SY658 @ ( hAPP @ SY657 @ SY656 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SY661 ) @ SY660 ) @ SY659 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SY658 ) @ SY657 ) @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(1888,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i,SV240: $i] :
( ( ! [SY662: $i,SY663: $i,SY664: $i,SY665: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY665 @ SY664 @ SY663 @ SY662 ) @ SV240 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SY664 @ SY663 @ SV206 ) @ SV152 ) )
| ( ( hAPP @ SY662 @ ( hAPP @ SV240 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(1889,plain,
! [SV75: $i,SV153: $i,SV207: $i,SV231: $i,SV241: $i] :
( ( ! [SY666: $i,SY667: $i,SY668: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY668 @ SY667 @ SY666 @ SV241 ) @ SV231 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SY667 @ SY666 @ SV153 ) @ SV75 ) )
| ! [SY669: $i] :
( ( hAPP @ SV241 @ ( hAPP @ SV231 @ SY669 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY669 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(1890,plain,
! [SV76: $i,SV154: $i,SV208: $i] :
( ( ( class_Orderings_Oorder @ SV208 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV208 @ SV154 @ SV76 )
| ( SV154 != SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1891,plain,
! [SV77: $i,SV155: $i,SV209: $i,SV232: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV232 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV155 )
| ( SV155 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1892,plain,
! [SV79: $i,SV157: $i,SV210: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV210 @ SV157 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV210 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV79 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1893,plain,
! [SV80: $i,SV158: $i,SV211: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV211 @ SV158 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV211 @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV158 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1894,plain,
! [SV81: $i,SV159: $i,SV212: $i] :
( ( ~ ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
| ( SV212 = SV81 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1820]) ).
thf(1895,plain,
! [SV159: $i,SV81: $i,SV212: $i] :
( ( ~ ( ( SV212 != SV81 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1820]) ).
thf(1896,plain,
! [SV82: $i,SV160: $i,SV213: $i,SV233: $i,SV242: $i] :
( ( ! [SY670: $i,SY671: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY671 @ SY670 @ SV242 @ SV233 )
| ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
!= ( hAPP @ SV233 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SV242 @ ( hAPP @ ( c_Fun_Ocomp @ SY671 @ SY671 @ SY671 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SV242 @ SV82 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(1897,plain,
! [SV83: $i,SV161: $i,SV214: $i] :
( ( ( class_Orderings_Oorder @ SV214 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV214 @ SV161 @ SV83 )
| ( SV161 != SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1898,plain,
! [SV162: $i,SV84: $i] :
( ( ( SV84 = SV162 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV162 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1899,plain,
! [SV86: $i,SV164: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1900,plain,
! [SV86: $i,SV164: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1901,plain,
! [SV87: $i,SV165: $i,SV215: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV215 @ SV165 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV215 @ SV87 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV165 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1902,plain,
! [SV1: $i,SV88: $i,SV166: $i,SV216: $i,SV234: $i,SV243: $i] :
( ( ! [SY672: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY672 @ SV243 @ SV234 @ SV216 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SY672 @ SV234 @ SV88 ) @ SV1 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SV243 @ SV234 @ ( hAPP @ ( c_Fun_Ocomp @ SY672 @ SV243 @ SV166 @ SV216 ) @ SV88 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(1903,plain,
! [SV2: $i,SV89: $i,SV167: $i,SV217: $i,SV235: $i,SV244: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV244 @ SV235 @ SV217 @ SV167 ) @ SV89 ) @ SV2 )
= ( hAPP @ SV167 @ ( hAPP @ SV89 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1904,plain,
! [SV5: $i,SV90: $i,SV168: $i,SV218: $i,SV236: $i,SV245: $i] :
( ( ! [SY673: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY673 @ SV245 @ SV236 @ SV218 ) @ ( c_Fun_Oswap @ SV236 @ SY673 @ SV168 @ SV90 @ SV5 ) )
= ( c_Fun_Oswap @ SV236 @ SV245 @ SV168 @ SV90 @ ( hAPP @ ( c_Fun_Ocomp @ SY673 @ SV245 @ SV236 @ SV218 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(1905,plain,
! [SV101: $i,SV20: $i] :
( ( ( SV20
!= ( c_Nat_OSuc @ SV101 ) )
= $false )
| ( ( ~ ! [SY480: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SY480 )
| ( SV20
!= ( c_Nat_OSuc @ SY480 ) ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1906,plain,
! [SV21: $i,SV102: $i,SV174: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ SV174 @ SV102 @ SV21 )
| ( SV102 = SV21 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV174 @ SV21 @ SV102 )
= $true )
| ( ( class_Orderings_Olinorder @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(1907,plain,
! [SV22: $i,SV103: $i,SV175: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV103 @ SV22 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV22 @ SV103 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1908,plain,
! [SV23: $i,SV104: $i,SV176: $i,SV220: $i] :
( ( ( class_Orderings_Oorder @ SV220 )
= $false )
| ( ( ( SV176 != SV104 )
| ~ ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV104 )
| ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1909,plain,
! [SV177: $i,SV24: $i,SV105: $i] :
( ( ( ~ ( ( SV105 != SV24 ) ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1910,plain,
! [SV25: $i,SV106: $i,SV178: $i,SV221: $i,SV237: $i,SV246: $i] :
( ( ! [SY674: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY674 @ SV246 @ SV237 @ SV221 ) @ SV178 )
!= SV106 )
| ( ( hAPP @ SV221 @ ( hAPP @ SV178 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(1911,plain,
! [SV26: $i,SV107: $i,SV179: $i,SV222: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV222 @ SV179 )
= $false )
| ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV107 @ SV179 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV222 @ SV26 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV107 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1912,plain,
! [SV27: $i,SV108: $i,SV180: $i,SV223: $i] :
( ( ( class_Orderings_Opreorder @ SV223 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV108 )
| ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV108 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1913,plain,
! [SV28: $i,SV109: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(1914,plain,
! [SV28: $i,SV109: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(1915,plain,
! [SV181: $i,SV29: $i,SV110: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV110 @ SV29 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV181 ) @ SV29 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1916,plain,
! [SV112: $i,SV31: $i,SV183: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV31 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV112 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV183 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(1917,plain,
! [SV33: $i,SV114: $i,SV185: $i,SV224: $i] :
( ( ( class_Orderings_Oord @ SV224 )
= $false )
| ( ( ( SV185 != SV114 )
| ~ ( c_Orderings_Oord__class_Oless @ SV224 @ SV114 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SV224 @ SV185 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1918,plain,
! [SV34: $i,SV115: $i,SV186: $i,SV225: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV225 @ SV186 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV115 @ SV34 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV225 @ SV115 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV186 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1919,plain,
! [SV35: $i] :
( ( ( c_SEQ_Osubseq @ SV35 )
= $false )
| ( ( ! [SY345: $i,SY346: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY345 @ SY346 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY345 ) @ ( hAPP @ SV35 @ SY346 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1920,plain,
! [SV35: $i] :
( ( ( ! [SY347: $i,SY348: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY347 @ SY348 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SY347 ) @ ( hAPP @ SV35 @ SY348 ) ) ) )
= $false )
| ( ( c_SEQ_Osubseq @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(1921,plain,
! [SV36: $i,SV116: $i,SV187: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV116 @ SV36 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV36 @ SV116 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(1922,plain,
! [SV37: $i,SV117: $i,SV188: $i,SV226: $i,SV238: $i,SV247: $i] :
( ( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV247 @ SV238 @ SV226 @ SV188 )
| ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
!= ( hAPP @ SV188 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SV226 @ SV117 ) @ SV37 )
= SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(1923,plain,
! [SV38: $i,SV118: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(1924,plain,
! [SV118: $i,SV38: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(1925,plain,
! [SV41: $i,SV120: $i,SV189: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
| ( SV120 = SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1926,plain,
! [SV189: $i,SV41: $i,SV120: $i] :
( ( ( SV120 != SV41 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1854]) ).
thf(1927,plain,
! [SV43: $i,SV122: $i] :
( ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
!= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
= $true )
| ( ( SV122 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(1928,plain,
! [SV43: $i,SV122: $i] :
( ( ( SV122 != SV43 )
= $true )
| ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1929,plain,
! [SV44: $i,SV123: $i,SV190: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV123 @ SV44 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV44 @ SV123 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(1930,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 ) )
= $false )
| ( ( ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1860]) ).
thf(1931,plain,
! [SV192: $i,SV125: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1860]) ).
thf(1932,plain,
! [SV48: $i,SV127: $i,SV193: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV127 @ SV48 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV48 @ SV127 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(1933,plain,
! [SV49: $i,SV128: $i,SV194: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(1934,plain,
! [SV50: $i,SV129: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
| ( SV129 = SV50 ) )
| ~ ( ( SV129 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1935,plain,
! [SV51: $i,SV130: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV130 @ SV51 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SV130 )
= $true )
| ( ( SV130 = SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1936,plain,
! [SV52: $i,SV131: $i,SV195: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV131 @ SV52 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV52 @ SV131 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1937,plain,
! [SV53: $i,SV132: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ SV53 ) )
= $false )
| ( ( SV132 = SV53 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ ( c_Nat_OSuc @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1938,plain,
! [SV54: $i,SV133: $i,SV196: $i,SV227: $i] :
( ( ( class_Orderings_Oorder @ SV227 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV196 @ SV133 )
| ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV196 )
| ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1939,plain,
! [SV55: $i] :
( ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1940,plain,
! [SV55: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
= $false )
| ( ( SV55
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1941,plain,
! [SV56: $i,SV134: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ ( c_Nat_OSuc @ SV56 ) ) )
= $true )
| ( ( SV56 = SV134 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(1942,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( ~ ( ~ ( ( SV135 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ( SV135 != SV57 ) ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1943,plain,
! [SV58: $i,SV136: $i] :
( ( ( ( c_Nat_OSuc @ SV136 )
!= SV58 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV136 ) @ SV58 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV136 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1944,plain,
! [SV198: $i,SV59: $i,SV137: $i] :
( ( ( ~ ( ( SV137 != SV59 ) ) )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 ) )
= $true )
| ( ( class_Rings_Olinordered__idom @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(1945,plain,
! [SV60: $i,SV138: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV138 @ ( sK4_SY520 @ SV60 @ SV138 ) )
| ( SV60
!= ( c_Nat_OSuc @ ( sK4_SY520 @ SV60 @ SV138 ) ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1875]) ).
thf(1946,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1947,plain,
! [SV63: $i,SV141: $i,SV200: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1948,plain,
! [SV200: $i,SV63: $i,SV141: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1949,plain,
! [SV64: $i,SV142: $i] :
( ( ( ~ ( ( SV142 != SV64 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(1950,plain,
! [SV64: $i,SV142: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) ) )
= $true )
| ( ( SV142 != SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1951,plain,
! [SV68: $i,SV146: $i,SV202: $i,SV228: $i] :
( ( ( class_Orderings_Oorder @ SV228 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV228 @ SV202 @ SV146 )
| ( SV202 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SV228 @ SV68 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1952,plain,
! [SV70: $i,SV148: $i,SV203: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 ) )
= $true )
| ( ( ~ ( ( SV148 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(1953,plain,
! [SV71: $i,SV149: $i,SV204: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV204 @ SV149 @ SV71 ) )
= $true )
| ( ( SV71 != SV149 )
= $true )
| ( ( class_Orderings_Oorder @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(1954,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i] :
( ( ! [SY675: $i,SY676: $i,SY677: $i,SY678: $i,SY679: $i] :
( ( ( hAPP @ SY679 @ ( hAPP @ SY678 @ SY677 ) )
!= ( hAPP @ SY676 @ ( hAPP @ SY675 @ SV248 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SY679 ) @ SY678 ) @ SY677 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SY676 ) @ SY675 ) @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(1955,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i,SV240: $i,SV249: $i] :
( ( ! [SY680: $i,SY681: $i,SY682: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY682 @ SY681 @ SY680 @ SV249 ) @ SV240 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SY681 @ SY680 @ SV206 ) @ SV152 ) )
| ( ( hAPP @ SV249 @ ( hAPP @ SV240 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(1956,plain,
! [SV75: $i,SV153: $i,SV207: $i,SV231: $i,SV241: $i,SV250: $i] :
( ( ! [SY683: $i,SY684: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY684 @ SY683 @ SV250 @ SV241 ) @ SV231 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SY683 @ SV250 @ SV153 ) @ SV75 ) )
| ! [SY669: $i] :
( ( hAPP @ SV241 @ ( hAPP @ SV231 @ SY669 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY669 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(1957,plain,
! [SV76: $i,SV154: $i,SV208: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV208 @ SV154 @ SV76 ) )
= $true )
| ( ( SV154 != SV76 )
= $true )
| ( ( class_Orderings_Oorder @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(1958,plain,
! [SV77: $i,SV155: $i,SV209: $i,SV232: $i] :
( ( ( class_Orderings_Oord @ SV232 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV155 )
| ( SV155 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(1959,plain,
! [SV81: $i,SV159: $i,SV212: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
| ( SV212 = SV81 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(1960,plain,
! [SV159: $i,SV81: $i,SV212: $i] :
( ( ( SV212 != SV81 )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(1961,plain,
! [SV82: $i,SV160: $i,SV213: $i,SV233: $i,SV242: $i,SV251: $i] :
( ( ! [SY686: $i] :
( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SY686 @ SV251 @ SV242 @ SV233 )
| ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
!= ( hAPP @ SV233 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SV242 @ ( hAPP @ ( c_Fun_Ocomp @ SY686 @ SY686 @ SY686 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SV242 @ SV82 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(1962,plain,
! [SV83: $i,SV161: $i,SV214: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV214 @ SV161 @ SV83 ) )
= $true )
| ( ( SV161 != SV83 )
= $true )
| ( ( class_Orderings_Oorder @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(1963,plain,
! [SV86: $i,SV164: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(1964,plain,
! [SV86: $i,SV164: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(1965,plain,
! [SV1: $i,SV88: $i,SV166: $i,SV216: $i,SV234: $i,SV243: $i,SV252: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV243 @ SV234 @ SV216 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SV252 @ SV234 @ SV88 ) @ SV1 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV166 @ SV243 @ SV234 @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV243 @ SV166 @ SV216 ) @ SV88 ) ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(1966,plain,
! [SV5: $i,SV90: $i,SV168: $i,SV218: $i,SV236: $i,SV245: $i,SV253: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV253 @ SV245 @ SV236 @ SV218 ) @ ( c_Fun_Oswap @ SV236 @ SV253 @ SV168 @ SV90 @ SV5 ) )
= ( c_Fun_Oswap @ SV236 @ SV245 @ SV168 @ SV90 @ ( hAPP @ ( c_Fun_Ocomp @ SV253 @ SV245 @ SV236 @ SV218 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(1967,plain,
! [SV101: $i,SV20: $i] :
( ( ( SV20
= ( c_Nat_OSuc @ SV101 ) )
= $true )
| ( ( ~ ! [SY480: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SY480 )
| ( SV20
!= ( c_Nat_OSuc @ SY480 ) ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(1968,plain,
! [SV21: $i,SV102: $i,SV174: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV174 @ SV102 @ SV21 )
= $true )
| ( ( SV102 = SV21 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV174 @ SV21 @ SV102 )
= $true )
| ( ( class_Orderings_Olinorder @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(1969,plain,
! [SV22: $i,SV103: $i,SV175: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV175 @ SV103 @ SV22 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV175 @ SV22 @ SV103 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(1970,plain,
! [SV23: $i,SV220: $i,SV104: $i,SV176: $i] :
( ( ( SV176 != SV104 )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV104 )
| ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV176 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(1971,plain,
! [SV177: $i,SV24: $i,SV105: $i] :
( ( ( SV105 != SV24 )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(1972,plain,
! [SV25: $i,SV106: $i,SV178: $i,SV221: $i,SV237: $i,SV246: $i,SV254: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV254 @ SV246 @ SV237 @ SV221 ) @ SV178 )
!= SV106 )
| ( ( hAPP @ SV221 @ ( hAPP @ SV178 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(1973,plain,
! [SV26: $i,SV222: $i,SV179: $i,SV107: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV107 @ SV179 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV222 @ SV26 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV107 @ SV26 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV222 @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1974,plain,
! [SV27: $i,SV108: $i,SV180: $i,SV223: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV108 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV108 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV27 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(1975,plain,
! [SV28: $i,SV109: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1976,plain,
! [SV28: $i,SV109: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
| ( SV109 = SV28 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1977,plain,
! [SV181: $i,SV29: $i,SV110: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV110 @ SV29 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV181 ) @ SV29 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV181 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1978,plain,
! [SV112: $i,SV31: $i,SV183: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV31 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV112 ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV31 @ SV183 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV183 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1979,plain,
! [SV33: $i,SV224: $i,SV114: $i,SV185: $i] :
( ( ( SV185 != SV114 )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV224 @ SV114 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SV224 @ SV185 @ SV33 ) )
= $true )
| ( ( class_Orderings_Oord @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(1980,plain,
! [SV186: $i,SV225: $i,SV34: $i,SV115: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV115 @ SV34 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV225 @ SV115 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV186 @ SV34 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV225 @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(1981,plain,
! [SV35: $i,SV255: $i] :
( ( ( ! [SY687: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV255 @ SY687 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SV255 ) @ ( hAPP @ SV35 @ SY687 ) ) ) )
= $true )
| ( ( c_SEQ_Osubseq @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(1982,plain,
! [SV35: $i] :
( ( ( ! [SY688: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( sK5_SY347 @ SV35 ) @ SY688 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ ( sK5_SY347 @ SV35 ) ) @ ( hAPP @ SV35 @ SY688 ) ) ) )
= $false )
| ( ( c_SEQ_Osubseq @ SV35 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1920]) ).
thf(1983,plain,
! [SV36: $i,SV116: $i,SV187: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV187 @ SV116 @ SV36 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV187 @ SV36 @ SV116 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1984,plain,
! [SV37: $i,SV117: $i,SV188: $i,SV226: $i,SV238: $i,SV247: $i] :
( ( ( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV247 @ SV238 @ SV226 @ SV188 ) )
= $true )
| ( ( ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
!= ( hAPP @ SV188 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SV226 @ SV117 ) @ SV37 )
= SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(1985,plain,
! [SV38: $i,SV118: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1986,plain,
! [SV118: $i,SV38: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1987,plain,
! [SV41: $i,SV120: $i,SV189: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
= $true )
| ( ( SV120 = SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(1988,plain,
! [SV189: $i,SV41: $i,SV120: $i] :
( ( ( SV120 != SV41 )
= $true )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(1989,plain,
! [SV43: $i,SV122: $i] :
( ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
= $false )
| ( ( SV122 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(1990,plain,
! [SV43: $i,SV122: $i] :
( ( ( SV122 = SV43 )
= $false )
| ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV122 )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1991,plain,
! [SV44: $i,SV123: $i,SV190: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV190 @ SV123 @ SV44 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV190 @ SV44 @ SV123 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(1992,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true )
| ( ( ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1993,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(1994,plain,
! [SV48: $i,SV127: $i,SV193: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV193 @ SV127 @ SV48 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV193 @ SV48 @ SV127 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(1995,plain,
! [SV49: $i,SV128: $i,SV194: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(1996,plain,
! [SV50: $i,SV129: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
| ( SV129 = SV50 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(1997,plain,
! [SV50: $i,SV129: $i] :
( ( ( ~ ( ( SV129 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(1998,plain,
! [SV51: $i,SV130: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV130 @ SV51 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SV130 )
= $true )
| ( ( SV130 = SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(1999,plain,
! [SV52: $i,SV131: $i,SV195: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV195 @ SV131 @ SV52 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV195 @ SV52 @ SV131 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2000,plain,
! [SV53: $i,SV132: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ SV53 )
= $true )
| ( ( SV132 = SV53 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV132 @ ( c_Nat_OSuc @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(2001,plain,
! [SV54: $i,SV133: $i,SV196: $i,SV227: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV196 @ SV133 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV196 )
| ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV133 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2002,plain,
! [SV55: $i] :
( ( ( SV55
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1939]) ).
thf(2003,plain,
! [SV55: $i] :
( ( ( SV55
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2004,plain,
! [SV56: $i,SV134: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ ( c_Nat_OSuc @ SV56 ) )
= $false )
| ( ( SV56 = SV134 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV134 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2005,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( ~ ( ~ ( ( SV135 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(2006,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ( SV135 != SV57 ) ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(2007,plain,
! [SV58: $i,SV136: $i] :
( ( ( ( c_Nat_OSuc @ SV136 )
= SV58 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV136 ) @ SV58 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV136 @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(2008,plain,
! [SV198: $i,SV59: $i,SV137: $i] :
( ( ( SV137 != SV59 )
= $false )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 ) )
= $true )
| ( ( class_Rings_Olinordered__idom @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2009,plain,
! [SV60: $i,SV138: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV138 @ ( sK4_SY520 @ SV60 @ SV138 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1945]) ).
thf(2010,plain,
! [SV138: $i,SV60: $i] :
( ( ( SV60
!= ( c_Nat_OSuc @ ( sK4_SY520 @ SV60 @ SV138 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1945]) ).
thf(2011,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2012,plain,
! [SV140: $i,SV62: $i,SV199: $i] :
( ( ( ~ ( ~ ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2013,plain,
! [SV63: $i,SV141: $i,SV200: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2014,plain,
! [SV200: $i,SV63: $i,SV141: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2015,plain,
! [SV64: $i,SV142: $i] :
( ( ( SV142 != SV64 )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2016,plain,
! [SV64: $i,SV142: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
= $false )
| ( ( SV142 != SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2017,plain,
! [SV68: $i,SV146: $i,SV202: $i,SV228: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV228 @ SV202 @ SV146 ) )
= $true )
| ( ( ( SV202 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SV228 @ SV68 @ SV146 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2018,plain,
! [SV70: $i,SV148: $i,SV203: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 ) )
= $false )
| ( ( ~ ( ( SV148 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2019,plain,
! [SV71: $i,SV149: $i,SV204: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV204 @ SV149 @ SV71 )
= $false )
| ( ( SV71 != SV149 )
= $true )
| ( ( class_Orderings_Oorder @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2020,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i,SV256: $i] :
( ( ! [SY689: $i,SY690: $i,SY691: $i,SY692: $i] :
( ( ( hAPP @ SY692 @ ( hAPP @ SY691 @ SY690 ) )
!= ( hAPP @ SY689 @ ( hAPP @ SV256 @ SV248 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SY692 ) @ SY691 ) @ SY690 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SY689 ) @ SV256 ) @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2021,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i,SV240: $i,SV249: $i,SV257: $i] :
( ( ! [SY693: $i,SY694: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY694 @ SY693 @ SV257 @ SV249 ) @ SV240 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SY693 @ SV257 @ SV206 ) @ SV152 ) )
| ( ( hAPP @ SV249 @ ( hAPP @ SV240 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2022,plain,
! [SV75: $i,SV153: $i,SV207: $i,SV231: $i,SV241: $i,SV250: $i,SV258: $i] :
( ( ! [SY695: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY695 @ SV258 @ SV250 @ SV241 ) @ SV231 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SV258 @ SV250 @ SV153 ) @ SV75 ) )
| ! [SY669: $i] :
( ( hAPP @ SV241 @ ( hAPP @ SV231 @ SY669 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY669 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2023,plain,
! [SV76: $i,SV154: $i,SV208: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV208 @ SV154 @ SV76 )
= $false )
| ( ( SV154 != SV76 )
= $true )
| ( ( class_Orderings_Oorder @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2024,plain,
! [SV77: $i,SV155: $i,SV209: $i,SV232: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV155 ) )
= $true )
| ( ( ( SV155 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV77 ) )
= $true )
| ( ( class_Orderings_Oord @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2025,plain,
! [SV81: $i,SV159: $i,SV212: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
!= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
= $true )
| ( ( SV212 = SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2026,plain,
! [SV159: $i,SV81: $i,SV212: $i] :
( ( ( SV212 != SV81 )
= $true )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2027,plain,
! [SV82: $i,SV160: $i,SV213: $i,SV233: $i,SV242: $i,SV251: $i,SV259: $i] :
( ( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV259 @ SV251 @ SV242 @ SV233 )
| ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
!= ( hAPP @ SV233 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SV242 @ ( hAPP @ ( c_Fun_Ocomp @ SV259 @ SV259 @ SV259 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SV242 @ SV82 ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2028,plain,
! [SV83: $i,SV161: $i,SV214: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV214 @ SV161 @ SV83 )
= $false )
| ( ( SV161 != SV83 )
= $true )
| ( ( class_Orderings_Oorder @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2029,plain,
! [SV86: $i,SV164: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2030,plain,
! [SV86: $i,SV164: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV164 @ SV86 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV164 ) @ ( c_Nat_OSuc @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2031,plain,
! [SV20: $i,SV101: $i] :
( ( ( ! [SY480: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SY480 )
| ( SV20
!= ( c_Nat_OSuc @ SY480 ) ) ) )
= $false )
| ( ( SV20
= ( c_Nat_OSuc @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2032,plain,
! [SV103: $i,SV22: $i,SV175: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV175 @ SV22 @ SV103 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV175 @ SV103 @ SV22 )
= $false )
| ( ( class_Orderings_Opreorder @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2033,plain,
! [SV23: $i,SV220: $i,SV104: $i,SV176: $i] :
( ( ( SV176 = SV104 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV104 )
| ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV176 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2034,plain,
! [SV177: $i,SV24: $i,SV105: $i] :
( ( ( SV105 = SV24 )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 )
| ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2035,plain,
! [SV25: $i,SV106: $i,SV178: $i,SV221: $i,SV237: $i,SV246: $i,SV254: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV254 @ SV246 @ SV237 @ SV221 ) @ SV178 )
!= SV106 )
= $true )
| ( ( ( hAPP @ SV221 @ ( hAPP @ SV178 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2036,plain,
! [SV26: $i,SV222: $i,SV179: $i,SV107: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV107 @ SV179 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV222 @ SV26 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV107 @ SV26 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV222 @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2037,plain,
! [SV27: $i,SV108: $i,SV180: $i,SV223: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV108 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV108 @ SV27 )
| ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV27 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2038,plain,
! [SV28: $i,SV109: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
= $true )
| ( ( SV109 = SV28 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2039,plain,
! [SV28: $i,SV109: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ SV28 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2040,plain,
! [SV28: $i,SV109: $i] :
( ( ( SV109 = SV28 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV109 @ ( c_Nat_OSuc @ SV28 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2041,plain,
! [SV33: $i,SV224: $i,SV114: $i,SV185: $i] :
( ( ( SV185 = SV114 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV224 @ SV114 @ SV33 )
| ( c_Orderings_Oord__class_Oless @ SV224 @ SV185 @ SV33 ) )
= $true )
| ( ( class_Orderings_Oord @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2042,plain,
! [SV186: $i,SV225: $i,SV34: $i,SV115: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV115 @ SV34 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV225 @ SV115 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV186 @ SV34 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV225 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2043,plain,
! [SV35: $i,SV260: $i,SV255: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV255 @ SV260 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SV255 ) @ ( hAPP @ SV35 @ SV260 ) ) )
= $true )
| ( ( c_SEQ_Osubseq @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2044,plain,
! [SV35: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( sK5_SY347 @ SV35 ) @ ( sK6_SY688 @ SV35 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ ( sK5_SY347 @ SV35 ) ) @ ( hAPP @ SV35 @ ( sK6_SY688 @ SV35 ) ) ) )
= $false )
| ( ( c_SEQ_Osubseq @ SV35 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1982]) ).
thf(2045,plain,
! [SV116: $i,SV36: $i,SV187: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV187 @ SV36 @ SV116 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV187 @ SV116 @ SV36 )
= $false )
| ( ( class_Orderings_Opreorder @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2046,plain,
! [SV37: $i,SV117: $i,SV188: $i,SV226: $i,SV238: $i,SV247: $i] :
( ( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV247 @ SV238 @ SV226 @ SV188 )
= $false )
| ( ( ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
!= ( hAPP @ SV188 @ SV37 ) )
| ( ( hAPP @ ( hAPP @ SV226 @ SV117 ) @ SV37 )
= SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2047,plain,
! [SV38: $i,SV118: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2048,plain,
! [SV38: $i,SV118: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV118 @ SV38 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV38 @ ( c_Nat_OSuc @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2049,plain,
! [SV41: $i,SV120: $i,SV189: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
= $false )
| ( ( SV120 = SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2050,plain,
! [SV189: $i,SV41: $i,SV120: $i] :
( ( ( SV120 = SV41 )
= $false )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV120 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV189 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2051,plain,
! [SV123: $i,SV44: $i,SV190: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV190 @ SV44 @ SV123 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV190 @ SV123 @ SV44 )
= $false )
| ( ( class_Orderings_Opreorder @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2052,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( ~ ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) ) )
= $true )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2053,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $false )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2054,plain,
! [SV127: $i,SV48: $i,SV193: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV193 @ SV48 @ SV127 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV193 @ SV127 @ SV48 )
= $false )
| ( ( class_Orderings_Opreorder @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2055,plain,
! [SV49: $i,SV128: $i,SV194: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2056,plain,
! [SV50: $i,SV129: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
| ( SV129 = SV50 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1996]) ).
thf(2057,plain,
! [SV50: $i,SV129: $i] :
( ( ( ( SV129 != SV50 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2058,plain,
! [SV51: $i,SV130: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV130 @ SV51 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV51 @ SV130 )
= $true )
| ( ( SV130 = SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2059,plain,
! [SV131: $i,SV52: $i,SV195: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV195 @ SV52 @ SV131 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV195 @ SV131 @ SV52 )
= $false )
| ( ( class_Orderings_Oorder @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2060,plain,
! [SV54: $i,SV133: $i,SV196: $i,SV227: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV227 @ SV196 @ SV133 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV196 )
| ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV133 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2061,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( ~ ( ( SV135 != SV57 ) )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2062,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
| ( SV135 != SV57 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2063,plain,
! [SV198: $i,SV59: $i,SV137: $i] :
( ( ( SV137 = SV59 )
= $true )
| ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 )
| ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 ) )
= $true )
| ( ( class_Rings_Olinordered__idom @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2064,plain,
! [SV60: $i,SV138: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV138 @ ( sK4_SY520 @ SV60 @ SV138 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2065,plain,
! [SV138: $i,SV60: $i] :
( ( ( SV60
= ( c_Nat_OSuc @ ( sK4_SY520 @ SV60 @ SV138 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ SV138 ) @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2066,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
| ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2067,plain,
! [SV140: $i,SV62: $i,SV199: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
| ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2012]) ).
thf(2068,plain,
! [SV63: $i,SV141: $i,SV200: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2069,plain,
! [SV200: $i,SV63: $i,SV141: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV141 @ SV63 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV141 ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV200 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2070,plain,
! [SV64: $i,SV142: $i] :
( ( ( SV142 = SV64 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2071,plain,
! [SV64: $i,SV142: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
= $false )
| ( ( SV142 != SV64 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2072,plain,
! [SV142: $i,SV64: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 )
= $false )
| ( ( SV142 != SV64 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2073,plain,
! [SV68: $i,SV146: $i,SV202: $i,SV228: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV228 @ SV202 @ SV146 )
= $false )
| ( ( ( SV202 != SV68 )
| ( c_Orderings_Oord__class_Oless @ SV228 @ SV68 @ SV146 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2074,plain,
! [SV70: $i,SV148: $i,SV203: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 )
= $true )
| ( ( ~ ( ( SV148 != SV70 ) )
| ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2075,plain,
! [SV204: $i,SV149: $i,SV71: $i] :
( ( ( SV71 = SV149 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV204 @ SV149 @ SV71 )
= $false )
| ( ( class_Orderings_Oorder @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2076,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i,SV256: $i,SV261: $i] :
( ( ! [SY697: $i,SY698: $i,SY699: $i] :
( ( ( hAPP @ SY699 @ ( hAPP @ SY698 @ SY697 ) )
!= ( hAPP @ SV261 @ ( hAPP @ SV256 @ SV248 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SY699 ) @ SY698 ) @ SY697 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SV261 ) @ SV256 ) @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2077,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i,SV240: $i,SV249: $i,SV257: $i,SV262: $i] :
( ( ! [SY700: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY700 @ SV262 @ SV257 @ SV249 ) @ SV240 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SV262 @ SV257 @ SV206 ) @ SV152 ) )
| ( ( hAPP @ SV249 @ ( hAPP @ SV240 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2078,plain,
! [SV75: $i,SV153: $i,SV207: $i,SV231: $i,SV241: $i,SV250: $i,SV258: $i,SV263: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV263 @ SV258 @ SV250 @ SV241 ) @ SV231 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SV258 @ SV250 @ SV153 ) @ SV75 ) )
| ! [SY669: $i] :
( ( hAPP @ SV241 @ ( hAPP @ SV231 @ SY669 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2079,plain,
! [SV208: $i,SV76: $i,SV154: $i] :
( ( ( SV154 = SV76 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV208 @ SV154 @ SV76 )
= $false )
| ( ( class_Orderings_Oorder @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2080,plain,
! [SV77: $i,SV155: $i,SV209: $i,SV232: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV155 )
= $false )
| ( ( ( SV155 != SV77 )
| ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV77 ) )
= $true )
| ( ( class_Orderings_Oord @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2081,plain,
! [SV81: $i,SV159: $i,SV212: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
= $false )
| ( ( SV212 = SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2082,plain,
! [SV159: $i,SV81: $i,SV212: $i] :
( ( ( SV212 = SV81 )
= $false )
| ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV212 @ SV159 )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ SV81 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2083,plain,
! [SV82: $i,SV160: $i,SV213: $i,SV233: $i,SV242: $i,SV251: $i,SV259: $i] :
( ( ( ~ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV259 @ SV251 @ SV242 @ SV233 ) )
= $true )
| ( ( ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
!= ( hAPP @ SV233 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SV242 @ ( hAPP @ ( c_Fun_Ocomp @ SV259 @ SV259 @ SV259 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SV242 @ SV82 ) @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2084,plain,
! [SV214: $i,SV83: $i,SV161: $i] :
( ( ( SV161 = SV83 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV214 @ SV161 @ SV83 )
= $false )
| ( ( class_Orderings_Oorder @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2085,plain,
! [SV20: $i,SV101: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ ( sK7_SY480 @ SV20 @ SV101 ) )
| ( SV20
!= ( c_Nat_OSuc @ ( sK7_SY480 @ SV20 @ SV101 ) ) ) )
= $false )
| ( ( SV20
= ( c_Nat_OSuc @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2031]) ).
thf(2086,plain,
! [SV176: $i,SV104: $i,SV23: $i,SV220: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV104 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV176 )
= $true )
| ( ( SV176 = SV104 )
= $false )
| ( ( class_Orderings_Oorder @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2087,plain,
! [SV24: $i,SV105: $i,SV177: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 )
= $true )
| ( ( SV105 = SV24 )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2088,plain,
! [SV25: $i,SV106: $i,SV178: $i,SV221: $i,SV237: $i,SV246: $i,SV254: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV254 @ SV246 @ SV237 @ SV221 ) @ SV178 )
= SV106 )
= $false )
| ( ( ( hAPP @ SV221 @ ( hAPP @ SV178 @ SV25 ) )
= ( hAPP @ SV106 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2089,plain,
! [SV180: $i,SV27: $i,SV108: $i,SV223: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV223 @ SV108 @ SV27 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV27 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV108 )
= $false )
| ( ( class_Orderings_Opreorder @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2090,plain,
! [SV185: $i,SV33: $i,SV114: $i,SV224: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV224 @ SV114 @ SV33 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV224 @ SV185 @ SV33 )
= $true )
| ( ( SV185 = SV114 )
= $false )
| ( ( class_Orderings_Oord @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2091,plain,
! [SV35: $i,SV260: $i,SV255: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV255 @ SV260 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SV255 ) @ ( hAPP @ SV35 @ SV260 ) )
= $true )
| ( ( c_SEQ_Osubseq @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2092,plain,
! [SV35: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( sK5_SY347 @ SV35 ) @ ( sK6_SY688 @ SV35 ) ) )
= $false )
| ( ( c_SEQ_Osubseq @ SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2093,plain,
! [SV35: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ ( sK5_SY347 @ SV35 ) ) @ ( hAPP @ SV35 @ ( sK6_SY688 @ SV35 ) ) )
= $false )
| ( ( c_SEQ_Osubseq @ SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2094,plain,
! [SV238: $i,SV247: $i,SV226: $i,SV37: $i,SV188: $i,SV117: $i] :
( ( ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
!= ( hAPP @ SV188 @ SV37 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV226 @ SV117 ) @ SV37 )
= SV37 )
= $true )
| ( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV247 @ SV238 @ SV226 @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2095,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( ( SV192 != SV125 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $false )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2096,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( SV192 != SV125 )
= $false )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2097,plain,
! [SV192: $i,SV125: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2098,plain,
! [SV128: $i,SV49: $i,SV194: $i] :
( ( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
| ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2099,plain,
! [SV50: $i,SV129: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) ) )
= $true )
| ( ( SV129 = SV50 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2100,plain,
! [SV50: $i,SV129: $i] :
( ( ( SV129 != SV50 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2101,plain,
! [SV133: $i,SV196: $i,SV54: $i,SV227: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV196 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV133 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV227 @ SV196 @ SV133 )
= $false )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2102,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( ~ ( ( SV135 != SV57 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2103,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) ) )
= $true )
| ( ( SV135 != SV57 )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2104,plain,
! [SV59: $i,SV137: $i,SV198: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 )
= $true )
| ( ( SV137 = SV59 )
= $true )
| ( ( class_Rings_Olinordered__idom @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2105,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2106,plain,
! [SV140: $i,SV62: $i,SV199: $i] :
( ( ( ~ ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2067]) ).
thf(2107,plain,
! [SV64: $i,SV142: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 )
= $true )
| ( ( SV142 = SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2108,plain,
! [SV64: $i,SV142: $i] :
( ( ( SV142 = SV64 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV142 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2109,plain,
! [SV64: $i,SV142: $i] :
( ( ( SV142 = SV64 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV64 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2110,plain,
! [SV146: $i,SV228: $i,SV68: $i,SV202: $i] :
( ( ( SV202 != SV68 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV228 @ SV68 @ SV146 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV228 @ SV202 @ SV146 )
= $false )
| ( ( class_Orderings_Oorder @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2111,plain,
! [SV203: $i,SV70: $i,SV148: $i] :
( ( ( ~ ( ( SV148 != SV70 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2112,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i,SV256: $i,SV261: $i,SV264: $i] :
( ( ! [SY702: $i,SY703: $i] :
( ( ( hAPP @ SY703 @ ( hAPP @ SY702 @ SV264 ) )
!= ( hAPP @ SV261 @ ( hAPP @ SV256 @ SV248 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SY703 ) @ SY702 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SV261 ) @ SV256 ) @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2113,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i,SV240: $i,SV249: $i,SV257: $i,SV262: $i,SV265: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV265 @ SV262 @ SV257 @ SV249 ) @ SV240 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SV262 @ SV257 @ SV206 ) @ SV152 ) )
| ( ( hAPP @ SV249 @ ( hAPP @ SV240 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2114,plain,
! [SV75: $i,SV153: $i,SV207: $i,SV231: $i,SV241: $i,SV250: $i,SV258: $i,SV263: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV263 @ SV258 @ SV250 @ SV241 ) @ SV231 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SV258 @ SV250 @ SV153 ) @ SV75 ) )
= $true )
| ( ( ! [SY669: $i] :
( ( hAPP @ SV241 @ ( hAPP @ SV231 @ SY669 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY669 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2115,plain,
! [SV209: $i,SV232: $i,SV77: $i,SV155: $i] :
( ( ( SV155 != SV77 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV77 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV155 )
= $false )
| ( ( class_Orderings_Oord @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2116,plain,
! [SV82: $i,SV160: $i,SV213: $i,SV233: $i,SV242: $i,SV251: $i,SV259: $i] :
( ( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV259 @ SV251 @ SV242 @ SV233 )
= $false )
| ( ( ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
!= ( hAPP @ SV233 @ SV160 ) )
| ( ( hAPP @ ( hAPP @ SV242 @ ( hAPP @ ( c_Fun_Ocomp @ SV259 @ SV259 @ SV259 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SV242 @ SV82 ) @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2117,plain,
! [SV20: $i,SV101: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ ( sK7_SY480 @ SV20 @ SV101 ) ) )
= $false )
| ( ( SV20
= ( c_Nat_OSuc @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2118,plain,
! [SV101: $i,SV20: $i] :
( ( ( SV20
!= ( c_Nat_OSuc @ ( sK7_SY480 @ SV20 @ SV101 ) ) )
= $false )
| ( ( SV20
= ( c_Nat_OSuc @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2119,plain,
! [SV176: $i,SV104: $i,SV23: $i,SV220: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV104 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV220 @ SV23 @ SV176 )
= $true )
| ( ( SV176 = SV104 )
= $false )
| ( ( class_Orderings_Oorder @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2120,plain,
! [SV24: $i,SV105: $i,SV177: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 )
= $true )
| ( ( SV105 = SV24 )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2121,plain,
! [SV180: $i,SV27: $i,SV108: $i,SV223: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV223 @ SV108 @ SV27 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV27 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV223 @ SV180 @ SV108 )
= $false )
| ( ( class_Orderings_Opreorder @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2122,plain,
! [SV185: $i,SV33: $i,SV114: $i,SV224: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV224 @ SV114 @ SV33 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV224 @ SV185 @ SV33 )
= $true )
| ( ( SV185 = SV114 )
= $false )
| ( ( class_Orderings_Oord @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2123,plain,
! [SV35: $i,SV260: $i,SV255: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV255 @ SV260 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ SV35 @ SV255 ) @ ( hAPP @ SV35 @ SV260 ) )
= $true )
| ( ( c_SEQ_Osubseq @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2124,plain,
! [SV35: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( sK5_SY347 @ SV35 ) @ ( sK6_SY688 @ SV35 ) )
= $true )
| ( ( c_SEQ_Osubseq @ SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2125,plain,
! [SV238: $i,SV247: $i,SV226: $i,SV37: $i,SV188: $i,SV117: $i] :
( ( ( ( hAPP @ SV117 @ ( hAPP @ SV188 @ SV37 ) )
= ( hAPP @ SV188 @ SV37 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV226 @ SV117 ) @ SV37 )
= SV37 )
= $true )
| ( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV247 @ SV238 @ SV226 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2126,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( SV192 != SV125 )
= $false )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2127,plain,
! [SV192: $i,SV125: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2128,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( SV192 = SV125 )
= $true )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2129,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2130,plain,
! [SV128: $i,SV49: $i,SV194: $i] :
( ( ( ~ ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2131,plain,
! [SV194: $i,SV128: $i,SV49: $i] :
( ( ( ~ ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2132,plain,
! [SV50: $i,SV129: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
= $false )
| ( ( SV129 = SV50 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2133,plain,
! [SV50: $i,SV129: $i] :
( ( ( SV129 = SV50 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ ( c_Nat_OSuc @ SV50 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV129 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2134,plain,
! [SV133: $i,SV196: $i,SV54: $i,SV227: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV196 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV227 @ SV54 @ SV133 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV227 @ SV196 @ SV133 )
= $false )
| ( ( class_Orderings_Oorder @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2135,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( SV135 != SV57 )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2136,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
= $false )
| ( ( SV135 != SV57 )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2137,plain,
! [SV59: $i,SV137: $i,SV198: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 )
= $true )
| ( ( SV137 = SV59 )
= $true )
| ( ( class_Rings_Olinordered__idom @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2138,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2139,plain,
! [SV140: $i,SV62: $i,SV199: $i] :
( ( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2140,plain,
! [SV146: $i,SV228: $i,SV68: $i,SV202: $i] :
( ( ( SV202 = SV68 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV228 @ SV68 @ SV146 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV228 @ SV202 @ SV146 )
= $false )
| ( ( class_Orderings_Oorder @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2141,plain,
! [SV203: $i,SV70: $i,SV148: $i] :
( ( ( SV148 != SV70 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2142,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i,SV256: $i,SV261: $i,SV264: $i,SV266: $i] :
( ( ! [SY704: $i] :
( ( ( hAPP @ SY704 @ ( hAPP @ SV266 @ SV264 ) )
!= ( hAPP @ SV261 @ ( hAPP @ SV256 @ SV248 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SY704 ) @ SV266 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SV261 ) @ SV256 ) @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2143,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i,SV240: $i,SV249: $i,SV257: $i,SV262: $i,SV265: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV265 @ SV262 @ SV257 @ SV249 ) @ SV240 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SV262 @ SV257 @ SV206 ) @ SV152 ) )
= $true )
| ( ( ( hAPP @ SV249 @ ( hAPP @ SV240 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2144,plain,
! [SV75: $i,SV153: $i,SV207: $i,SV231: $i,SV241: $i,SV250: $i,SV258: $i,SV263: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV263 @ SV258 @ SV250 @ SV241 ) @ SV231 )
= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SV258 @ SV250 @ SV153 ) @ SV75 ) )
= $false )
| ( ( ! [SY669: $i] :
( ( hAPP @ SV241 @ ( hAPP @ SV231 @ SY669 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SY669 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2145,plain,
! [SV209: $i,SV232: $i,SV77: $i,SV155: $i] :
( ( ( SV155 = SV77 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV77 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV232 @ SV209 @ SV155 )
= $false )
| ( ( class_Orderings_Oord @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2146,plain,
! [SV251: $i,SV82: $i,SV259: $i,SV242: $i,SV160: $i,SV233: $i,SV213: $i] :
( ( ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
!= ( hAPP @ SV233 @ SV160 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV242 @ ( hAPP @ ( c_Fun_Ocomp @ SV259 @ SV259 @ SV259 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SV242 @ SV82 ) @ SV160 ) )
= $true )
| ( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV259 @ SV251 @ SV242 @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2147,plain,
! [SV20: $i,SV101: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ ( sK7_SY480 @ SV20 @ SV101 ) )
= $true )
| ( ( SV20
= ( c_Nat_OSuc @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2148,plain,
! [SV101: $i,SV20: $i] :
( ( ( SV20
= ( c_Nat_OSuc @ ( sK7_SY480 @ SV20 @ SV101 ) ) )
= $true )
| ( ( SV20
= ( c_Nat_OSuc @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV101 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2149,plain,
! [SV24: $i,SV105: $i,SV177: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV177 @ SV105 @ SV24 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV177 @ SV24 @ SV105 )
= $true )
| ( ( SV105 = SV24 )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2150,plain,
! [SV46: $i,SV125: $i,SV192: $i] :
( ( ( SV192 = SV125 )
= $true )
| ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2126]) ).
thf(2151,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2152,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2153,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2154,plain,
! [SV128: $i,SV49: $i,SV194: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
| ( SV49 = SV128 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2130]) ).
thf(2155,plain,
! [SV194: $i,SV128: $i,SV49: $i] :
( ( ( ( SV49 != SV128 )
| ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2131]) ).
thf(2156,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( SV135 = SV57 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
| ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2157,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
= $false )
| ( ( SV135 != SV57 )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2158,plain,
! [SV135: $i,SV57: $i,SV197: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 )
= $false )
| ( ( SV135 != SV57 )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2159,plain,
! [SV59: $i,SV137: $i,SV198: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV198 @ SV137 @ SV59 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV198 @ SV59 @ SV137 )
= $true )
| ( ( SV137 = SV59 )
= $true )
| ( ( class_Rings_Olinordered__idom @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2160,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
| ( SV140 = SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2161,plain,
! [SV140: $i,SV62: $i,SV199: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2162,plain,
! [SV199: $i,SV62: $i,SV140: $i] :
( ( ( SV140 = SV62 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2163,plain,
! [SV203: $i,SV70: $i,SV148: $i] :
( ( ( SV148 = SV70 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV203 @ SV70 @ SV148 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV203 @ SV148 @ SV70 )
= $true )
| ( ( class_Orderings_Olinorder @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2164,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i,SV256: $i,SV261: $i,SV264: $i,SV266: $i,SV267: $i] :
( ( ( ( hAPP @ SV267 @ ( hAPP @ SV266 @ SV264 ) )
!= ( hAPP @ SV261 @ ( hAPP @ SV256 @ SV248 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SV267 ) @ SV266 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SV261 ) @ SV256 ) @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2165,plain,
! [SV74: $i,SV152: $i,SV206: $i,SV230: $i,SV240: $i,SV249: $i,SV257: $i,SV262: $i,SV265: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV265 @ SV262 @ SV257 @ SV249 ) @ SV240 )
= ( hAPP @ ( c_Fun_Ocomp @ SV230 @ SV262 @ SV257 @ SV206 ) @ SV152 ) )
= $false )
| ( ( ( hAPP @ SV249 @ ( hAPP @ SV240 @ SV74 ) )
= ( hAPP @ SV206 @ ( hAPP @ SV152 @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2166,plain,
! [SV207: $i,SV250: $i,SV258: $i,SV263: $i,SV75: $i,SV153: $i,SV268: $i,SV231: $i,SV241: $i] :
( ( ( ( hAPP @ SV241 @ ( hAPP @ SV231 @ SV268 ) )
= ( hAPP @ SV153 @ ( hAPP @ SV75 @ SV268 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV263 @ SV258 @ SV250 @ SV241 ) @ SV231 )
= ( hAPP @ ( c_Fun_Ocomp @ SV207 @ SV258 @ SV250 @ SV153 ) @ SV75 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2167,plain,
! [SV251: $i,SV82: $i,SV259: $i,SV242: $i,SV160: $i,SV233: $i,SV213: $i] :
( ( ( ( hAPP @ SV213 @ ( hAPP @ SV233 @ SV160 ) )
= ( hAPP @ SV233 @ SV160 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV242 @ ( hAPP @ ( c_Fun_Ocomp @ SV259 @ SV259 @ SV259 @ SV82 ) @ SV213 ) ) @ SV160 )
= ( hAPP @ ( hAPP @ SV242 @ SV82 ) @ SV160 ) )
= $true )
| ( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ SV259 @ SV251 @ SV242 @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2168,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2169,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2170,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2171,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2172,plain,
! [SV192: $i,SV125: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2173,plain,
! [SV128: $i,SV49: $i,SV194: $i] :
( ( ( ~ ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) )
= $true )
| ( ( SV49 = SV128 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2174,plain,
! [SV194: $i,SV128: $i,SV49: $i] :
( ( ( SV49 != SV128 )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2175,plain,
! [SV57: $i,SV135: $i,SV197: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 )
= $true )
| ( ( SV135 = SV57 )
= $true )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2176,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( SV135 = SV57 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV135 @ SV57 )
= $false )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2177,plain,
! [SV197: $i,SV57: $i,SV135: $i] :
( ( ( SV135 = SV57 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV197 @ SV57 @ SV135 )
= $false )
| ( ( class_Orderings_Olinorder @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2178,plain,
! [SV140: $i,SV62: $i,SV199: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
= $true )
| ( ( SV140 = SV62 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2179,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV62 @ SV140 )
= $false )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2180,plain,
! [SV62: $i,SV140: $i,SV199: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV199 @ SV140 @ SV62 )
= $false )
| ( ( SV140 = SV62 )
= $false )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2181,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i,SV256: $i,SV261: $i,SV264: $i,SV266: $i,SV267: $i] :
( ( ( ( hAPP @ SV267 @ ( hAPP @ SV266 @ SV264 ) )
!= ( hAPP @ SV261 @ ( hAPP @ SV256 @ SV248 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SV267 ) @ SV266 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SV261 ) @ SV256 ) @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2182,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2183,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2184,plain,
! [SV192: $i,SV125: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2185,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2186,plain,
! [SV192: $i,SV125: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2187,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2188,plain,
! [SV128: $i,SV49: $i,SV194: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) )
= $false )
| ( ( SV49 = SV128 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2189,plain,
! [SV194: $i,SV128: $i,SV49: $i] :
( ( ( SV49 = SV128 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2190,plain,
! [SV73: $i,SV151: $i,SV205: $i,SV229: $i,SV239: $i,SV248: $i,SV256: $i,SV261: $i,SV264: $i,SV266: $i,SV267: $i] :
( ( ( ( hAPP @ SV267 @ ( hAPP @ SV266 @ SV264 ) )
= ( hAPP @ SV261 @ ( hAPP @ SV256 @ SV248 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV239 @ SV229 @ SV205 @ SV267 ) @ SV266 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV151 @ SV229 @ SV73 @ SV261 ) @ SV256 ) @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2191,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2192,plain,
! [SV192: $i,SV125: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2193,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2194,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2185]) ).
thf(2195,plain,
! [SV128: $i,SV49: $i,SV194: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
= $true )
| ( ( SV49 = SV128 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2196,plain,
! [SV128: $i,SV49: $i,SV194: $i] :
( ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV49 @ SV128 )
= $false )
| ( ( SV49 = SV128 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ SV194 @ SV128 @ SV49 )
= $true )
| ( ( class_Orderings_Olinorder @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2197,plain,
! [SV46: $i,SV192: $i,SV125: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV125 @ SV192 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV46 @ SV125 ) @ SV192 ) )
= $true )
| ( ( SV192 = SV125 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV192 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2198,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1299,2197,2196,2195,2194,2193,2192,2190,2187,2186,2184,2180,2179,2178,2177,2176,2175,2172,2167,2166,2165,2163,2159,2149,2148,2147,2145,2140,2134,2133,2132,2125,2124,2123,2122,2121,2119,2109,2108,2107,2093,2088,2084,2082,2081,2079,2075,2069,2068,2065,2064,2059,2058,2054,2051,2050,2049,2048,2047,2045,2042,2040,2039,2038,2036,2032,2030,2029,2007,2004,2003,2002,2000,1990,1989,1978,1977,1968,1966,1965,1903,1901,1898,1893,1892,1883,1882,1881,1861,1859,1855,1844,1842,1824,1817,1811,1808,1799,1776,1775,1752,1751,1677,1676,1675,1674,1673,1672,1595,1594,1590,1589,1586,1584,1583,1512,1498,1423,1422,1421,1420,1419,1418,1417,1416,1415,1414,1413,1412,1411,1410,1409,1408,1407,1406,1405,1404,1403,1402,1401,1400,1399,1398,1397,1396,1395,1394,1393,1392,1391,1390,1389,1388,1387,1386,1385,1300]) ).
thf(2199,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW209+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.20 % Computer : n009.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Oct 6 16:51:48 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.44/3.19 .......
% 17.44/3.19
% 17.44/3.19 No.of.Axioms: 127
% 17.44/3.19
% 17.44/3.19 Length.of.Defs: 0
% 17.44/3.19
% 17.44/3.19 Contains.Choice.Funs: false
% 17.44/3.19 ..................................................
% 17.44/3.19
% 17.44/3.19 ********************************
% 17.44/3.19 * All subproblems solved! *
% 17.44/3.19 ********************************
% 17.44/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:128,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2198,loop_count:0,foatp_calls:1,translation:fof_full)
% 17.44/3.19
% 17.44/3.19 %**** Beginning of derivation protocol ****
% 17.44/3.19 % SZS output start CNFRefutation
% See solution above
% 17.44/3.20
% 17.44/3.20 %**** End of derivation protocol ****
% 17.44/3.20 %**** no. of clauses in derivation: 1166 ****
% 17.44/3.20 %**** clause counter: 2198 ****
% 17.44/3.20
% 17.44/3.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:128,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2198,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------